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QUANTUM OPTICAL COMMUNICATIONS SYSTEM FOR
MICRO ROBOTS

presented by

JOHN DANIEL LEKKI

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QUANTUM OPTICAL COMMUNICATIONS SYSTEM FOR
MICRO ROBOTS

By

John Daniel Lekki

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Electrical and Computer Engineering

2008

ABSTRACT

QUANTUM OPTICAL COMMUNICATIONS SYSTEM FOR
MICRO ROBOTS

By

John Daniel Lekki

One way to improve the acquisition of planetary information from robotic landers is to
use many smaller robotic explorers that can cover more ground than a single
conventional rover. The development of such robots presents very significant
technological challenges to enable essential functions, such as mobility and
communication, given the small size and limited power generation capability. The
research presented here has been focused on developing a communications system that
has the potential for providing ultra-low power communications for robots such as

these.

The communication system is a variant of photon-counting based communications.
Instead of counting individual photons the system only counts the arrival of time
coincident sets of photons that have distinct correlations. The utilization of sets of
photons significantly decreases the bit error rate because they are highly identifiable in
the presence of ambient light. The sets of photons can be generated in two ways.
Quantum Entangled photons are one such set that can be generated through
Spontaneous Parametric Down Conversion. This process is not energy efficient, but
Quantum Entangled photons have an effective range that is hundreds of times greater

than for photon sets that are not entangled. This is due to the highly correlated

momenta for entangled photons, which translates into positional correlation in the
transmitted beam. A transmitter based on quantum entangled photons was built and
tested. A one bit value was coded by sending photons of like polarization and a zero
bit value was coded by sending photons with orthogonal polarizations. The system
successfully transmitted data at a remarkably low power level, a received optical

power of 1 Pico joule per bit, in the presence of significant background noise.

The second way to generate sets of photons is to utilize multiple sources that are
pulsed simultaneously. This has the benefit of being much more energy efficient than
3 Quantum Entangled photon source. A transmitter utilizing this concept was built for
evaluation. The components used in this system were chosen so that they could in the
future be integrated into a cubic centimeter device. The experimental system was able
to achieve a Bit Error Rate of 10'3 while transmitting data at a rate of 100 Kbits/ sec
over a distance of 70 meters with a background level that was above the signal level
(received Signal to Noise Ratio was -0.7 dB) using only 760 pW of transmitted power.
Even with very low electrical to optical energy efficiency ~1%, an optimized optical
system utilizing this technique would still use only 76 nw of electrical power. This is
a power level that can be sustained by a power scavenging micro robot. The operating
characteristics of this system have been modeled and used to extrapolate future
performance improvements that can be achieved utilizing improved components that

can be readily built.

To my wife Rebecca, my sons Ethan, Nathaniel and Caleb and also to my
parents John and Helen. I so much appreciate the understanding and
sacrifices that my wife and children have made while I completed this

work. I also appreciate all the encouragement I got fiom my parents.

iv

ACKNOWLEDGEMENTS

I would like to first acknowledge my advisor, Dr. Timothy Grotjohn, for his guidance
and tutelage through this process. He not only helped me during the doctoral program
but he also was my instructor for an independent study in optical systems during my
undergraduate program. It was in this course that I realized how much I enjoyed this
area of work and I have since followed a career path in this field. I am very grateful to
him for his part in helping me to realize that I wanted to pursue a career in optical

systems.

The work described here was part of a research project at the National Aeronautics and
Space Administration Glenn Research Center. The experiments that were conducted as
a part of this dissertation were accomplished with contributions from all of the members
on that project team. I would like to recognize the talented team of researchers,
engineers and technicians who have worked together on the Quantum Sensing and
Communications project. This team includes Dr. Quang-Viet Nguyen, Mr. Binh
Nguyen, Mr. Tom Bizon, Dr. Jun Kojima, Dr. Murad Hizlan, Mr. Quang Tran, Mr.
James Williams, Mr. Ken Weiland and Mr. Bertram Floyd. Their friendship and

collaboration made this one of the best experiences of my career.

TABLE OF CONTENTS

LIST OF TABLES ......................................................................................................... ix
LIST OF FIGURES ........................................................................................................ x
CHAPTER 1
INTRODUCTION .......................................................................................................... 1
1.1 Motivation .................................................................................................... 2
1.2 Objective ....................................................................................................... 7
1.3 Planned Research Activities ......................................................................... 9
1.3.1 Modulated Quantum Entanglement Experiment ......................... 10
1.3.2 Monolithic Optical Transmitter Concept ..................................... 11
1.3.3 Perform calculations to quantify the capabilities of this
communications system ............................................................... 16
1.4 Conclusion .................................................................................................. 17
CHAPTER 2
BACKGROUND .......................................................................................................... 18
2.1 Literature Review of quantum entanglement for communication .............. 18
2.2 State of the Art ............................................................................................ 23
2.2.1 Low power RF ............................................................................. 23
2.2.2 Low power optical ....................................................................... 25
2.3 Summary ..................................................................................................... 30
CHAPTER 3
COINCIDENT PHOTON COMMUNICATION THEORY ....................................... 32
3.1 General theory for On / Off keyed Quantum Entangled Photon
Communication — improvement in bit contrast ratio ................................. 32
3.2 Bit error rate for communication utilizing quantum entangled photons
with on off keying for bit coding ................................................................ 38
3.3 Bit error rate for communication using quantum entangled photons
with two state coding ................................................................................. 41
3.4 Bit error rate for time coincident communications ..................................... 48
3.5 Theory for time coincident photon communication range ......................... 53
3.5.1 Communication Range for Quantum Entangled source system.. 54
3.5.2 Range of time coincident photon communication ....................... 61
3.6 Range Comparison ..................................................................................... 62
3.7 Summary ..................................................................................................... 66

vi

CHAPTER 4
EXPERIMENTAL SETUP FOR QUANTUM ENTANGLED PHOTON

COMMUNICATION ................................................................................................... 67
4.1 Introduction ................................................................................................ 67
4.2 Concept ....................................................................................................... 67
4.3 Experimental Setup ..................................................................................... 69
4.4 Summary ..................................................................................................... 75

CHAPTER 5

EXPERIMENTAL RESULTS AND DISCUSSION FOR QUANTUM

ENTANGLED PHOTON COMMUNICATION ......................................................... 76
5.1 Introduction ................................................................................................ 76
5.2 Experimental Results .................................................................................. 76
5.3 Discussion ................................................................................................... 84
5.4 Discussion of potential given high contrast modulator .............................. 87
5.5 Conclusion .................................................................................................. 90

CHAPTER 6

EXPERIMENTAL SETUP FOR COINCIDENT

COMMUNICATIONS EXPERIMENT ....................................................................... 92
6.1 Introduction ................................................................................................ 92
6.2 Transmitter .................................................................................................. 93

6.2.1 Optical Transmitter concept ........................................................ 93
6.2.2 Experimental Transmitter .......................................................... 100

6.3 Receiver .................................................................................................... 103
6.4 Experimental Plan ..................................................................................... 107
6.5 Experimental Setup and Experimental Operation .................................... 109
6.6 Summary ................................................................................................... 114

vii

CHAPTER 7
EXPERIMENTAL RESULTS AND DISCUSSION FOR COINCIDENT PHOTON

COMMUNICATIONS EXPERIMENT ..................................................................... 115
7.1 Introduction .............................................................................................. 115
7.2 Experimental Measurement and Data Analysis ........................................ 115
7.3 Experiment 1: Effect of varying background noise .................................. 117
7.4 Experiment 2: Effect of varying signal levels .......................................... 124
7.5 Experiment 3: Effect of varying coincidence time windows on system
performance .............................................................................................. 127
7.6 Experiment 4: Data rate effect on system performance ........................... 129
7.7 Experiment 5: Effect of (Simulated) range on system performance ........ 132
7.8 Discussion ................................................................................................. 136
7.9 Summary ................................................................................................... 141
CHAPTER 8
CONCLUSION .......................................................................................................... 142
8.1 Dissertation Accomplishments ................................................................. 142
8.2 Comparison of general results from QE, coincident photons and SOA
communication methods ................................................................................ 146
8.3 Future Work ............................................................................................. 148
8.4 Concluding Remarks ................................................................................ 151
APPENDIX A
MATHCAD WORKSHEET FOR CALCULATING BER FROM EXPERIMENT
COINCIDENCE DATA ............................................................................................. 152
APPENDIX B
COMMUNICATION DATA ANALYSIS FOR ON / OFF KEYED DATA ............ 153
APPENDIX C
COMMUNICATION DATA ANALYSIS FOR TWO-STATE DATA .................... 163
APPENDIX D
BIT ERROR RATE CALCULATION FOR TIME COINCIDENT PHOTON
COMMUNICATION ................................................................................................. 1 74
REFERENCES ........................................................................................................... 177

viii

LIST OF TABLES

Table 5.1: Test average coincidence detector counts per second at 30 mW laser
power in the presence of minimal background light .................................................... 80

Table 5.2: Steady-state detector counts per second in the presence of
minimal background light ............................................................................................. 81

Table 5.3: Average Coincidence counts per bit in the presence of maximum
background light at a data rate of 30 bps ...................................................................... 86

Table 5.4: Average Coincidence counts per bit in the presence of maximum
background light, with a data rate of 30 bps and modified error coincidence
rates to represent the operation of a better modulator .................................................. 89

Table 6.1: Truth table or logic chart for schematic shown in Fig. 6.1. Light
emitters fire in pairs with complementary wavelengths and identical polarizations... 96

Table 6.2: Truth table or logic chart for an alternate embodiment (not shown)
but based on Figure 6.1 where up to 2-bits (4 states) of information can be
sent at a time through the use of perpendicular polarization states of 2.. and 2.2 .......... 98

Table 6.3: Truth table or logic chart for schematic shown in Figure 6.2. Light
emitters fire in pairs with complementary wavelengths and polarizations .................. 99

ix

LIST OF FIGURES

Figure 1.1: Graph of power output for a fuel cell that is assumed to linearly decrease
as size decreases. Fuel cell Power Generation (F PG) is an estimate of the capability
of future fuel cells. .......................................................................................................... 5

Figure 1.2: The conceptual system for generating highly correlated photon sets.
Figure created by Dr. Jun Kojima of the Ohio Aerospace Institute. ............................ 14

Figure 3.1: This figure gives a plot of the increased contrast ratio that is possible
when utilizing quantum entangled photons (non-classical) for communication at
low SNR when compared to classical optical communications. .................................. 37

Figure 3.2: Concept for on/off keying quantum entangled communication ................ 39

Figure 3.3: Block diagram of the two state system utilizing photons with an
entangled state. ............................................................................................................. 47

Figure 3.4: A time coincident photon communication system made from classical
sources. ......................................................................................................................... 52

Figure 3.5: Drawing of Spontaneous Parametric Down Conversion of a pump beam
(Plane X) with a Gaussian intensity distribution and wave-vector kp into signal and
idler beams (Planes X1, X2) with Gaussian photon positional probability distributions
and wave-vectors k, and k,-. ........................................................................................... 56

Figure 3.6: The top portion of this figure shows how the down converted photon
vectors are linked so that momentum is conserved in down conversion. The

bottom portion illustrates how the geometrically recombined beams will have

differing angles when the magnitude of momentum is not equivalent between the

two photons ................................................................................................................... 59

Figure 3.7: In this figure the fall off of the two different signaling sources are
compared as a function of range R. Both sources have near unity while the beams

are collimated. After the range at which the beams begin to spread, R3, the two
independent sources fall off at I/R” while the entangled photon source falls off

at I/R" until the photon pairs begin to separate significantly at the range R, ............... 62

Figure 3.8: An illustration of the affect that collirnating optics has on the photon
pair system. The angles and lateral distances are exaggerated for illustrative

purposes. ....................................................................................................................... 64

Figure 4.1: Quantum Entangled Photon Communicator Block Diagram .................... 69

Figure 4.2: Schematic of Quantum Communication System with a picture of the

experimental setup ........................................................................................................ 72
Figure 4.3: GRC Quantum Communicator BER Tester interface. ............................... 74
Figure 5.]: BER with minimal background light ......................................................... 78
Figure 5.2: BER with maximum background light ...................................................... 78
Figure 5.3: BER with minimal background light ........................................................ 83

Figure 5.4: (A) BER with maximum background light. (B) BER with maximum
background light and SNR calculated as ratio of coincidences to single photons. ...... 83

Figure 5.5: The calculated BER in this figure is obtained by using equations measured
coincidence numbers is compared here to the directly measured BER as a function of

SNR for 30 bps data rate ............................................................................................... 87

Figure 5.6: This graph illustrates the potential of the communication system if the
modulator had higher contrast. The calculated series is generated by modifying the
off state data by reducing it to a contrast level equal to the steady state contrast. ....... 90

Figure 6.1: Schematic of the logic diagram for the multi-wavelength time-coincident
optical transmitter. The oscillator provides a steady stream of alternating low (0) and
high (1) digital clock pulses at say, 1 GHz. The data stream is sent to the appropriate
AND gate which then determines which optical emitter to fire. The AND gate allows
the clock signal to control the pulse width of each source. The clock period is much
smaller than the data bit period so that multiple pulses are sent during one data bit.
The logic states are shown in the truth table in Table 1. The optical emitters can be,
but are not limited to light emitting diodes (LED) or diode lasers, quantum-dots, etc.
Depending on the emitter that is fired, each has a certain wavelength or spectral
channel and a polarization associated with it. In this way, both wavelength and
polarization states are used to effectively increase the SNR for single-photon data
transmissions. ............................................................................................................... 96

Figure 6.2: This is a schematic of the three channel configuration. Here, the emitter
that is of wavelength 1 provides synchronization and a reference polarization. This
emitter has a fixed wavelength and polarization. The second set of emitters is of a
different wavelength than the sync emitter. The data is encoded by the relative
polarization of the emitter that is fired from the second wavelength when compared to
the reference emitter polarization. When the emitter of wavelength 2 that is fired is
the same polarization as the wavelength 1 emitter then this encodes a zero bit. When
the emitter of wavelength 2 that is fired has a different polarization than the
wavelength 1 emitter then this encodes a one bit. ....................................................... 99

xi

Figure 6.3: Schematic of the two channel configuration. In this case the data is
encoded using on / off keying. A ‘1’ is communicated by transmitting the
complimentary photons of the same wavelength and orthogonal polarizations.

A ‘0’ is communicated by the lack of signal. This scheme requires the receiver

to compare the number of photon pairs received to a threshold to determine the

bit value. ..................................................................................................................... 100

Figure 6.4: Front view of the experimental transmitter. The four laser diodes are
utilized in the multiple configurations described previously. The output attenuation
filter is set so that an average of one photon per pulse is detected at the receiver. 101

Figure 6.5: The electronic components of the transmitter consist of a custom built
data source (lower right) and a Berkeley Nucleonics ENG 555 pulse generator. ...... 102

Figure 6.6: In this schematic the transmitter is shown working in conjunction with a
receiver. The internal optics of the receiver that sorts the received photons starts with
a telescopic front optic that collects and collirnates the received photons. After this
there are two filters, one that passes photons in band 1 while reflecting all other
wavelength photons and a second that passes photons in band 2. Behind the two
filters are Polarization Beam Splitters (PBS) that have extinction ratios of 1000:]
which they sort horizontally polarized photons from vertically polarized photons.

The front end optics therefore sorts the beams so that the photon counters only see
photons of a particular wavelength and polarization. ................................................. 104

Figure 6.7: Picture of the optical components of the receiver that is diagrammed
in Figure 6.6. .............................................................................................................. 105

Figure 6.8: Custom built coincidence detector takes pulse outputs from two pairs

of photon counting detectors and determines if a pair of detectors fire within the
programmable coincidence time window. When a coincidence is detected the

circuit outputs a pulse to a logic analyzer which logs the time the pulse occurred. 106

Figure 6.9: This figure shows the configuration of the ranged experiment. The
experiment was performed in a hallway that allowed for a total of 72 meters of
distance between the transmitter and receiver. ........................................................... 11 1

Figure 6.10: This picture shows the hallway where the long range experiments were
conducted. The picture is taken from the location where the transmitter and receiver
is located and the mirror that reflects the beam back to the receiver can be seen at the
end of the hallway ....................................................................................................... 112

Figure 6.11: For ease of alignment the transmitter and receiver were located next to
one another. Both are pointed down the hallway at the top of the picture. ............... 113

Figure 6.12: Front view of the transmitter and receiver with the white cardboard to
reflect the light sources located in front. The receiver was covered in black cloth so
that very little of the noise photons go directly to the photon counters but instead
reflect fiom the screen to the mirror and back to the receiver. ................................... 113

xii

Figure 7.1: In this figure a comparison of single channel photon counting
communication to time coincident photon counting communication for different

noise levels can be made. This graph directly compares the measured SNR to

BER. The variation in the magnitude between the maximum and minimum for

the different data points was caused by varying amounts of beam wander. The

beam wander would change because there was a large temperature difference along
the hallway where the experiment was conducted that was made worse by the

building heating system turning on periodically during the experiment. ................... 118

Figure 7.2: Top: A graph of photon detections as a fimction of time for the single
channel baseline. Bottom: A graph of photon coincidence detections as a function

of time for the 2 channel configuration. The bottom axis for both of these graphs is

in units of seconds. The dashed line shows the transmitted waveform for

reference. .................................................................................................................... 1 19

Figure 7.3: In this graph the signal-to-noise ratio has been calculated with the signal
summed for all of the channels used in a particular configuration. The noise however
was calculated as an average for a single channel. ..................................................... 120

Figure 7.4: In this graph a comparison of the expected BER calculated from the BER
equations and the measured BER is shown. In this case the bias caused by the laser
not completely turning off has been compensated by counting the laser photon

counts outside of the pulses in with the noise for that detector. ................................. 122

Figure 7.5: In this figure the BER of the two channel system and one channel system
are directly compared for the following conditions. The signal is held constant at

one million photon counts per second for both cases. The one channel system has a
signal level equal to 1 million photons per second in the single channel the two
channel system has 500000 photons per second in each channel. The threshold

level for determining the bit value was held constant. ............................................... 123

Figure 7.6: In this graph the variability of the Bit Error Rate as a function of

Signal to Noise Ratio for the one, three and four channel configurations is shown.

In this case only the signal level was changed and all other parameters were kept
constant. The SNR in this case is the ratio of the signal to the average noise per
channel as discussed in the previous experiment. The error bars for the measured

data points are the maximum and minimum data values for that point. ..................... 125

Figure 7.7: In this figure the performance of the 3 channel system is shown for
various coincidence times. In this case only the coincidence time in the receiver
coincidence circuit was changed and all other parameters were kept constant. The
fixed parameters were: Aperture Diameter: 4.5 cm, Data Rate: 100 KBit/sec, Average
Signal Counts per Channel: 500,000, Average Noise Counts per Channel: 985,000

and Average SNR: -2.88. The calculated data points in this case are made from

signal and noise rates that have laser noise counted with the noise as discussed in

the Experiment 1. The error bars for the measured data points are the maximum and
minimum data values for that point. ........................................................................... 127

xiii

Figure 7.8: In this figure the performance of time coincident communication

system at multiple bit periods is shown. In this case only the transmitter bit period
was changed and all other parameters were kept constant. The calculated data points
in this case are made from signal and noise rates that have laser noise counted with the
noise as discussed in the Experiment 1. The error bars for the measured data points
are the maximum and minimum data values for that point. ....................................... 131

Figure 7.9: In this figure the noise and laser (signal) photon detection counts for

one representative detector (C) are graphed for the different aperture settings. This
figure shows that the laser beam had a beam diameter of about 2 cm and so all
aperture settings larger than 2 cm affected only noise while all aperture settings
smaller than 2 cm affected noise and signal. .............................................................. 133

Figure 7.10: In this figure the laser noise compensated signal to noise ratio for each
configuration is graphed according to the simulated range. The points greater than
200 m simulate the affect of greater range. Below 200 m it does not successfully
simulate increased range because the SNR is increasing. .......................................... 134

Figure 7.11: This figure shows the experimental results that different simulated
ranges have on system performance. These results show that the coincident
communication systems (2 and 3 channel) are more sensitive to changes in signal,

but less sensitive to changes in noise, than the single channel traditional photon
counting system. The error bars for the measured data points are i one-sigma. ...... 135

Figure 7.12: In this figure the system performance is graphed for the experimental
configuration (diamonds), an improved system with a 1 ns pulse width and
coincidence time (squares) and a further improved system that uses 15 pulses

instead of 10 (triangles). ............................................................................................. 140

xiv

NOMENCLATURE

(II/(1))
(II/(0))

CR

average number of photon coincidences for a ‘1’ bit value
average number of photon coincidences for a ‘0’ bit value

Contrast Ratio

CRde-ona, = Contrast Ratio for traditional photon counting communications

I

BER

SNR

rn

the entangled photon pair intensity generated from the transmitter (non
dimensional counts / second)

is the background photon intensity captured by the receiver (non
dimensional counts / second)

the fiaction of transmitted photon pairs captured by the receiver

photon counter quantum efficiency

wavelength (nm)

Bit Error Rate (non dimensional bit errors / second)

Signal to Noise Ratio

frequency (Hz)

rate of ambient noise photons detected at photon counter n (non
dimensional counts / second)

rate of photon coincidences due to ambient light (non dimensional counts /
second)

coincidence time window (in seconds)

bit period (in seconds)

XV

CHAPTER 1

INTRODUCTION

The objective of this research is to develop a free space optical communication system
that demonstrates the capability to transmit information over reasonable distances at very
low radiated power levels. This work is in general inspired by the need to develop a
communication capability that will be applicable for a planetary exploration concept that
involves the mass spreading of very small robots, working in conjunction with small
numbers of larger robots, on the surface of a planet. This method of exploration is meant
to increase the information gathering capability of a mission while not increasing the
mass that needs to be launched. In order for this to be possible it will be necessary to
minimize the mass of these robots while retaining certain fundamental capabilities such
as mobility, sensing and remote communications. The communication system developed

and tested in this research has been designed with this usage as the primary motivator.

The communication system is optical because a small transmitter can confine an optical
beam to a smaller divergence angle than is possible with radio frequency transmissions.
Optical communication has the additional advantage that the receiver can have a very
large gain when using photon counting detectors. These two reasons make optical
communications a strong candidate for a small transmitter that must operate on very low
power levels. Photon counting is very susceptible to ambient light conditions and it is for
this reason that this research is focusing on a system that generates time coincident sets of

photons that can be more easily recognized in sunlight. The research presented in this

dissertation includes new work in two systems that both communicate using sets of
photons but generate them in different manners. The first system generates a set of
photons by creating quantum entangled photon pairs. The second system generates the
set by pulsing pairs of diode lasers in coincidence. In this dissertation the underlying
mathematics that describes these systems is presented as well as experimental tests that

verify the operating characteristics of these systems.

1.1. Motivation

NA SA ’3 National Nanotechnology Initiative Grand Challenge

The proposed research path is motivated by the National Nanotechnology Initiative
(NNI) Grand Challenge issued to the National Aeronautics and Space Administration
(NASA) to develop Microcraft for Space Exploration and Industrialization. The vision
for this Grand Challenge is summarized as: “Continuous presence in space outside of the
solar system with nanotechnology enabled low powered microspacecraft. Reduce the size
and energy consumption ten fold. ” [National Science and Technology Council 2000]
This vision is further expanded upon as follows: “Microspacecraft development is a key
thrust for the exploration of space. Motivators for this demand include the high cost of
launching into space, the desire to reach ever more remote and hostile environments in
our solar system, and the unique capabilities of missions involving large numbers of
cooperative spacecraft. To fulfill the promise that microspacecraft hold for exploring
space, these spacecraft cannot be scaled down versions of larger spacecraft, limited in
capability. This new breed of spacecraft must surpass the current state of technology in

today’s fleets of vehicles. Long duration missions (decades) to the outer reaches of the

solar system; exploration into the interiors of planets, comets, and moons, searching for
the subtle clues of the presence of life; fleets of telescopes, acting in concert, imaging
Earthly planets around other stars; all these long range goals for space exploration in
the 21 st century will be enabled through the development of advanced nanoscale
technology.” [National Science and Technology Council 2000] The strategy for
implementing this vision states that there will be needs for research focused on

nanostructured materials, nanoelectronics and biomimetic systems.

This research task will focus on the development of electronic and optical systems for the
purpose of enabling microcrafi communication as envisioned in the NNI. This research
will focus on a communications system that is consistent with all the requirements that
are unique for microspacecraft. These requirements are further described in the NNI:
Initiative and Implementation plan as “extreme demands on the electronics for ultra low
power consumption, radiation tolerance, and safety. ” These demands will require the
“development of transistors and other circuit elements utilizing single quantum
excitations (electrons, Cooper pairs, photons) enable spacecraft to collect, process and
then transmit information that will far surpass the capabilities of current missions.”

[National Science and Technology Council 2000]

The requirements as described in the NNI are both challenging and vague. To further
understand the requirements of a communications system for Microspacecraft some
assumptions in regards to Microspacecrafi (MSC) size and mission are needed. The first

assumption is that due to the size of the MSC it is not possible for the MSC to send data

directly to the Earth but instead will transmit information to a classically sized relay
spacecraft. The size of the Microspacecraft should be driven by the requirements in the
NNI which call for micro devices built from nano components. The micro devices are
defined as devices on the dimensional scale from microns to centimeters that depend on
the understanding and control of materials in the nanoscale. For this research effort the
communications system will be assumed to be for a MSC with a length scale of I

centimeter or less.

Power Requirements for Microspacecraft

The volume of the MSC will dictate the power requirements for the communications
system. The power that can be generated by a MSC can be estimated from the volume, in
the case of a battery type power supply, or from surface area in the case of photovoltaic
power. In Figure 1.1 the power output estimate for a MSC with a high efficiency fuel
cell is graphed in relation to the length scale. The assumptions used to create this graph
are the following: the fuel tank takes up one half of the total volume of the MSC and the

fuel is used for 24 hours of operation.

 

 

 

 

 

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Figure 1.1: Graph of power output for a fuel cell that is assumed to linearly
decrease as size decreases. Fuel cell Power Generation (FPG) is an estimate of the

capability of future fuel cells.

For instance, for a MSC with 1 cubic centimeter of volume that is operating with a power
supply that is an extremely efficient fuel cell, it is estimated that the power generation
capability would be approximately 40 microwatts given a power generation capacity of
6.9 kW/L [Kimble 2004]. Given that only a fraction of the available power can be used
for communications, the communication system must be designed to use only a quarter of
that power, on the order of 10 microwatts of power. Since 1 centimeter is the length
scale that is used as the maximum size for a MSC, 10 microwatts of communications

power can be used as the maximum power usage for the MSC communication system.

Such a small amount of generated power implies that the device must be very efficient in
signal transfer, or throughput, from transmitter to receiver. Throughput is defined as the
ratio of signal energy received by the receiver divided by the energy sent from the
transmitter. To achieve this level of throughput requires significant gain fi'om beam
forming, also described as a low level of beam divergence, or spreading, and a collector
at the receiver the captures much of the transmitted beam. We will assume that the
collector must be made of a reasonable size and so the parameter to optimize is the beam

divergence.

The difficulty of building radio frequency antennas with significant gain given such very
small dimensions is a second challenge that can further compound the power problem.
The antenna gain is a function of both aperture size and signal frequency. Since the
aperture is limited by the size of the transmitter the only parameter left to optimize is
signal frequency. The relationship between beam divergence, 60, which is a measure of

the beam forming gain, and frequency, v, is

C

60 11-11

 

—72'WOU’

where W0 is the beam waist radius and c is the speed of light [Saleh 1991]. Gain is
inversely proportional to divergence, as a smaller divergence angle means greater long
distance confinement of the beam and hence higher transmitter gain. So gain is therefore
directly proportional to frequency. As gain is proportional to signal frequency, this

suggests that the optimal frequency for remote communication, given robots of this scale,

is in the highest frequency possible, which is in the optical region. Another benefit of
optical frequencies is that it is possible to count photons at a receiver. This allows the
receiver to be able to detect a signal that has very little energy, while at the same time
providing a significant amount of intrinsic noise immunity from photons of energy below
the band gap of the detector material. The advantages of beam forming and detectors
capable of photon counting have made optical photons a very good candidate for
communications for MSC devices. The research presented here is focused on a solution
to the communication needs for MSC devices that is based on optical communication

because of these reasons.

1.2. Objective

The overall goal for the National Aeronautics and Space Administration quantum optical
communication research project is working toward energy-efficient, miniaturized,
integrated (photon source, modulator, receiver and antenna on a chip) wireless
technologies for robotic missions on planetary surfaces, on orbit and within space
vehicles. The goal for this effort is to research a communication system, both transmitter
and receiver, that is appropriate, in terms of power and capability to be fabricated in an
extremely small package, for micro robotic communications. The manner in which this
will be accomplished is in using an optical communication system that is based on

quantum entangled, or highly correlated, photons.

Quantum Entangled (QE) photons are photons which are created by passing a pump
beam through a nonlinear optical crystal. As the pump photons pass through the
nonlinear crystal they sometimes spontaneously down convert into two photons whose
individual energies add up to the pump photon energy. These two photons are created
nearly simultaneously and because the two are created from one pump photon they are a
part of a composite quantum state. An example of a 2 photon quantum state, PP)”, that is

composed of photons that are entangled in polarization, is

 

Ht)” =|H>1|Vl2j§|V>1lH>2 [1-2]

where IH) indicates that a photon, 1 or 2, is horizontally polarized and IV) indicates that a
photon is vertically polarized [Bouwmeester 2000]. The meaning of this quantum state
is that either photon 1 is found horizontally polarized and photon 2 is found vertically
polarized or photon l is vertically polarized and photon 2 is horizontally polarized. This
quantum state is therefore a superposition of photon product states that cannot be
factored. This means that it is impossible to describe the polarization state of one of the
individual photons only in terms of itself. The photons therefore are highly correlated and
this degree of correlation, along with the fact that they are produced simultaneously,

makes them useful for low power communications in the presence of ambient noise.

The utility of QB photons for communication can be understood by considering the
ambient photons detected by a receiver with two photon counters that detect specific

wavelength and polarization photons. If a receiver has a narrow field of view and the

ambient photons are sufficiently filtered by polarization and for narrow bands of
wavelength, then even in the presence of sunlight the photon counts can be reduced to
millions or even hundreds of thousands of counts per second. With photon counting
detectors that can discriminate photon arrival times down to the nanosecond the detection
of a photon can be considered a one nanosecond event. Even with a million of photons
per second detected, the potential detector events are only one thousandth occupied. If
only the times when both detectors detect photons within one nanosecond of one another
are counted, then this significantly reduces the number of events from ambient photons.
The number of coincident events in this scenario is only one thousand times per second.
The mathematics supporting this will be further described in Chapter 3 but the important
point is that the number of ambient noise events drops fi'om one million per second to one
thousand per second. The QE photons however pass through the optical and time
coincidence filtering. They have highly correlated wavelengths and polarizations so the
receiver filters can be matched to pass only photon pairs with these particular
correlations. Also because the QE photons are generated at the same time they will arrive
at the receiver at the same time and be time coincident. So while the receiver filters out a
significant amount of the background noise, the QE signal is not attenuated and this

makes the low power communication possible.

1.3 Planned Research Activities

There are three major activities planned for this research effort to develop low power
communications for MSC. The first is to expand the development of communications

systems based on QE photons. The second activity is to develop a system that emulates

the QE communication system by coincidently pulsing individual sources. This system
will hereafter be referred to as the Coincidently Pulsed Sources (CPS) system. Each of
these systems has advantages and disadvantages that will be discussed later in this
chapter. The last activity will be to develop the mathematical formulae that accurately
predict the performance of both the expanded. QE system and also the CPS system.

Further details on these three efforts follow.

1.3.1 Modulated Quantum Entanglement State Communication Experiment

The idea of using photons that are quantum entangled for communication in very low
signal-to-noise ratio (SNR) environments has been around for some time. Mandel
[Mandel 1984] first proposed one such system in 1984 and a demonstration experiment
was performed by Hong, et al., [Hong 1985] in 1985. In this experiment pairs of
polarization entangled photons are generated and transmitted to the receiver over two
beams of light that are on/off keyed with the data. In contrast to the system demonstrated
by Hong et a1. [Hong 1985], which encoded information through on/off keying, a system
is presented here that instead encodes information with two symmetric entanglement
states. This makes the receiver simpler to operationally implement than an on/off keyed
system because the there is no threshold level, which is dependent upon ambient noise
and hence influenced by the operational environment, to be concerned with. The QE
system also has potentially greater range, as will be explained in Chapter 3, than the CPS
system so further development of the QE system is appropriate as it may be the better

choice for long distance low power communication.

10

This experiment also provided a good starting point because it is very similar to Hong’s
et al. [Hong 1985], and so this paper provided a good reference and provided a solid
foundation to begin with. Also because the transmitter is an incremental improvement
over the previous work, this experiment allowed many of the components for the CPS
system, which is totally new, to be fully tested in a situation that has fewer unknowns.
Upon completing this experiment critical experimental building blocks for the next stage,

such as the photon counters and coincidence detection circuits, had been validated.

1.3.2 Monolithic Optical Transmitter Concept and Experiment

The general objective of the monolithic Optical transmitter research activities was to
develop a communication system based on time coincident photon pair communication
that can be built into a miniaturized transmitter and is very efficient in terms of the
amount of electrical power used to transmit a bit of information. The nonlinear
generation of quantum entangled (QE) photons is extremely energy inefficient and is not
feasible at present for usage in MSC devices. In order for this communication method to
be used it is necessary to develop an energy efficient method for generating the signal
photons. There is no known method for efficiently creating photon pairs that share a
quantum state and are hence “quantum entangled”. However, the QE communication
method can be emulated. The communication method works because of the time
coincident generation of photon pairs that have highly correlated wavelengths and
polarizations. It is possible to build a transmitter that efficiently generates photons with
these correlations. The subject of this research is a transmitter concept that will be able

to generate correlated photon sets, which look like entangled photons to a receiver, in an

11

energy efficient manner. This transmitter will be built from components that can
eventually be incorporated into a very energy efficient monolithic device that is

appropriate for a MSC.

As previously stated, the purpose of this work is to develop an optical transmitter that
will meet the power and size requirements for a micro robotic device as was defined in
the NNI. This means that the transmitter will have to have an overall diameter between
10 microns and 1 centimeter, and require less than 10 microwatts of power. It has been
previously shown that quantum entangled photons are detectable even when swamped by
background noise. The next step is to develop a monolithic source with driving
electronics and optical sources integrated in a single solid state device with external beam
forming optics. Since this source would require years of development, instead a
prototypical transmitter that could in principle be built as a monolithic device was built
and tested. The objective of the experiments performed with this system was to test the
efficacy of both a transmitter that can generate the low power, highly detectable signal
from commercial off the shelf components and a reciever to detect this particular signal.
The commercial components for the transmitter were selected so that they can in the
future be integrated into a low power monolithic device. This meant that a non linear
crystal was not acceptable for this implementation. Instead solid state laser diodes and
standard electronics were used to generate the detectable signal as they can be

incorporated into a multi layer solid state device.

12

The block diagram for this transmitter concept is shown in Figure 1.2. The device works
by modulating a signal from an oscillator or clock, for example at a 1 GHz rate. This
modulated signal drives optical sources of different wavelengths. These sources (which
may be LEDs, Laser Diodes, Quantum Wells or Quantum Dots) are driven with very
small, and very fast pulses of electrical energy so that a burst of photons generally
numbering less than one thousand per source, are generated. Since very small numbers
of photons are required, the power can be significantly reduced from that of traditional
On-Off Keyed optical transmitters, because very energy efficient optical sources can be
used. The photons from all four optical emitters are sent coaxially along the same optical
path to a receiver whereby they are decoded according to wavelength and polarization
state. Various optical configurations can be used to spatially superimpose the signals
from all emitters along a common optical path, inluding, but not limited to, dichroic
beamsplitters and/or polarizing beam splitters, or a combination of a diffractive element

such as a prism or grating and polarizers.

13

Time-Coincident Multi-Color
Warm.

 

BM = Ultra-short photon

Encoding pulses

  

Transmitter

     
      
    
    
     
 

 

 

  

__ ill \
/ i Red
Collecting lens --, a \
(Telescope) (D .. 4 -' . “ Polan'zer
‘ 1 Opt. filters H
., \—~ ll
‘9’ f H Green V * \
Signal DUOIOUS \
and noise €93 /
Coincidence circuit
(ultra-high freq.)

as a true signal finder

ifold Spatial-Tem ral- mg
Reduction S tern

Figure 1.2: The conceptual system for generating highly correlated photon sets. Figure created by
Dr. Jun Kojima of the Ohio Aerospace Institute.

In order to convey an idea of the power levels that are achievable, it is possible to

estimate the power per bit of information transmitted for an integrated device that utilizes

14

this signalling method. This calculation is best done by starting with the required signal at
the receiver. It is known from the experiments performed up until now that the
communication system has a reasonably low bit error rate if the number of coincidences
registered by the receiver is greater than 10 per bit. Assuming a detector has a quantum
efficiency of 70% means that the receiver must collect at least 14 photon pairs per bit to
register 10 per bit. For the transmitter, it can be assumed that a very advanced nanolaser
will have a 50% conversion efficiency of electrical to optical energy [Gourley 1998,
Miyasawa 2005, Arakawa 2002, Mac 2004]. The transmission loss can be fixed as the
range is bounded to the distance at which most of the transmitted photons are captured by
the reciever [Jackson 2002]. This can be estimated as the distance where the transmitted
beam falls off to 50% and so the transmission loss is set at 50%. From these assumptions
it can be estimated that 56 photons / bit must be emitted from the transmitter to get 10
coincidences at the reciever. The electrical energy to generate these photons is equivelent

to the energy of 112 photons per bit.

This is a simplified calculation and other factors, such as the inability to generate precise
numbers of photons on demand and the fact that using two sources means there are two
independent probabilities for generating a photon pair, capturing pairs and detecting
pairs, will significantly increase the amount of electrical power required. If these
additional considerations are roughly estimated to require an additional 400% of power
then the energy the transmitter uses per bit would be around 500+ photons, which is
about 150 x 10'18 joules. At 1 a Mbit/second data rate this works out to be a power of

140 picowatts, which is an extremely low power tranrnitter. Again the fundamental goal

15

of this dissertation is to take significant steps to demonstrate just such a transmitter as

well as the requisite reciever.

1 .3.3 Perform calculations to quantify the capabilities of this

communication system

This communications system utilizes a simple technique for the production and
transmission of time-correlated photon bursts over a multiplicity (minimum of two) of
wavelengths or channels in a spectrum of wavelengths. Information is encoded by
modulating the relative quantum state such as the polarization of the photons in each
wavelength or spectral channel. The time-correlation of the photon bursts in addition to
the modulation of the quantum states enable the detection of an ultra low-power signal
that is comprised of at minimum, a single-photon from each spectral channel reaching a
receiver. Thus, the transmitted signal comprised of multiple pairs of photons per bit is
extremely low in radiated power (atto-Watts) making this technology useful for ultra low-
power free-space optical communications applications. It should be noted that the time-
correlation of photons at the separate spectral channels provides greater noise immunity
than can be accomplished by increasing the radiated power from a single channel to a
level equivalent to the combined power of the multiple channel transmission as described
here. It is anticipated that the tranmitter described here will enable the development of
ultra low-power free-space or fiber optic optical quantum systems using a simple and

cost-effective electro-optics architecture.

16

1.4 Conclusion

In this chapter the motivation for developing a low power optical communication system
for micro robots has been described. The research steps that have been taken, and are
described in this work, have also been described. The plarmed accomplishments for this
dissertation are to research, build and test, in a relevant environement, the efficacy of low
radiated power communication system based on both quantum entangled sources and also
coincidently pulsed sources. The new knowledge that has been generated from this effort
include:
1. Quantified capabilities of both communication systems
2. Confirmation of the capabilities of a Quantum Entangled communication
system with two-state coding through experiment
3. An original electronic photon pair communication system whose capabilities
are confirmed through experiment.

The subsequent chapters support these three major efforts.

l7

CHAPTER 2

BACKGROUND

In this chapter the key research in state of the art low power communications systems is
discussed. First the previous work in utilizing quantum entangled photons for classical
communications will be covered. From this previous research, particular equations that
are important stepping stones for the research presented in this dissertation are discussed
in detail, as well as known experimental demonstrations. Secondly, other state of the art
low power communications systems, both RF and optical, will also be discussed in an
effort to benchmark existing technology, so that the technological developments and

results provided in later chapters can be evaluated.

2.1 Literature review of quantum entanglement for communication

State of the art optical systems include quantum communication systems which generate
photons that share a quantum state, or in other words are entangled. It should be noted
that in the literature quantum communications generally refers to the teleportation of a
quantum state [Vilnrotter 2001, Lee 2000, Barnett 2001, Rarity 2003, Bouwrneester
2000, Nielsen 2000]. The other major area of quantum optical communication systems
includes the used of single photons for both fiee-space and fiber optic Quantum
Cryptographic Key communications. Single photons are used because it is possible to
encode information in the quantum state of a photon in such a way that should an
eavesdropper try to intercept the transmission they will not be able to reproduce the

quantum state completely. If they cannot reproduce the state completely then the

18

transmitter and receiver can detect that eavedropping is being attempted and will know
not to use the transmitted key. This allows for the reliable communication of
cryptographic keys. These systems have been demonstrated by, among others, Los
Alamos National Laboratories. These systems typically utilize a bright, higher power,
synchronization laser in conjunction with a low power photon source and so is not

suitable for this low power micro robotic application [Nordholt 2002, Alde 2002].

The most important work in quantum communications that is applicable for low power
optical communications has been work focused on utilizing quantum entangled photons
to enhance the classical capacity of free space and fiber optic communications [Mandel
1984, Hong 1985, Jackson 2002, Banaszek 2004]. The systems that utilize entangled
photon transmission are complicated large-scale systems requiring a ultraviolet (UV)
pump laser to excite a non-linear crystal to produce time-coincident photons [Dmitriev
1999, Rarity 1990, Joobeur 1994, Kurtsiefer 2001, Kwiat 1995, Oberparleiter 2000,
Takeuchi 2001, Eckardt 1990, Bumham 1970, Rarity 2003]. Because of the necessity of
the pump laser and nonlinear photon pair creation the previous work by itself is not
directly applicable to low power communication. However, the essentially important
kernel from this work is the finding that enhanced signal recognition is achievable, even
with a significantly higher level of background light, when utilizing entangled pairs of
photons for classical communication. This kernel is the basis of the work contained
herein and so the significant points of the prior research in this area will be discussed in
detail to provide the basis for the research dedicated towards creating a system that

generates these low power yet recognizable signals in an energy efficient manner.

19

Utilizing Quantum Entangled (QE) photons for communication was first proposed by
Leonard Mandel. In ‘Proposal for almost noise-free optical communication under
conditions of high background’ Mandel [1984] introduced this work. In this paper it was
suggested that with quantum entangled photons “it should be possible for weak signals
that are greatly exceeded by background or noise to be used for communication, with
relatively little loss of information” [Mandel 1984]. Mandel’s initial work has since been
expanded upon by Hong et al. [1985] and Jackson [2002]. These analysis’s support the
assertion that optical communications utilizing pairs of photons that have an entangled
quanttun state have significant noise immunity benefits. They show that by only
registering photons that are detected at the receiver in pairs, i.e. detected at the same time,
a certain amount of noise immunity can be expected. This detection of photon
coincidences can be thought of as an added level of temporal filtering to the system that

further decreases noise effects.

Jackson’s paper [2002] talked about particular communication instances such as when the
sun was directly in line with the communication path. This paper concluded with two
requirements: “(1) that an intrinsically two-photon detector be developed (this rejects
noise without being saturated by it) and (2) that most of the transmitted photons be
collected (which can be done in free space over distances up to about 1000 km)”. The
first conclusion is not completely applicable to the implementation for nanotechnology
because detector saturation is dependent upon the environment where the MSC is used.
This means the coincidence detector does not have to necessarily be an intrinsic two

photon detector. The second conclusion however is critical for implementation of QB

20

communication in MSCs because it will be a serious limiting factor for micro scale

devices which will have significant beam divergence due to their small size.

Hong et a1. [1985] not only expanded upon Mandel’s [1984] analysis but also performed
an experiment that demonstrated this noise immunity. In this experiment entangled
photon pairs were generated by sending a 351 nm laser beam through a nonlinear crystal.
The message was encoded using “on off” keying by turning the pump beam on and off.
It was shown that a message that registered between 8 and 17 coincidences per bit was
clearly distinguishable even when the individual photon counters detected an average of

more than 2000 individual photons per hit.

From Mandel’s and Hong et al. analysis, the total rate at which coincident photons are
counted is a sum of the entangled photon pairs that are counted as well as the counted
uncorrelated photons that accidentally overlap. The rate at which entangled photon pairs
are counted, RC5, is the product of the rate at which one of the conjugate photons is
counted at one detector, R12, and the probability that the second photon of the pair will be
detected at the other detector, which is equal to the quantum efficiency of that detector
an. These rates are equivalent because the entangled photons are always produced in

pairs

RCE =R1a2 =R2 051- [2-11

21

The accidental photon coincidence rate is the sum of the ambient noise photon rate for
each detector, r1, 2, and also the rates, R1(1-a2) and R2(1-al), which account for the case
where one entangled photon of a pair is detected while the second one is not. From the
accidental and conjugate photon coincident rates we have the following photon

coincidence rate

R. =[0—a2)R1 +nl[(1—a1)R2 +1216: +R1a2, 12-21

where (St is the time window in which the arrival of a photon at both detectors is

registered as a coincidence.

When data is transmitted using on / off coding, the average number of coincidences
registered when the pump laser is on, which represents a one data bit, is described by the
equation

(N(1)) = [(1 —a,)Rl +r,][(1 -a,)R, +5151]; +R, a, T5, [23]

where T, is the time period for each bit. When the laser is turned off, which represents a

zero, the average number of photon coincidences detected is

(Nan) = r1 r26t Ts- 12-41

22

The noise immunity of this system can be seen by looking at the effect of the coincidence
time window. If the coincidence time window is very small, on the order of a nano
second, then the average number of coincidences for a ‘1’ bit value will largely be
dependent upon the entangled photon rate until the background photon rates approach 109
photons per second. For a narrow region of the optical spectrum this is a fairly
significant ambient optical power. As previously mentioned, this noise immunity of
correlated pairs of photons forms the basis for the present research into low power optical

communication.

2.2. State of the Art

To further understand how this research effort is beneficial an examination of the current
State-of-the-art is necessary. The following sections covering Radio Frequency (RF) and
optical communications are primarily focused on technological development rather than
theoretical studies. The state of the art comparisons are therefore made to systems that

have been, to some experimental level, built and tested.

2.2.]. Low power RF

State-of-the-art small-scale communications is presently achieved by very small RF
transmitters. These transmitters have the benefit of omni directional communication but

are limited in range. Currently, the development of the state-of-the-art miniature RF

23

transmitters is being led by a group at U.C. Berkeley [Rabaey 2002]. The goal of the
Berkeley group is to build RF transmitters so small and inexpensive that they will be
ubiquitous in everyday uses and can be used as disposable embedded sensor/transmitters.
The Berkeley group has demonstrated a micro-RF transmitter that is about 4 mm2 in size,
and requires less than 100 uW of power to operate at a frequency of 1.9 GHz. Perhaps
one of the biggest challenges of their technology is the fact that they draw power (as
much as 10 uW) even when they are not transmitting (standby mode). This type of drain
alone can deplete the small energy reserves of micro-robotic exploration vehicles.
Whereas optical communication technologies only require power when they are actually

transmitting photons, thus they are more efficient in the long-run.

As advanced as this miniature RF technology is compared to existing RF technologies
that use 10’s of mW’s, it still requires an external wire antenna that is of order cm’s long
in order to efficiently transmit its signal through space. It is the requirement of relatively
large external antenna that poses a fundamental barrier to using RF technologies for
micro- or nano-robotic exploration vehicles as the mass and size of the antenna alone
may exceed that of the vehicle itself. It is in this area that by using fi'ee-space ultra-low
power optical communications proves beneficial: the size of an optical antenna can be
very small as the wavelength of light is much smaller. Thus, practical optical transmitters

can be much smaller than 1 mm in size.

24

2.2.2. Low power optical

In general free space or wireless optical communications are primarily used for wireless
network links for personnel computers or for high bandwidth trunk links between
buildings [Heatley 1998]. State of the art optical systems also include classical optical
communication systems based on lasers and single, as well as multiple, frequency
transmissions [McEliece 1981, Atkin 1994, Polishuk 2003, Arnon 2003, Andrews 1998,
Pierce 1978]. The classical multi-frequency free space systems utilize time coincident
classical pulses on two or more wavelengths to overcome atmospheric scintillation [Kim
1997, Kim 1998, Strickland 1999, Grant 2005]. The wireless communication between
buildings and for personnel computer networks are in general not as power limited as the
research considered here and so they are not elaborated upon. Free space optical links are
also considered for deep space communication [Wilson 2000, Pierce 1981], satellite links
[Hemmati 2000] and also for communications for novel miniature sensors called by their
designers “Smart Dust” [Warneke 2001, 2002]. Deep space networks are a somewhat
similar problem because the signals are so very weak at their destination and so some
description of this work will be made. The most similar state of the art work is in optical
communications for integrated robots that are so small (~1cm) that they are called “Smart
Dust”. This work is considered the most relevant for comparison to the research

described in this dissertation.

Optical communication for deep space networks has received more attention recently

because of the increased bandwidths desired to support new technologies such as hyper-

25

spectral imaging and HDTV. A recent paper, summarizing efforts at the Jet Propulsion
Laboratory, described a developmental laser communication system that is being used for
various studies and demonstrations [Wilson 2000]. The transmitter utilizes a Q-switched
Nd:YAG laser that encodes data using Pulse Position Modulation (PPM). The receiver is
planned to be a 1 to 10 meter telescope with an avalanche photo diode as the detector
[Ortiz 2000]. The deep space communication problem is a similar one to the micro
robotic communication problem. The power levels of the transmitter are higher but the
long distance and high background light make this a comparable case. By using PPM it
is possible to achieve very low power communication. This is because PPM is a block
encoding communication method where an entire block of data is sent by a single pulse.
The data word sent is defrned by the slot position of the transmitted pulse. The number
of time slots, M, in a flame determines the number of bits that are transmitted with each
pulse. So a system which has M = 256 will transmit 8 bits of information with each
optical pulse, neglecting synchronization pulses. In comparison, the most common
optical pulsed modulation system utilizes On Off Keying (00K) with Manchester
coding, and these systems require 1 laser pulse per bit. So PPM modulation in this case

represents an average transmitted power reduction of a factor of 8.

In 2000, Gerardo Ortiz et al [Ortiz 2000] published a very good description of the design
of a Mars to Earth optical communication link that included significant operational
parameters such as data rates and background light. The Mars transmitter was specified
as a one watt Q-switched Nd:YAG laser (wavelength 1064 nm), with a 10 cm aperture

telescope that was PPM (M=256, pulse width = 25ns) modulated with Reed Solomon

26

coding. The receiver included the following specifications: silicon APD detector, 10
meter diameter telescope aperture, an optical bandpass filter with a 0.2 nm bandwidth and
a receiver sensitivity of 323 photons per pulse. The link distance is 300 million Km, the
required bit error rate is 105, and the number of nighttime background photons per pulse
slot is in the range 156 photons per slot. The data rate obtainable with these parameters is
46 kbps and the received signal is 646 photons / pulse. The energy efficiency of this
system is best examined from the required signal at the receiver. The received signal
pulse of 646 photons is the amount of optical signal required to receive 8 bits of
information, neglecting coding and synchronization. This works out to be one bit of
information per 80 photons captured by the receiver. If the signaling method had been
Manchester OOK then the required signal at the receiver would have been closer to the
646 photons per bit when the background is around 156 photons per pulse. In comparing
the research in this text to this system, the comparison will be made in terms of the 00K
parameters. The comparison will be to 00K because PPM is essentially a preceded
version of 00K. That is an OOK system can be modulated as a PPM system. In
referring to modulations such as PPM Harnkins wrote “All the other orthogonal
modulations considered in this paper are constrained versions of 00K, in the sense that
the other modulations can be viewed as a preceding operation followed by ordinary

00K.” [Hamkins 2004]

The communication system considered for the Smart Dust project has a great deal of
applicability as it is meant for essentially the same application and has size and power

constraints very comparable to the goals of this research. The stated goal for Smart Dust

27

is to develop a device, which is apprexirnately a cubic millimeter in size, capable of
sensing, computing and communicating that will work together with like devices to form
a massive sensing array [Warneke 2001, 2002]. The device can be solar or battery

2 solar cell is 1

powered. When solar powered the predicted power levels for a 1mm
joule per day in sunlight and from 1 to 10 millijoules per day indoors [Warneke 2001]. In
terms of watts this would be an average power of 11.5 microwatts outdoors and 11.5 to

115 nanowatts indoors. These are very similar to the estimate in Chapter 1, which was 10

microwatts, so the conclusions drawn from the Smart Dust research is very applicable.

The researchers in this program have pointed out several advantages of optical
communication over RF communication for energy constrained devices such as these.
They cite current RF transmitters requiring “minimum power levels in the multiple
milliwatt range due to analog mixers, filters, and oscillators” [Warneke 2001]. They also
address the need for an antenna of at least 1 cm as being a limiting factor in producing
small RF transmitters that retain energy efficiency. Optical communication is in
contrast described as “intrinsically small” while the “transmission and detection circuitry
for on/off keyed optical communication is more amenable to low-power operation than
most radio schema” and most importantly “optical power can be collimated in tight
beams even from small apertures” [Warneke 2001]. These are essentially the same
arguments that have been made in chapter one that motivates this optical communication

research.

28

In the two papers cited [Warneke 2001, 2002], two different optical communication
systems are described. The first is a passive optical transmitter built from a modulated
Corner Cube Retroreflector (CCR) while the second is an active transmitter built from a
laser diode with beam steering optics. The comer cube transmitter works by modulating
the ref’troreflection of an interrogation beam that originates from the device that is to be
communicated with. The retroreflection is modulated by putting one of the mirrors that
forms the comer cube on a swing arm that can be tilted. By tilting this mirror so that it is
no longer orthogonal to the other two mirrors, the three mirrors will no longer work as a
retroreflector and so the interrogation beam can thus be on/off modulated by tilting this
mirror. This system has significant power advantage for a low power sensor node
working with a higher power central node because the transmitter only uses the power
required to move the mirror a slight angle, which for a micro rrrirror can be a very low
power. The disadvantages are that devices that utilize a CCR will not be able to
communicate with one another and the effective range is not easily extended beyond 1
km. F or these reasons the researchers developing the Smart Dust devices state that the

nodes “must be active and have their own onbeard light source” [Warneke 2001].

The active system described in the Smart Dust project consists of a laser diode with a
collimating lens followed by a steering mirror. In order to operate in outdoor ambient
light the receiver has a narrow band filter and an imaging detector. The imaging detector
further limits the ambient light because the individual cell in the detector array sees only
a limited area of background light around the transmitter. The imaging detector also

allows for multiple transmitters to be detected simultaneously. One issue with the

29

imaging reciever is that the data rate is limited to video frame rates so an active research
area for this project is to build an imaging array with an analog reciever associated with
each pixel. Using this technique the Smart Dust project anticipates the need for a
transmitte power of only 10 picojoules per hit for short ranged indoor commrmication.
Since ambient outdoor light is about 1000 times greater than indoor light, the short range
transmitted power estimate for outdoors communications is probably on the order of 10
nanojoules per bit. For 50 kbps transmission rate that would be a power of 500 uw

outdoors and 500 pw indoors.

2.3. Summary

Previous work in utilizing quantum entangled photons for classical communication has
been summarized. The optical systems that were used to generate entangled photons
required large amounts of power and so they are not directly applicable to the present
research. The signals however are foundational for the present work and so the
summarized equations will be the basis in the next chapter to describe the low power

quantum communication system.

State of the art short range RF devices are now at about 100 uw of power when
transmitting and 10 uw in standby. They do not work efficiently when built so small that
the antenna is less than one quarter wavelength in size. Pulsed optical communication
systems have advantages in beam forming and in standby power usage. The required

power level for these is dependent on ambient light conditions and is in the range of 500

30

pW to 500 uW. To build energy efficient classical optical transmitters, pulse position
modulation is used to further reduce power. When comparing an OOK system to a PPM
system, it is fair to compare the signal to noise ratio of the time slot containing the PPM
signal pulse to the signal to noise ratio of an individual OOK pulse. This is because PPM
is a preceded version of 00K and so an 00K system can always be made into a PPM
system. The figure of merit in terms of required signal captured by the receiver, can thus
be taken from the deep space optical communication research. That level is therefore 646
signal photons when the background is 156 photons. These parameters will be used for

comparison in later chapters.

31

CHAPTER 3

COINCIDENT PHOTON COMMUNICATION THEORY

In this chapter the improvement in hit contrast ratio by utilizing quantum entangled
photons for classical communication coded by on / off keying (00K) is derived. An
improved communication system utilizing quantum entangled photons for symmetrically
coded communications is introduced and the Bit Error Rate (BER) for this system is
derived. The BER for a system that electronically generates photon pairs is also derived.
Finally this chapter includes a section where the ranges of the two different

communication systems are examined.

3.1 General theory for On / Off keyed Quantum Entangled Photon

Communication - improvement in hit contrast ratio

A comparison of the bit contrast ratios for the technique based on utilizing Quantum
Entangled (QE) photons and traditional single source photon counting communications
shows the utility of utilizing QE photons for low signal power situations. From Shannon
information theory it is known that the larger the noise, or background, in a discrete
channel, the lower the rate at which information can be transmitted [Shannon 1948]. If
the noise level were to exceed the signal then the information becomes useless. The
obvious way to overcome the noise for successful communication is to increase the signal
strength. However with a fixed signal strength, which is below the ambient noise, the

proposed optical system using quantum entangled photos for communication becomes

32

necessary. The QE system can perform favorable even when the signal strength is as low
as a few photons and noise level is extremely high. By further analyzing the equations
derived by Mandel it is possible to derive a comparison of QE photonic communication
system versus a traditional single source photon counting communication system
[Mandel 1984]. Hereafter the typical single source and single detector photon counting

system will be referred to as the traditional photon counting system.

The effectiveness of this signaling technique can be realized by looking at the contrast
ratio for the ‘1’ and ‘0’ bit value. The contrast ratio in the case of registering single

photons or QE photon coincidences is defined as the following ratio:

CR = (MD) [34]

(M0) ’

 

and is described as the ratio for the average number of single photons or coincident
photons for the one bit level, WU», to the average number of single photons or
coincident photons for a zero bit level, (N(0)). For traditional photon counting these

values are

N1 =ai+afll [3‘2]
< (l)

(N(0)) = at [3-3]

33

where I is the signal photon intensity, i is the noise intensity, or is the quantum efficiency
of the detector and ,6 is the fraction of transmitted photons that are captured at the
receiver. From Equations [3-l,2,3] the contrast ratio for traditional photon counting

optical communication (CR,,ad,-,,-0,,al) is

I
CRtradional = 1+ fl ' 7 , [3'4]-

The contrast ratio for the QE based photon counting communication can be derived using
Equations [2-3], [2-4] and [3-1]. It can be presented in a clearer manner by assuming the
rates of the photons going to the two detectors is equal for both the entangled photons
(Ru) and the ambient noise photons (r,,) and representing these parameters as R and r

respectively.

_Ra+[(1—a)R+r]26t

CRQE r2 5t

[3-51

 

The equation can be further simplified by expanding the R and r photon rates to account
for beam divergence and quantum efficiency of the detectors through the following

relationships:

R=aflIQE and r=ai, [3-6]

34

where IQE is the entangled photon intensity generated from the transmitter. This

substitution produces a Contrast Ratio for the entangled photon communication that is

a2 flIQE +[(l-a)aflIQE +ai]2 (St
CRQE = a2 i2 6t . [3-7]

 

By looking at the case where the quantum efficiency is assumed to be equal to 1 it is
easier to compare the QE contrast ratio to the contrast ratio for traditional photon

counting cemrnunication. Setting or to one further simplifies the QE Contrast Ratio to:

131le

CR E=1+ .
Q 1251

 

[3-3I

From this equation and the traditional photon counting contrast ratio equation, the

Contrast Gain (CG) can be expressed, in terms of decibels, by:

 

1+fl_IQ_E_ q 2
CG=10 log M :10 log 'Z‘SHWQE . [3-9]
”El i6t+i6tfl1
I

 

 

If the intensity of QE photons is equal to the intensity of traditional source then from this

equation it is apparent that the entangled photon communication method can produce

35

significant gain as long as the i and 6t product is smaller than one. This bounding
equation provides a means to calculate the maximum background intensity where this
technique will prove useful. Assuming that the minimum coincidence window that is
possible to obtain with existing electronics is approximately 100 pico seconds, this makes
the maximum background photon rate at the detector to be approximately 10'0 photons /
second for this method to prove useful. If the QE intensity is less than the intensity for
traditional photon counting, then this difference directly reduces the maximum
background photon rate where the system has merit. The need for high efficiency QE

sources is apparent from this relationship.

A plot that compares the bit contrast ratio of classical on-eff keying optical
communication with this non classical technique is shown in Figure 1. For this plot the

following parameters were used: fraction of captured photons ,6 = .3, coincidence

resolving time 6 t = 1 ns, detector quantum efficiencies a = 1 and a fixed signal rate I of

104 photons/s. The amount of noise was varied to generate different levels of Signal to

Noise Ratio (SNR).

36

 

 

 

 

 

70 1 1 1 1 1 T
cor

a

“U

.9 50"

a

M

g 40*

C‘.

O

9.

a» _

5 30

U

a

in 20”

U)
10— _
0 _______ r- - r------ L- ...... L ......... L """""" 1'-
-25 -20 -15 ‘10 -5 0 5 10

SNR(dB)

— Contrast Ratio for non-classical
""" Contrast Ratio for classical
— ‘ Contrast Gain

Figure 3.1: This figure gives a plot of the increased contrast ratio that is possible
when utilizing quantum entangled photons (non-classical) for communication at low

SNR when compared to classical optical communications.

At less than -25 dB, the noise and background dominate and the QE signal photons are
largely lost in the noise. Below this SNR commrmication would be impractical because
the contrast ratio of the quantum entangled optical system is similar to the traditional
photon counting system and there are no contrast gains. However at slightly higher
signal-to-neise ratios (greater than -22 dB) the contrast ratio of QE system irnpreves
significantly in comparison to the traditional photon counting system and the contrast
gain is greater than 3 dB at SNR of -20 dB. This region between -20 dB and 10 dB is

where communication with entangled photons is useful. Beyond SNR of 10 dB it is

37

unnecessary to utilize the QE photon based technique and the contrast gain begins to drop
significantly. The use of entangled photons together with photon coincidence detection
permits good discrimination against background noise at the SNRs that an ultra-low

power MSC can be anticipated to operate at.

3.2 Bit error rate for communication utilizing quantum entangled photons with on

off keying for bit coding

The experiment performed by Hong, et. al., in 1985 is illustrated in Figure 3.2 [Hong
1985]. The pairs of polarization entangled photons are generated and transmitted to the
receiver over two beams of light that are on-off keyed with the data. The receiver
detectors can detect individual photon arrivals. The coincidence detector circuit produces
a pulse when a pair of photons triggers detectors 1 and 2 in temporal coincidence. If there

is no signal present, ambient light incident on the detectors will produce what are called

accidental coincidences at a rate ra=r1 r2 (9 7",, where r, and r; are the detector 1 and

detector 2 count rates due to ambient light, in photons/s, and 6t is the two-sided
coincidence window size in seconds and Ts is the bit period. By making the coincidence
window time smaller, the rate of accidental coincidences from ambient light can be made
to be much smaller than the rate of coincidences due to the arrival of entangled photon
pairs, which are inherently time coincident. In general, more than one set of entangled
photons will be transmitted during a bit period. Bit value decisions can be made by
comparing the number of coincidences per data bit duration to a threshold value. This

process results in a relatively high detector output SNR fi'om a very small detector input

38

SNR, making reliable communications possible where classical detectors would be

swamped by the presence of ambient light.

___-,. ._.. - llllllll Hillllll ll

 

 

 

 

 

 

 

 

 

[I Photon ”l

y‘ Detector I Coincidence ‘

Polarization- pelarizaltion imbicnl light \_-__4/ Detector i

Entangled Photon I l l I |
Pair Source photong pairs

Photon

'{ Detector 2 I
¥W7

 

Figure 3.2: Concept for on/ofl' keying quantum entangled communication

The experiment performed by Hong et al, was for quantum entangled photons used in an
on/off keying mode. In this case, bit values are determined by comparing the number of
photon pairs received to a threshold value, k. If the number of photons pairs received is
larger than k then it is a ‘1’ bit value and if less coincidence photons are received than the
threshold it is a ‘0’ bit value. The error rate for this coding scheme is tied to the average
number of transmitted correlated photon pairs that are received (m), the average number
of noise pairs received during a ‘0’ bit (mg), the average number of noise pairs received

during a ‘1’ bit (m 1) and the threshold value. These averages are defined [Hong 1985] by

”1:01 Rsz=a2R1Ts
=[(1—a2)R,+n][(1—a,)R2+rQ]6th, [3-10]
=(RI +r1)(R2 +r2)6th

39

where R]; are the rates of conjugate signal photons detected by detectors 1 and 2 except
for the m0 equation where they are the rates of photons from a compensation light that

was turned on when the laser was off, and or. ,2 is the quantum efficiency of the two

detectors.

Photon coincidence counts obey Poisson statistics and so the error probability of a ‘1’ to
be incorrectly interpreted as a ‘0’ and vice versa is described respectively by the

following probabilities [Hong 1985]

k—l r
P(0|1)=e_(’"+’"1)2 M [3-11]
r=0 r
”"0 k—l m6
P(1|0)=1-e go?!— {3.12}

where r is the summation variable. These error probabilities are asymmetric because an
increase in noise increases the probability for a ‘0’ to be mistaken as a ‘ 1’ bit value, by
increasing m0, and decreases the probability for a ‘1’ to be mistaken as a ‘0’ bit value,
because m1 is increased. This will force the selection of a threshold that needs to be

biased toward the ‘1’ bit value depending upon the amount of noise.

The Bit Error Rate comes directly from these error probabilities and is equal to the

average of the error probabilities [Saleh 1991]

40

_P(1|0)+P(0|1)
_ 2 ,

BER

 

[3-13]

The BER calculation produces some remarkable results given these sample conditions:
10 QE photon pairs detected per bit, over 6000 noise photons per bit, and a coincidence

time of 1 ns produces a minimum BER of 1.5x10'3 with a k of 3.

3.3. Bit error rate for communication using quantum entangled photons with two

state coding

The necessity of setting a threshold value for an 00K system that is asymmetrically
affected by noise is not optimal. To resolve this problem, a two state coding scheme has
been developed. What is meant by the two state coding scheme is that a ‘0’ bit is
represented by a zero state rather than simply by off or lack of a signal. The ‘0’ bit in a
two state coding is represented by a particular set of photon states and a ‘1’ bit is

represented by another orthogonal set of photon states.

In contrast to the system demonstrated by Hong, which encoded information through
on/off keying, this system encodes information with two symmetric entanglement states
and will therefore have nominally symmetric affects from noise. Figure 3.3 shows the
block diagram of the architecture for the two-state implementation. The optical source
consists of a UV laser-pumped spontaneous parametric down conversion (SPDC)
entangled photon source which generates two beams of light with identical, but random

polarizations, similar to the source described by Kwiat et al. [Kwiat 1995]. For the

41

receiver, photon detectors 1 and 2 are set to detect only H photons whereas detector 3 is
set to detect only V photons through the use of a polarizing filter and polarizing beam
splitter. Binary data modulates a variable phase retarder, keeping H and V photons intact
under state “I,” and changing H photons into V, and V photons into H under state “0.” As
a result, photon detectors 1 and 2 trigger H photon coincidences in coincidence detector 1
when state “1” is transmitted, and detectors 1 and 3 trigger V photon coincidences in
coincidence detector 2 when state “0” is transmitted. Decisions are made by comparing
the number of coincidences per data bit from the two coincidence detectors. If
coincidence detector 1 count is greater than coincidence detector 2 count then the
receiver records a “1;” if not the receiver records a “0”. As in the conceptual system,
accidental coincidences due to ambient light and un-entangled photons fi'om the laser
source are expected to be much smaller than signal coincidences, affording reliable

commturications under very low SNR.

In comparing Figure 2 and Figure 3 it can be seen that the essential differences from the
on/eff keying experiment conducted by Hong are that a polarization rotator is added to
the transmitter and a third detector is added to the receiver. When the polarization rotator
is off the quantum entangled photon pairs are only detected by detectors 1 and 2. This is
nominally the same as having the laser on with 00K and so the average number of
coincidences detected by coincidence detector 1 are the likewise the same. The bit value
can be defined as a one with the polarization rotator off and so the average number of

coincidences for a one value is

42

<N(1))=[(1—a2>R1 villa—ask. +516”; +11, or. T.- 13-141

When the polarization rotator is ‘on’ the coincidences are then detected with detector 1
and 3 and this is defined as the zero value for a bit. The average number of coincidences
when a zero is being transmitted is simply determined by replacing the detector 2

parameters with detector 3

<N(0))=I(1-a3)R1“Ilia-“0R3 ”3]?th +R1 a3 Ts- [3-15]

The value of a bit is determined at the receiver by comparing the number of coincidences
registered for a 1 to those registered for a 0 during a given bit period. Since a comparison
is being made between coincidence detector 1 and 2 to determine a received bit value, the
coincidences registered by coincidence detector 2 represent noise when a one is being
transmitted and likewise the coincidences registered by coincidence detector 1 are noise
for a zero. The average number of these noise coincidences [<N(I|0)>, <N(0|I)>] is
derived from the expressions for <N(0)> and <N(I)> by accounting for the lack of
entangled photons registered at detector 3 when a one is transmitted and also lack of
entangled photons registered at detector 2 when a zero is transmitted. The expressions

for these noise coincidences when a zero is transmitted is therefore

<N(110))=[(1—a2>R1 “110215th [3-161

and the noise coincidences when a one is transmitted is likewise

43

(No | 1)) = [(1 —a3)R. +r1 Il’3l51Ts- 13-171
The probability for an error when a 1 is transmitted is

P(0|1)=P[N(1)<N(0|1)] [3-18]
and likewise the probability for an error with a zero is

P(l|0)=P[N(0)<N(1|O)]. [3-19]
The probability of error therefore is the probability that a random value from the noise
probability distribution will be equal or larger than a random value from the signal
probability distribution. This probability that a random number from one distribution
firnction is larger, by a value 2, than a random number from another distribution function

can be found by summing all of the probabilities for positive values in the difference

between the two fimctions. This is expressed for the case of a ‘0’ bit error by

P[N(1 | 0) > N(0)] = Z P [N(l | 0) — N(O) = z]. {3.20}

z>0

The difference between Poisson variables has been shown [Haight 1967]

44

Z

P[N(1I 0)- N(0) _____ Z] = e_(<N(l|0)l+<N(0)>) [W]; [Z (2J<N(1 I 0)) <N(0)>) 9

 

[3-21]

where 12() is a modified Bessel function of the first kind. The probability of error for a
‘0’ bit is therefore

2

 

P(IIO) =2” <)+N(110) <N(0)>)[<_z%%)_>]21,(2J(N(1|0))(N(0))). [3-22]

In the same manner the probability of error for the ‘1’ bit is found to be

Z

P(0|1)_ =34; (+N)(Oll) N((0))[<1<V_]S:.ll_;>)_>]E 1,(2J(N(0|1))(N(1))). [3-23]

 

The difference between the summation for the ‘1’ bit error starting at z=0 and the ‘0’ bit
error starting at z=1 comes from an arbitrary decision to assign a tie in coincident counts

as a ‘0’ bit. The BER is again the average of these two error probabilities

P(l l 0)+P(O| 1)

B :
ER 2 . [3-24]

 

The BER for a symmetric system with 10 signal pairs per bit, 6000 noise single photon

counts per bit and a coincidence time of 1 ns, is 5.4x10'5. While the BER is significantly

45

 

lower than the BER OOK system, the signal for this system is 3 dB higher than for the
00K system. If the signal levels are equal then the performance for the two systems is
very similar. With the two-state system however, there is the added irnprevement of
consistently optimal operation no matter what the noise level is. In contrast, with an
OOK system the threshold level has to be dynamically set in order to achieve the optimal

BER because of variations in ambient noise.

46

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ragram 0

Block d'

Figure 3.3

47

3.4 Bit Error Rate for time coincident communications

A time coincident photon communication system is shown as a block diagram in Figure
3.4. In this figure the details of how the beams are put together at the transmitter and
likewise separated at the receiver are left out, to be included in later chapters of course, so
that the basics of the signaling method can be understood. To transmit a one, photon
source 1 and 2, which are separately identifiable by either wavelength, polarization or
both, are pulsed at the same time to send pairs of photons to the receiver. A zero is
likewise transmitted by pulsing sources 3 and 4. The sources will be pulsed several times
during the bit period so that a significant count can be recorded at the receiver. The pairs
are detected by photon detectors 1 and 2 for a ‘one’ and 3 and 4 for a ‘zero’ and,
assuming they arrive at the same time, result in a coincidence detected by the coincidence
detectors. The receiver compares the number of coincidences from coincidence detector

1 to coincidence detector 0 to determine the value of the bit.

The photons from pulsed photon sources are not definitely produced in pairs as they are
with a QB source. They instead can be designed so that both sources produce an average
of one or more photons per pulse. The probability of a pair being detected during a pulse
time TI, is therefore equal to the product of the average counts at detector one and the
probability a second photon will be counted by detector 2. The probability a second
photon will be detected is a function of the quantum efficiency for detector 2, the ratio of

pulses that contain at least one photon captured by detector 2 and also the ratio of the

48

coincidence time to the pulse width. When a one is transmitted the average coincidences

at the receiver due to photons from the sources one and two will therefore be

R “—252.91, [3-25]
‘ R T
P P

where R)D is the pulse rate and T p is the pulse width. This equation is valid for Tp 2 a,
otherwise 5t / T p = I. When a second photon of a pulsed pair is missed another

contributor to coincidences are due to a photon from one of the transmitters being

detected in coincidence with a noise photon expressed by
[(1 —a2) R1 r2 + (1 — 5:1)qu ](5t TS. [3-26]

The last contributor to coincidences is due to accidental coincidences from ambient
photons expressed by r1 r2 (9 T3. Adding all these contributions gives the average number

of coincidences detected by detectors 1 and 2 when a ‘1’ is transmitted

R 6t
<N(I)> = R, a2 E; T T, +[(1—09))?1 r2 +(1 «1)qu +r1r2]6t TS. [3-27]

P P

The noise that can contribute to a ‘1’ being misinterpreted as a zero is only due to

ambient photons being detected by detectors 3 and 4 and is

49

<N(Ol 1)) =r3 r4 5: TS. [3-28]

Because the data is coded in a symmetric fashion the equation for the average numbers of
coincidence when a ‘0’ is transmitted is the same as for a ‘1’ only with photon counter 3

and 4 replacing the l and 2 subscripts

R 6!
<N(0)> = R3 (14 R—4 T— T, +[(1-a4)R3 r4 + (1 —a3) R4r3 + r3r4]5t T, {3.29}

P P

and likewise the equation for noise when a ‘0’ is transmitted is
<N(1|0))=r1 r2 6t TS. [3-30]

The probability for an error when a 1 is transmitted is, as with the symmetric QE two

state coding,
P(0|1)=P[N(1)>N(O|l)] [3-31]
and likewise the probability for an error with a zero is

P(l | 0) = P [N(O) < N0 10)]. [3-32]

50

These error probabilities have the same solution as the previous section with only the
average values for the number of coincidences being different. This leads to a BER

which is an average of these two error probabilities.

It should be noted that the performance of the two coincident channel system with data
encoded by on-off keying can be predicted using several of the previous equations. In the
two channel case <N1> is still calculated using Equation [3-27] and <N0> is calculated
by equation [3-30] with <N0> replacing the <N(1 l0)>.. The error probability equations
for this system are the same as they are for the QE based system so Equations [3-11] and
[3-12] are used to calculate the probability of error. The BER is again the average of

these two error probabilities.

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A time coincident photon communication system made from classical

Figure 3.4

SOIII‘Cfi.

52

3.5. Theory for time coincident photon communication range

In this section the signal intensity as a function of range is considered for optical
communication systems that utilize quantum entangled sets photons for information
encoding. Two systems are examined, one that generates pairs of photons that have an
entangled quantum state and another where the pairs of photons are generated fi'om a pair
of pulsed photon sources. The signal intensity as a function of range is analyzed as a
qualitative first order approximation for these two techniques. For the first time, to this
author’s knowledge, it is shown that pairs of photons that share a quantum state, and
hence have highly correlated momenta, can produce communication systems that have a
high degree of noise immunity and are viable for ranges significantly beyond the
collimated range of the transmitter, which up until now is considered the maximum

range.

Optical communications systems utilizing time coincident pairs, or sets, of photons have
been shown to have great utility in circumstances where the transmitted signal is of
significantly less power than the ambient optical environment [Mandel 1984, Hong 1985,
Jackson 2002, Lekki 2005]. Two cases that illustrate this are for optical communication
where the transmitter is in direct line with the sun and also for a very low power optical

transmitter operating in sunlight.

53

3.5.1 Communication Range for Quantum Entangled source system

Time coincident photon signals can be generated through Spontaneous Parametric Down
Conversion (SPDC) or by simply pulsing two photon sources at the same time [Kwiat
1995, Takeuchi 2001]. In the case of SPDC a photon from a pump beam passing through
an appropriate nonlinear crystal can down convert into two photons that meet the

conservation of energy and momentum criteria

(up = (as + 60,-, [3-33]

kl, = k, + kg, [334]

where mp3,; the frequency and kw; is the wave-vector for the pump, signal and idler

photons. It should be noted that the pump, signal and idler photons have a bandwidth so

that equation 1 can be expressed

(mp0 iAwp) = (0,0 iAwS)+(a),-0 iAwi), [3-35]

where wp0,so,i0 are the average frequencies and .4pr are the bandwidths for the pump,

signal and idler beams. For the purposes of communication, the crystal and pump beam
can be selected so that the down converted photons are collinear or the down converted

beams can be combined using a geometrically symmetric optical system.

54

The second way to generate the set of photons is to pulse a pair of single photon sources
at the same time and use a geometrically symmetric optical system to combine the two
beams into one. Both of these techniques will generate a signal that will be recognizable
at signal power levels significantly below the ambient noise and, at short ranges, have
nearly identical signal to noise ratios. In this second case, the photon pair signal can be
generated using significantly less power than in the first case, because pulsing two micro
sized photon sources is very energy efficient whereas generating SPDC photon pairs is a

very power inefficient non linear process.

At the distance where the signal beam diameter starts to spread to be larger than the
receiver aperture, Rs, however these two communication techniques are not equivalent.
In the first case the entangled photons are highly correlated by momentum, and therefore
the probability that a photon pair will be detected is a conditional probability relationship
between each of the probabilities the receiver will capture each individual photon (Pn) of

the pair

1’. =13an =(I11P2)(P2). 13-361

The relationship between the two momentum entangled position probabilities is shown in
Figure 3.5. In this figure an example is illustrated where a pump beam with a Gaussian
intensity distribution generates two down converted quantum entangled beams that also
have Gaussian distributions which represent the photon positional probability

distributions. The down conversion depicted here is for a nonlinear crystal that has good

55

phase matching, which produces nearly degenerate signal and idler beams with
momentum vectors that have opposite components of equal magnitude that are
perpendicular to the pump beam momentum vector. For clarity of the diagram the
nonlinear crystal that is in the 1: plane is not shown. A single line is shown in the pump
intensity distribution to denote an arbitrary point in x where a pump photon down
converts into a signal —- idler photon pair. In these conditions, this pair of photons will,
have highly correlated angles relative to the momentum of the pump photon they were
created from [Abouraddy 2001, Friberg 1985, Pittman 1995]. The momentum
uncertainty of the pump photon will translate into an uncertainty of the nominal center of
the signal and idler pair, but does not affect the relative momentums of the signal and

idler to each other.

 

within pump beam where
a photon down
converts to signal and
idler photons

\

If

B:

x \\‘~\\ ‘

Arbitrary location “~\‘ ~

p

1'2 ‘r\

Figure 3.5: Drawing of Spontaneous Parametric Down Conversion of a pump beam

(Plane X) with a Gaussian intensity distribution and wave-vector k, into signal and

56

idler beams (Planes X1, X2) with Gaussian photon positional probability

distributions and wave-vectors k, and k}.

The relative momentum of the photon pair dictates the conditional probability of capture
by a receiver and is derived here. The difference in relative momentum between the two
down converted photons is derived from bandwidth of the photons. In degenerate down
conversion the signal and idler beams are the same center frequency, denoted by (00. If
the down converted photons are filtered at the output by a narrow bandpass filter they
will have the same bandwidth as the filter denoted Awbp, which represents the Full Width
Half Maximum (FWHM) bandwidth of the filter. In the following calculations the
derivation of the range at which the combined degenerate signal and idler photons remain
close spatially is developed. In order to develop a bounding equation, two new
frequencies will be introduced, a), and 02, that represent the lower and upper bounds of

the signal and idler frequencies so that

(1)1 = (1)0 —-Aa)bp and (02 = (00 +Acobp. [3-37]

This bandwidth definition for a), and a); is used so that a large percentage of the

transmitted photons have fiequency differences smaller than the a); and a); difference. If

the filter is approximated as Gaussian then the difference of 2 times the F WHM between

a), and a); translates to a bounding of well over 90% of the photons. The angles of the

57

signal and idler photons ,8}; will vary slightly depending upon the range of photon

frequencies, a), and is determined by the following relationship

(0] sin ,81 = (1)2 sin ,62. [3-38]

By using the bounding frequencies the largest angles, and hence the greatest spatial
separation, will be identified. From this relationship, and the illustration of the

recombination of the signal and idler beams shown in Figure 3.6, it is apparent that the
maximum transverse distance d, between the two photons as a function of the

propagation distance, R, is

d, = (sinfll -sin ,62) R. [3-39]

The situation of most interest is to determine the range at which the detection of a second
photon given the detection of one photon is nearly unity. This range, Ru, derived from
Equations [3-38] and [3-39] is approximately the range in which the pair of photons are

separated by less than half the receiver aperture diameter A,.

58

 

0' n
u o
'.,- .-.'.o
........
o
_-
......
.-
u.-
0"
,5
."
0"
u
0".

.
.5
.,
0..
_.
d.
.-
I."
a.
,
0'-
.v
.u
u
_.
.-

v
0‘.
a
n
o
a
n
. o'
......
o a.
o .o
u' ,-
o ,0
.-
a
.0
u
a
'-

.
l"
o

v.
fill" i q ,1

Figure 3.6: The top portion of this figure shows how the down converted photon

 

vectors are linked so that momentum is conserved in down conversion. The bottom
portion illustrates how the geometrically recombined beams will have differing
angles when the magnitude of momentum is not equivalent between the two

photons.

The derivation of Ru begins with a substituting for sin ,6, from Equation [3-38] into
Equation [3-39] and also replacing the photon separation distance d, with the aperture

diameter A, to obtain

A, 4530:1132 —sin 32) R". [340]

59

By solving for Ru the equation becomes

 

__ Arml
“ ‘ (ea-«11032 ’ ‘34”

and recognizing that a), subtracted from a); is equal to 211605,, simplifies the equation to

 

_ Ar ‘01
R” — 2Awbp sin ,62 ° [3.42]

This can also be expressed in terms of wavelength

 

_ Ar 31
R" “ 2M”, sin/3, ' [3‘43]

Note that the different beta subscripts in these two equations come from the inverse
relationship of wavelength and frequency and also the ratio of photon frequencies and

angles in Equation [3-3 8].

The probability P" of a transmitted photon being captured by the receiver in an ideal case,
where there are no losses due to scattering etc. and the quantum efficiency of the detector
is unity, is only a function of beam spreading given a fixed receiver aperture. At a range
where the transmitted beam expands to a diameter larger than the receiver aperture the

photon capture probabilities for each beam, P1, 2, are proportional to 1/R2 [Siegman 1986].

60

If the beams have been symmetrically co-aligned and the distance between the transmitter
and receiver is less than Ru then the conditional probability for a photon pair being
detected is unity (or more exactly greater than 90%), because of the momentum
correlation [F riberg 1985]. This reduces the coincidence probability to PC = P2. Thus the

coincidence probability of quantum entangled, momentum correlated photons is simply

reduced to the probability of a limited aperture capturing a photon in an angularly
diverging spherical wave, which is a probability proportional to 1/R2 for R < R“. This

result, incidentally, is the same proportion for signal intensity as a function of range for

classical optical communication.

3.5.2 Range of time coincident photon communication

The effective range for the second case, where two separate sources are used to generate
the time coincident photons, is much more limited. For two separate photons, with
Gaussian positional probability distributions that have been collinearly combined, there is
no position correlation between one photon generated in one beam and the second photon
of the pair generated in the second beam. Therefore the probability of capturing a photon
pair in the aperture of the receiver is a function of two independent probabilities, one
corresponding to each source. The probability of the individual photons being captured
by the receiver again is proportional to HR2 when the photon probability distribution is
larger than the receiver aperture. The probability of coincident photon capture at large

distances is

61

P. =11 P2 z}; 13-441

which significantly limits the range of this type of transmitter. In Figure 3.7 the manner
in which the quantum entangled source and the two independent sources fall off as a

function of range is summarized.

 

 

 

 

 

 

 

RS Ru
Quantum Entangled A i i g R
Unity E 1/R2 1/R‘
I
Independent - 1 p R
Sources \ \/ /:\ V
Unity I/R‘

Figure 3.7: In this figure the fall off of the two different signaling sources are

compared as a function of range R. Both sources have near unity while the beams
are collimated. After the range at which the beams begin to spread, R3, the two
independent sources fall off at I/R‘ while the entangled photon source falls off at

UK: until the photon pairs begin to separate significantly at the range R...

3.6 Range Comparison

To finther illustrate the difference between these two techniques these ranges can be
calculated for a case where a transmitter and receiver both have 1 meter optical apertures

and are utilizing a wavelength of lSOOnm. In this case the range at which the receiver

62

captures nearly 100 percent, R3, of the transmitted photons can be approximated as the

collimated range [Ag/(7%)] [Siegman 1986]. This range, where there is essentially no

signal loss, is therefore about 212 km. In the case of two independent sources the signal
falls off at UK4 beyond this range and therefore this represents a nominal effective range

for this technique.

In the case of the quantum entangled photons ,6, must be calculated to determine the
range, Ru, at which the probability of photon pair capture will fall off in proportion to
UK". This angle is determined by the type of nonlinear crystal used, the cut angle of the
crystal and the tuning angle of the pump beam relative to the input face of the nonlinear
crystal. This calculation is well covered in the literature so it is not included here

[Dmitriev 1999].

The effect of the collimating transmitting optics, illustrated in Figure 3.8, must also be
accounted for. The angle ,6" is reduced because of the beam diameter magnification.
Also, because the photons separate in the distance between where they are created and
where they enter the collimating optics another parameter is included, represented by do,
that accounts the initial lateral separation of the photon pair. This separation is increased
by the subsequent magnification of the beam diameter by the collimating optics and so

this magnification of do must be included in the calculation.

63

Distance ab M

 

 

 

 

 

 

Distance do /
}" ,
Angle fl" Angle Pn/ M

Figure 3.8: An illustration of the affect that collimating optics has on the photon
pair system. The angles and lateral distances are exaggerated for illustrative

purposes.

These parameters associated with the collimating optics will modify Equation [3-43] in

the following manner

(ff-aroma
Ru = , [3-45]

Albp sing—

 

where M is the magnification of the beam diameter. To perform this calculation the
following parameters are assumed: 1,, is 1500 nm, All. is 1 nm, 6,, is 2 mrad, and M is

200. It should be noted that the wavelength bandwidth is a very significant parameter. If
the bandwidth were smaller the range would be increased but the number of photons

generated would likewise decrease and it should be noted that the system still has a 1/R2

loss to overcome between R, < R < Ru. The selection of 1 nm is a reasonable trade off

64

between the loss of transmitted photons from making the bandwidth smaller and the
probability that a photon counting receiver will be saturated by making the bandwidth
larger. If the nonlinear crystal is fairly close to the beam expansion optics, ~10 cm, then

the maximum separation of the entangled photons do is 0.2 mm. With these parameters
Ru is 69,000 km which gives the momentum correlated photons an effective range that is

325 times that of the photon pair that does not have a momentum correlation.

In summary, the two sources of correlated photons have been discussed. The first source,
generating momentum correlated pairs of photons, has application at significantly greater
ranges than the second source, which consists of two independently pulsed photon
sources. The momentum correlated source is very energy inefficient and so it should
only be considered for longer ranges. It should be noted that the energy efficiency of
these sources has improved significantly in the last 15 years but more improvement is
necessary for a source to be used in this application. The second source can be made to
be energy efficient but has a range effectively limited to the distance where the
transmitted beams diverge to become larger than the receiver’s aperture. The first source
has a range that makes it usable for intra orbit or ground to orbit communications. The
second source should be considered only for ranges of less than 200 to 1000 km,

depending on wavelength.

65

3.7 Summary

In this chapter the supporting mathematics for the contrast gain and the BER has been
developed for the multiple configurations of time coincident photon communications.
The different configurations addressed included a summary of the on/off communications
system developed by Hong and the two state QE photon communications developed as a
part of this dissertation to improve signal to noise ratio. The BER for the electronic
photon pair system has also been described. This system is included because it has very
good potential for very power efficient communication. Also the range for QB photon
source and electronic photon pair source has been developed. Here it has been found that
the effective range of the QB based system can be significantly greater than the electronic
pair system. This is because the momentum correlation of the QE photons can be used to
generate a positional correlation that increases the range at which photon pairs fall off a

rate equivalent to classical optical communications.

66

CHAPTER 4
EXPERIMENTAL SETUP FOR QUANTUM ENTANGLED PHOTON

COMMUNICATION

4.1 Introduction

In this chapter experimental setup for a two-state communications system based on
Quantum Entangled (QE) photons is presented. This system exploits the temporal
coincidence property of quantum-entangled photons to communicate at power levels
several orders of magnitude less than what is currently achievable through classical
means. Quantum entangled photons are studied here because there are multiple benefits,
such as the photons are always generated at very close to the same time, within
picoseconds, and also there are advantages to utilizing entangled photons at longer
ranges. As shown in Chapter 3, a system based on QE photons can have a effective range
that is hundreds of times greater than a system based on coincidentally pulsed sources.
The main disadvantage to utilizing quantum entangled photons is that there is no known
way to generate the photon pairs efficiently. The low efficiency to generate the signal is
a significant drawback but the other advantages coupled with the potential that the

efficiency may be increased, makes this a technique that deserves continued attention.

4.2 Concept

In this experiment pairs of polarization entangled photons are generated and transmitted

to the receiver over two beams of light that are on-off keyed with the data. The receiver

67

detectors can detect individual photon arrivals. The coincidence detector circuit produces
a pulse when a pair of photons triggers detectors 1 and 2 in temporal coincidence. If there
is no signal present, ambient light incident on the detectors will produce what are called

accidental coincidences at a rate

Ra = Rlet [4-1]

where R 1 and R 2 are the detector 1 and detector 2 count rates, in photons/s, and r is the
two—sided coincidence window size in seconds. By making the coincidence window time
smaller, the rate of accidental coincidences from ambient light can be made to be much
smaller than the rate of coincidences due to the arrival of entangled photon pairs, which
are inherently coincident. In general, more than one set of entangled photons will be
transmitted during a bit period. Bit value decisions can be made by comparing the
number of coincidences per data bit duration to a threshold value. This process results in
a relatively high detector output SNR from a very small detector input SNR, making
reliable communications possible where classical detectors would be swamped by the

presence of ambient light.

68

4.3 Experimental Setup

Variable Phase Retarder
(Binary Modulator)
H (H) photons only

  

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L l l l I, Photon , _
polarization- LL\ . Detector 1
. . H Polanzer
Polanzation- entangled . .
Entangled Photon H and V Polanzrng
Pair Source photons Beamsplitter H photons only
1 II I l l l___'
r A Photon .
' ' Detector B ,
V photons only ,1, 1
I I Coincidence
Detectorz Decision
Photon _, Device
Detector C
_ (1 >=< 2)
Figure 4.1: Quantum Entangled Photon Communicator Block Diagram

The block diagram for the advanced version of the quantum communicator is shown in
Figure 4.1. In contrast to the system demonstrated by Hong et al. [Hong 1985], which
encoded information through on/off keying, this system encodes information with two
symmetric entanglement states. Figure 4.1 shows the block diagram of the architecture
of the two-state implementation. The optical source consists of a UV laser-pumped
spontaneous parametric down conversion (SPDC) entangled photon source which
generates two beams of light with identical, but random polarizations. For the receiver,
photon detectors A and B are set to detect only H photons whereas detector C is set to
detect only V photons through the use of a polarizing filter and polarizing beam splitter,
as shown in Figure 4.1. Binary data modulates a variable phase retarder, keeping H and V

photons intact under state “1,” and changing H photons into V, and V photons into H

69

 

under state “0.” As a result, photon detectors A and B trigger H photon coincidences in
coincidence detector 1 when state “1” is transmitted, and detectors A and C trigger V
photon coincidences in coincidence detector 2 when state “0” is transmitted. Decisions
are made by comparing the number of coincidences per data bit from the two coincidence
detectors. If coincidence detector 1 count is greater than coincidence detector 2 count
then the receiver records a “1;” if not the receiver records a “0”. As in the conceptual
system, accidental coincidences due to ambient light and un-entangled photons fiom the
laser source are expected to be much smaller than signal coincidences, affording reliable

communications under very low SNR.

The experimental implementation of the above architecture is schematically shown in
Figure 4.2. Here, the beam from a 351 nm (< 150 mW) single-frequency argon-ion laser
is first spectrally filtered using a UV dispersing prism (not shown), and then passes
through a UV dielectric polarizing beam-splitter cube to produce a pump beam with
better than 1000:] polarization purity. A zero-order quartz half-wave plate sets the
polarization state of the beam to 45 degrees prior to passing through two thin (0.69 mm),
optically contacted, orthogonally-aligned, Type-I beta Barium Borate (BBO) crystals to
generate the SPDC light. Due to the 45 degree orientation of the polarization state of the
pump beam, it then has an equal probability of producing either a HH or VV SPDC
photon pair from either crystal. Thus, the photon pairs emitted from this source have
identical but random (in time) polarizations, constituting an efficient hyper-entangled
photon source as first described by Kwiat et al. [Kwiat 1999]. Similar setups have also

been previously described to use blue diode pumped twin BBO crystals with good

70

success [Dehlinger 2002]. The SPDC photons are emitted in a cone, with entangled
photons arranged diametrically along the cone. By selecting a fraction of the cone
emission using apertures, two beams of hyper—entangled photons are created. Although
the photons are hyper-entangled, only utilize the polarization properties of the photons in
this report. One of the beams then passes through a digital logic controllable liquid
crystal phase modulator set to act as a bi-state half-wave plate (0 or M2) which encodes
information onto the beam via polarization rotation (either H or V). The beam then
passes through a polarizing beam splitter analyzer, and is filtered using a bandpass filter
centered at 702 nm (2 nm F WHM) before being focused with a 75 mm focal length lens
onto the active area of a single-photon counting module (SPCM) consisting of a thermo—
electrically-cooled (TEC), actively quenched, avalanche photodiode (APD) operated in a
Geiger mode (Perkin Elmer SPCM-AQR-13). These detectors have an approximate 60%
quantum efficiency at 700 nm and a 50 ns dead-time between pulses, with < 250 dark
counts/s. In the Detector B & C beam path, similar optical components are used with the
exception of the polarizing beam-splitter analyzer which acts as polarization state sorter.

Detectors B & C use band pass filters centered at 702 nm but with a 5 nm FWHM.

71

I;\lmlu| iting
/Il’h: use Rel; Il"'(ltl

1

Detector ('

\\\

’0’. lleteetor .\

I’ttlztri/inu lit-um
/ Splitters

fiufllllmdilng lens
- and filter optics ‘

 

 

Receiver (Rx) Sedion , 1 _ _ .
(everything In dashed Bit ModulationCodmg
b0!)
Dot. c; 0 '1 State': Coinc. [A.B] Pol. State is
(APD) I H1H2 - LCPR set at Zero
1
I l . '0 State”: Coinc. [A,C] Pol. State is

 

1‘ Dot. 8 H,v2 _ LCPR set atuz
Colnc. (APD) '

l

l I

l 4 l - r n

’ 7 335 Iris tits Mirror
1 [I I

I If I

1

 

 

 

 

 

———..;_;-—-—_———__m———————r

 

 

touro) M2

Data . 1 , n

Polarizing beam
:3le cube

 

 

 

 

 

Figure 4.2: Schematic of Quantum Communication System with a picture of the

experimental setup

72

The photon arrivals at the detectors produce TTL logic signals that are resolved to within
350 ps and are coincidence-gated using discrete CAMAC logic modules to produce a 6.5
ns coincidence window. The coincidence pulses are then counted using two photon
counters controlled by a PC running a custom developed LabView software interface.
The whole apparatus is contained within a light-tight enclosure with black walls. In order
to simulate an ambient light source, an array of individually selectable incandescent light
bulbs (typical 60 W, 120 VAC) was placed above the system inside the enclosure. The
amount of background light is controlled by turning on various combinations of three red
and one white light bulbs, and a variable intensity fiber optic light source aimed at a
white cardboard difiuser placed around the BBQ crystal housing. After careful alignment
of the optical system, typical single photon rates from the BBQ crystal were in the

250,000 counts/sec range for 60 mW of laser pump power.

In order to determine the bit-error rate (BER) performance of the GRC Quantum
Communicator, custom software on National Instruments LabView 7.0 platform was
developed for generating, transmitting and receiving pseudorandom data sequences
(Figure 4.3). The software interfaces with two Dual Channel Gated Photon Counters
connected to coincidence detectors and photon detectors, controls the variable phase
retarder (modulator) and also therefore handles the synchronization of data transmission
and reception. With this set-up, the BER for any data rate with varying laser power and

background light intensity is determined. The software collects statistics and full

73

histogram data from individual photon detectors and coincidence counters, and

determines BER within any desired confidence level and interval.

The data transmission is real-time and the data rate is determined as the reciprocal of the

counting time allocated for each data bit. This is due to the 5 to 20-ms switching time

required by the liquid crystal variable phase retarder used for modulation. In fact, the

major contributor to the detection error in the laboratory setup is this particular

modulator, as will be discussed in the experimental analysis in Chapter 5.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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74

4.4 Summary

In this chapter the system concept for a two-state communication system based on
quantum entangled photons is presented. This system utilizes a pump laser with a
nonlinear crystal that generates quantum entangled photons through spontaneous
parametric down conversion. Information is encoded by rotating the polarization of one
of the entangled photons so that the entangled photons are either both horizontally
polarized for a ‘1’ bit or one is horizontally and the other vertically polarized for a ‘0’ bit.
The receiver consists of three detectors, which are photon counting avalanche
photodiodes, as well as a coincidence circuit to detemiine when photons are detected
within the coincidence time. The advantage of this system is that it always operates at an
optimal bit error rate for given ambient light conditions. This is because in contrast to
OOK, the two-state method does not require a threshold level to determine bit values.
With OOK systems the threshold level has to be dynamically set, based on ambient light
conditions, in order to minimize the bit error rate. A two-state system always operates at
the optimal bit error rate for a given set of conditions because the bit value is determined
by comparing the coincidence counts of one state to the other and assigning a bit value to
whichever state is higher for that bit. This simplifies the receiver operation in an
environment which has dynamic ambient light levels, which includes just about all

natural environments.

75

CHAPTER 5
EXPERIMENTAL RESULTS AND DISCUSSION FOR QUANTUM

ENTANGLED PHOTON COMMUNICATION

5.1 Introduction

The two-state communication system based on Quantum Entangled (QE) photons was
described in Chapter 4. The tests that were conducted on this system and experimental
results are discussed in this chapter. Several tests were conducted and the experimental
data is compared to values that were calculated from the mathematical formulae for this
system in Chapter 3. There were some limitations to the modulator used in this system
as has been described in Chapter 4. These limitations are examined more closely in this
chapter and so some predictions of how the system would perform with an improved

modulator are presented at the end of this chapter.

5.2 Experimental Results

Numerous tests have been conducted with varying data rates, laser intensities,
background light levels, coincidence window sizes, modulator setup times, optical
aperture settings and various other parameters. In Figures 5.1 and 5.2, representative
BER results are plotted for data rates of 10, 30, 100, 300 and 1000 bps at laser source
power levels of 3, 5, 10, 30, 50 and 100 mW and two-sided coincidence window size of

3.5 us in the presence of two extreme background light intensities. Figure 5.1 shows the

76

BER plots in the presence of minimal background light, corresponding to approximately
900 photons/s total detected on the three photon detectors, whereas Figure 5.2 shows
the same plots in the presence of maximum background light, corresponding to

approximately 250,000 photons/s total.

It can be immediately observed from Figures 5.1 and 5.2 that there is very little
difference in BER performance, especially for higher data rates, between the case with
minimal background light intensity and that with maximum background light intensity.
This is due to the relatively small size of the coincidence window that results in
approximately 20 accidental coincidences per second under maximum light and almost
none under minimal light. If the per-bit coincidences are considered, the comparative
detrimental effect of the two different background light intensities becomes relatively
insignificant, especially at higher data rates. The effect of background light can be

diminished even further by the use of smaller coincidence window sizes.

Another interesting observation is the relatively poor performance of the system at
higher data rates. Worse performance at higher data rates is expected since, for any
given laser power level, average coincidences per second will stay fixed but average
coincidences per data bit will decrease with increasing data rate. This closes the gap
between the ‘1’ state and the ‘0’ state in terms of the Poisson mean coincidence rate per
bit, resulting in higher error probabilities. However, the degradation in BER

performance was found to be much worse than what the theory predicted. This can be

77

attributed to the less-than-perfect modulator that was used in the laboratory setup and

this will be further discussed later in this chapter.

 

 

1.E+OO
1.E-01 .
m z ,

   

l

1.E-03 j—a—mObps
E -e—- 300 bps
1+ 1009 DPS. _.

 

 

 

 

 

1 .E-04 .
3 5 1 0 30 5O 1 00

Laser Power, mW

Figure 5.1: BER with minimal background light

 

 

   
 

 

 

 

 

 

 

1.E+00 1
1.E-O1
35 1.15-024
m 1-~~-- ,
1-4E>‘-1Obps .
1+30bps
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g—8-300bps
1—->_<—1000bpsfi
1.E-04 . - . .
3 5 1O 30 50 100

Laser Power, mW

Figure 5.2: BER with maximum background light

78

The liquid crystal variable phase retarder used for the modulator requires a finite setup
time, on the order of 5 to 20 ms, in order to completely switch states. As explained
earlier, this was accounted for in the BER test procedure. However, even after
significantly increasing the setup time, it was found that the phase retarder frequently
failed to completely switch states; more so at higher data rates. Table 5.1 displays the
average coincidence detector counts per second accumulated during the BER tests for
various data rates at a 30-mW laser source power in the presence of minimal
background light. It can be observed from this table that the ratio of transmitted state to
opposite state (contrast ratio) coincidence counts drops fiom about six at 10 bps to
about one or two at 1000 bps, while the total counts stay reasonably fixed for each
detector. These ratios would stay virtually fixed for a perfect modulator. Obviously, the
dropping ratios significantly affect the BER performance by seveme degrading the
separation between the two states. It is also observed from Table 1 that at higher data
rates, the modulator somewhat prefers the “0” state, as evidenced by the slight increase
in ratio for the AC coincidence detector counts at 300 bps to 1000 bps. Table 5.2
displays the detector counts per second under steady state for various laser power levels
in the presence of minimal background light. This data shows that in the steady state
condition, the contrast ratios (ACzAB for the ‘0’ state and ABzAC for the ‘1’ state), are
very good, generally ranging from 24 to 68. This demonstrates that by using an
improved polarization modulator, a significantly improved BER performance would be

expected.

79

Table 5.1: Test average coincidence detector counts per second at 30 mW laser

power in the presence of minimal background light

 

 

 

 

 

 

 

 

 

 

D AB counts per second AC counts per second
ata
Rate, AB 1:0 0:1
bps AB | “0” AB | ”1” Total Contrast AC | “0” AC | “1” AC Total Contrast
Ratio Ratio
10 99 612 711 6.2 607 113 720 5.4
30 180 464 624 2.6 464 188 652 2.5
100 257 456 712 1.8 433 268 701 1.6
300 282 423 705 1.5 372 234 606 1.6
1000 350 390 740 1.1 500 270 770 1.9

 

 

 

 

 

 

 

 

Another source of inefficiency in the laboratory setup is the generation of coincident
photons through the use of parametric down conversion. Because of this inherent
disadvantage, a relatively large laser source power was used in order to obtain a very
small number of coincident photons per second. The actual received energy may be

calculated by using the formula

E =__l__N 5-1
.- 1 1 1

where h is Planck’s constant, c is the speed of light, A is the wavelength of the light
source (7.02><10—ll m), and N is the photon count. In order to gain a better
understanding of the actual energy levels involved, the plots in Figure 5.1 were
recalculated as a function of received energy per bit using the data from Table 5.2,
where the received energy per bit is determined by the average total number of photons
received per bit on detectors A, B and C. Figure 5.3 shows the BER plots as a function

of received energy (Joules) per bit in the presence of minimal background light. It is

80

observed from Figure 5.3 that reliable communication is possible, with the addition of
error correction coding when necessary, at remarkably low received energy levels on
the order of a picoJoule per bit. It can also be seen from this figure that, when
normalized with respect to received energy per bit, performance differences among
different data rates become insignificant, especially considering the possible use of an

improved phase modulator.

 

 

 

 

 

 

 

 

Table 5.2: Steady-state detector counts per second in the presence of minimal
background light
:35" State “0” counts per second State “1” counts per second
OWCI'
(mW) A B G AB AC A B c AB Ac
3 1530 880 1230 l 24 2140 910 2150 24 0
5 4300 2620 2950 2 100 5250 2530 3000 110 1
10 9500 6000 6200 5 220 11000 5900 6200 260 l
30 31000 18100 15000 23 740 32500 17900 17200 760 9
50 44000 28000 24400 40 1250 40000 28000 27800 1375 20
100 94000 57200 55100 85 2540 97400 56000 59500 2750 46

 

 

 

 

 

 

 

 

 

 

 

 

 

In order to visualize the effect of background light, the plot in Figure 5.2 is recalculated
as a function of optical signal-to-noise ratio (SNR), where the data from Table 5.2 is
used for the average total number of photons received per second on detectors A, B and
C, and a background average total count of 250,000 photons/s, corresponding to the
maximum light setting, is used. The sum of the singles from Table 5.2 is proportional to
the signal power and the background average total count is proportional to the noise
power. Figure 5.4(A) shows the BER plots as a function of this SNR in the presence of
It can be observed from Figure 5.4(A) that reliable

maximum background light.

communication is possible at very low optical signal-to-noise ratio levels.

81

The singles in Table 5.2 are in effect mostly noise. In the calculation for Figure 5.4(A)
all of the singles registered fiom Table 5.2 have been counted as signal because they are
generated by the signaling device. However, most of these single photons are not
detected in pairs, and therefore appear as noise to the receiver, even though they are
generated by the signaling device. These photons are not detected in pairs because, due
to slight misalignment, the three detectors are seeing slightly different spatial portions
of the quantum entangled light. To illustrate how low the signal level is, the ratio of
coincident photons to single photons have been calculated, where the single photons are
those that are from both the background light and the uncorrelated singles from the
quantum entangled light. In the instance where the pump laser is at 30 mW this
correlates to an SNR of -5.8 dB in Figure 5.4(A). The coincident photon count to single
photon count ratio for this same instance is -26.6 dB. If the system were designed so
that photon pairs generated by the transmitter were reliably detected by the receiver
then the SNR for Figure 5.4(A) would be shifted lower by 20.8 dB. Figure 5.4(B)
shows the BER for the system with maximum background light with the SNR
calculated from the coincident photon count to single photon count ratio. It is believed
that this type of reliable transmission is possible, and so this result dramatically
illustrates that reliable communication is possible even when the transmitted signal

power is significantly less than the noise power.

82

 

1 .E+OO

1.5-01 —— e. a -

  
 

1.E-02 1 +1 17 1339

BER

 

 

' -o- 30 bps
—er- 100 bps 1

“5'03 —-9— 300 bps _ If _
51:1 999 15321

1.E-04 1

 

1E-14 1E-13 1E-12 1E-11 1E-10
Received Energy Per Bit, J

Figure 5.3: BER with minimal background light

 

 

    
   

     
 

 

 

 

 

 

 

1.E+00 1.E+00
1.E-01 - ~ A- - 1.E-01 1 -7 , , - __ _ -,
a:
E 1.E-02 _ ,, ,, -7 LLI 1.E-02 1- -—~— ~ - ___. . . ”2
CD CD
+105”, +10 bps l
1
i—o—3O bps A+30 bps ‘
1 z..- 300 bps l .0300 bps
l+1000bps1 1+1Qooopsl
1.1504 ‘ 1 11504
-20 -10 o 40 -30 -2o
SNR, dB SNR, dB
(A) (3)

Figure 5.4: (A) BER with maximum background light. (B) BER with maximum

background light and SNR calculated as ratio of coincidences to single photons.

83

5.3 Discussion

The limitations in switching of the liquid crystal phase retarder have made the data
obtained from this experiment disappointing in the higher bit rates. It can however be
used to compare the predicted results from the two state bit error rate equations derived
in Chapter 3. The equations derived in Chapter 3 [3-14, 15, 16, 17, 22, 23, and 24] are

repeated here in the same order:

<N(I)>=[(1—a2)Rt +n1[(1—a1)R2 +12161T1+R1a2 T. 15-21
<N(0)> = [(1— a3)Rt + n 1111 —a1)R3 + r316th +0 “3 T. 15-31
(N(110))=l(1-02)Rt“111015th 1541
(N1011)>=l(1-a3)R1 +r11101511. 15-51

2

p(1 I 0) = i e‘(<N(1|0)>+<N(°)>) [W]; 1, (2J(N(1|0))(N(0))) [5-6]
2:1

 

84

Z

P(0|1)_ Ze- (M1011) WIDTW]; 1,(2J(N(0|1))(N(1))) [5-7]

 

BER: P(l|0)+P(0|1)

 

[5-8]

Equations [5-2, 3, 4, 5] give the coincidence rates registered by the receiver as a
function of bit period, transmitted entangled photons (signal), noise photons and
detector coincidence window. It would have been ideal to calculate the BER as a
function of these parameters but it was not possible to measure both the coincident
photons and the individual channels concurrently because the equipment to record five
channels (2 for coincidence counting and 3 for the photon counting detectors) of photon
counting signals was not possessed at the time. Equations [5-2] to [5-5] have been
verified by Hong et al. [Hong 1985] so it is primarily necessary to verify the Equations

[5—6] and [5-7] in order to have confidence that Bit Error Rate is correctly calculated.

To verify these two equations the BER was calculated using these equations from the
coincidence counts measured in this experiment. The 30 bps data rate was used to do
this calculation because, as can be seen in Figure 5.4, this data rate does capture a good
range of bit error rates for very low signal to noise ratios. At low SNR the BER is very
high and at about -5 dB SNR the BER drops to a reasonable level for data transfer. The
data used for calculating this BER is shown in Table 5.3. Mathcad software was used to

make these calculations and the worksheet is shown in Appendix A.

85

Table 5.3:

Average Coincidence counts per hit in the presence of maximum

background light at a data rate of 30 bps

 

 

 

 

 

 

 

 

 

 

 

 

 

SNR State “0” counts per second State “1” counts per second
(113) AB or <N(I|0)> AC or <N(0)> AB or <N(I)> AC or <N(0|1)>
-l7.1 0.8 1.2 1.1 1.0
-12.7 1.5 3.1 2.5 1.4
-9.7 2.6 5.6 5.5 2.8
-4.8 7.0 16.3 16.3 7.2
-2.7 1 1.9 27.8 28.3 12.0
0.5 23.3 54.0 55.7 23.7

 

In Figure 5.5 the calculated BER is obtained by using Equations [5-6, 7, 8] and the

measured coincidence numbers in Table 5.3.

It has been compared to the directly

measured BER and the agreement is excellent. The single point in positive SNR do not

appear to be close but in this case there was one measured error is 1002 bits collected so

the variance is larger than the difference between the two values.

precision of the measurement the overall agreement is excellent.

86

Based on the

 

 

 

 

 

 

0.1
pi“ 0.01 —o—- Measured
CD + Calculated
0.001
0.0001
-20 -15 -10 -5 0

SNR

Figure 5.5: The calculated BER in this figure is obtained by using equations
measured coincidence numbers is compared here to the directly measured BER as

a function of SNR for 30 bps data rate.

5.4 Discussion of potential given high contrast modulator

The previous discussion and analysis confirm that he BER can be reliably calculated
from by knowing the number of coincidences detected for the ‘0’ and ‘1’ coincidence
detector. Though this system did not achieve the contrast ratio necessary to confirm
that a low BER can be maintained even when SNR is negative, in terms of decibels, it
did confirm the equations that predict BER and so some estimate can be made of

potential system performance given a higher contrast system.

87

The performance of the system given a higher contrast modulator can be estimated by
using the data Table 5.3 and adjusting the error coincidences to approximate a
modulator that has a contrast ratio as good as the steady state contrast ratio that was
achieved with the modulator used in the experiment. So the error coincidences in Table

5.3 were adjusted according to the following formulae

 

 

(1)/(110)): 21(23)>)+(N0ise) [5-9]
<N(0|1)>= 21:33)) + <Noise> [5-10]

where the <N(0)>, <N(I)> and <Noise> values are all what was measured in the
experiment and CR,,(0), CR,,(1) are the lowest steady state contrast ratios measured for

the ‘0’ and ‘1’ states obtained from Table 2. These calculated values are summarized in

Table 5.4.

The values in Table 5.4 and Equations [5-6, 7, 8] have been used to calculate the
potential BER if the modulator maintained a high contrast ratio when switched. These
bit error rates are plotted in Figure 5.6 as a function of signal to noise ratio. The
measured BER is also plotted in this Figure. From this plot it can be seen that the BER
could have been low (less than 102) even when the SNR is as low as -7 dB. The
calculated BER values are not much different for SNR less the -9 dB because the signal

is low enough that the lack of signal is starting to drive the error rate. Even without

88

noise there is a significant chance to receive no coincidences (signal) for a bit when the

average number of coincidences is less than 5.6 per bit.

Table 5.4: Average Coincidence counts per hit in the presence of maximum

background light, with a data rate of 30 bps and modified error coincidence rates

to represent the operation of a better modulator

 

 

 

 

 

 

 

 

 

State “0” counts per second State “1” counts per second
SNR dB
( ) AB or <N(I|0)> AC or <N(0)> AB or <N(I)> AC or <N(011)>
-17.1 0.62 1.2 1.1 0.8
-12.7 0.67 3.1 2.5 0.52
-9.7 0.9 5.6 5.5 0.91
-4.8 1.52 16.3 16.3 1.21
-2.7 2.53 27.8 28.3 1.94
0.5 4.66 54.0 55.7 3.33

 

 

 

 

 

 

89

 

 

 

0.01
0.0001 ~
+ Measured
8
1 E'08 + Calculated for
high contrast
1E'10 modulator
1 E-12
1 E-14

 

 

Figure 5.6: This graph illustrates the potential of the communication system if the
modulator had higher contrast. The calculated series is generated by modifying
the off state data by reducing it to a contrast level equal to the steady state

contrast.

5.5 Conclusion

Through the use of quantum-entangled photons, it has been shown that reliable
communication is possible at remarkably low received energy levels on the order of one
picoJoule per bit in the presence of an overwhelming background light equal to over

100 times the signal, resulting in exceptionally low optical signal-to-noise ratios. While

90

the experimental setup suffers from the inherent inefficiency of current quantum-
entangled photon generation processes, and the use of an imperfect liquid crystal phase

retarder as the modulator, it successfirlly demonstrates the feasibility of the concept.

The equations developed in Chapter 3 to describe the bit error rate of the two state
communication system have been checked against the data gathered in this experiment.
It was shown that the BER as predicted by those equations agrees very well with the
BER measured in this experiment. A further calculation to illustrate the potential of the
system developed here with a more capable polarization modulator has shown that the

system could have sustained low BER communication to a SNR of up to -7dB.

The demonstration of the feasibility of the two state quantum entangled photon
communication system and the confirmation of the two-state BER equations are the
important steps that have been taken in this chapter. The two-state system makes
synchronization between the transmitter and receiver much easier, as it allows bipolar
forms of encoding such as Differential Manchester signaling. The confirmation of the
BER equations is important because it is a significant building block for the further
developments in the time coincident system. It is a step beyond the formalism
developed for on / off keying by Hong, Friberg and Mandel [Hong 1985] and it is a step
in the direction of the time coincident system which is described in the next two

chapters.

91

CHAPTER 6
EXPERIMENTAL SETUP FOR COINCIDENT

COMMUNICATIONS EXPERIMENT

6.1 Introduction

In this chapter the concept and the experimental design of the time coincident photon
communication system, which is based on pulsing sets of sources simultaneously, is
described along with a series of experiments that have been conducted to examine the
efficacy of the system. The primary experiment to confirm the predicted fimctionality
of the communications system was conducted over a significant range with ambient
light levels that are in the range of a typical scene on a moderately sunny day. Ideally it
would have been very interesting to fabricate a source that would have nearly ideal
characteristics utilizing a quantum well source but this was impractical given the time
and resources allotted. The experimental system was instead built using mainly
components that are off the shelf. The off the shelf components were chosen so that
they in theory could be incorporated into a monolithic micro transmitter. This means
the control / driving electronics, optical sources and beam forming lens all can be
incorporated into a device the fits the NNI grand challenge, which is to have an overall
dimensional scale from microns to centimeters while incorporating nanometer scale
components. The receiver is made from macro components and is not necessarily
adaptable to fit the NNI scheme. Since the concept system is for micro robots working
in cooperation with macro scale robots there is not a need for the receiver components

to be potentially “shrinkable”.

92

In the first part of this chapter the concept and experimental design for the transmitter
made from time coincident pulsed sources is introduced. The photon counting reciever
is subsequently covered. The chapter is concluded with a description of the
experimental plan as well as the overall setup of the experiments. This leads into

Chapter 7 which will cover the results and a discussion of these experiments.

6.2 Transmitter

6.2.] Optical Transmitter Concept

The goal of the communication system described in this chapter is to emulate the
communication system based on quantum entangled photons with a much more energy
efficient transmitter. The system concept is based on multiple energy efficient sources
that are fired simultaneously. Like quantum entangled photons, these sources have the
same wavelength and polarization correlations essential for communication in the
presence of significant background light. The sources either have different
wavelengths, or sources of the same wavelength have orthogonal polarizations, and the
sources emit bursts of photons with these wavelength and polarization correlations
simultaneously. It should be noted that the photon pairs fi'om the multiple sources do
not have entangled quantum states. They only have the same correlations that make the
photon pairs readily identifiable to a reciever that detects pairs of quantum entangled
photons in the presence of ambient noise, such as the reciever that was described in

Chapter 4.

93

This transmitter is unique in that it is the only known transmitter utilizing the time
coincident photon information coding scheme in conjunction with traditional optical
sources, such as LEDs and Laser Diodes. This system has the unique advantage of not
requiring the use of a non-linear crystal and high power laser source for the generation

of single-photon pairs for the purposes of time-coincident communications.

The advantage of this system is that it will enable the transmission of information at
very low power levels and with a very small device. The scheme fits very nicely with
very small, low threshold sources that are very energy efficient but also lirnite in total
power. The calculated power levels are lower than any known transmitter. Another
advantage of this system is that everything can be fabricated on a single chip using
conventional microchip fabrication technologies with the only exception being the beam
forming optics. This would make the system very compact and also potentially low-

cost if manufactured in mass quantities.

The pulsed optical sources that would produce pairs or sets of photons at nearly the
same time have stringent but readily obtainable requirements. The optical sources
should have a narrow spectral linewidth, with a Full Width Half Maximmn (F WHM) in
terms of wavelength less than 2nm, and also have an optical lifetime for the radiative
state that is less than 1 as. The narrow linewidth is a requirement so that the receiver
spectral filter can be narrow enough so that the photon counting detector is not
saturated. A shorter radiative lifetime will lead to shorter coincidence time at the

receiver and therefore improved noise immunity. The coincidence time would also

94

nominally dictate the maximum data transmission rate if there were no dead-time
between received pulses of the single-photon detectors. However current detectors
made from high quantum efficiency Avalanche Photodiodes are actively quenched,
which means they have a dead-time of 40 us which limits the maximum data rate to 25

MHz.

A block diagram of the driver for the four channel system is shown in Figure 6.1. In
this diagram the manner in which the logic signals are converted to an electrical pulse
for exciting the diode laser such that it emits energy efficient photon bursts is presented.
In the experimental implementation the driver electronics will transmit data bits at a
frequency of 100 kHz, except where the fi'equency has been purposely varied. There
will be 10 pulses per bit emitted (to get 10 photon pairs per bit) that will have between
10-20 ns pulse duration. This pulse duration is the lower limit of the available laser

diodes.

95

Optical Single-photon
Drivers Optical Emitters

3—»>—£ +—->

Polarization

 

V V

 

 

 

l

 

 

Osc. >ll>

>0 29——»>—»O (___)...

Figure 6.1: Schematic of the logic diagram for the multi-wavelength time-coincident

 

 

 

 

 

 

V

 

 

 

 

0
iv 4 vv

 

 

 

V

 

 

optical transmitter. The oscillator provides a steady stream of alternating low (0) and
high (1) digital clock pulses at say, 1 GHz. The data stream is sent to the appropriate
AND gate which then determines which optical emitter to fire. The AND gate allows the
clock signal to control the pulse width of each source. The clock period is much smaller
than the data bit period so that multiple pulses are sent during one data bit. The logic
states are shown in the truth table in Table l. The optical emitters can be, but are not
limited to light emitting diodes (LED) or diode lasers, quantum-dots, etc. Depending on
the emitter that is fired, each has a certain wavelength or spectral channel and a
polarization associated with it. In this way, both wavelength and polarization states are

used to effectively increase the SNR for single-photon data transmissions.

 

 

 

 

 

Oscillator (Clock) Data Input Optical Output (A, polarization)
0 any 0
1 0 711 Vertical, A2 Vertical
1 1 A1 Horizontal, 2.2 Horizontal

 

 

 

Table 6.1: Truth table or logic chart for schematic shown in Fig. 6.1. Light

emitters fire in pairs with complementary wavelengths and identical polarizations.

96

 

The modulated signal drives optical sources of different wavelengths or polarizations.
These sources (which may be LEDs, Laser Diodes, Quantum Wells or Quantum Dots)
can be driven with low amplitude and very short pulses of electrical energy so that a
pulse of photons is generated. The photons fi'om all four optical emitters are sent
coaxially along the same optical path to a receiver whereby they are decoded according
to wavelength and polarization state. Various optical configurations can be used to
spatially superimpose the signals from all emitters along a common optical path,
including dichroic beam splitters, polarizing beam splitters, or a combination of a

diffractive element such as a prism or grating and polarizers.

This method of communicating using correlated photons provides many possibilities for
the assignment of physical parameters to bit values. In Table 6.1 a truth table defining
the way in which the information bits are encoded. According to Table 6.1, when the
receiver counts photons from wavelengths Al and 71.2 in temporal coincidence that have
identical and vertical polarizations then information bit is a "0"; when the receiver
counts photons that are in horizontal polarization states, then the information bit is a
" l ". Of course, other polarization coding schemes can be employed to achieve the same
effect, such as orthogonal polarizations for a “0” and identical polarizations for a “1”

and vice versa.

Note that by use of additional logic gates, a system can be devised to send up to 2 bits
(22) of data to yield a possible of 4 combinations versus the 2 possible combinations.

The truth table for this bit coding is shown in Table 6.2. For the communication

97

schemes shown Table 6.1 and Table 6.2, only two photons per pulse, one at each
wavelength, have to be captured by the reciever. Since only two photons have to make
it to the reciever, this implies that very few photons must be transmitted from the
transmitter. The actual number of photons transmitted depends on the reciever size and

quantum efficiency, the distance of the transmission and the directional capability of the

 

 

 

 

 

 

 

transmitter.
Oscillator (Clock) Data Input Optical Output (A, polarization)
0 any 0
1 0, 0 A1 Vertical, A; Horizontal
1 1, 0 1.] Horizontal, 1.2 Vertical
1 0, l M Vertical, 712 Vertical
1 1, l A] Horizontal, 3.2 Horizontal

 

 

 

Table 6.2: Truth table or logic chart for an alternate embodiment (not shown) but
based on Figure 6.1 where up to 2-bits (4 states) of information can be sent at a

time through the use of perpendicular polarization states of 2.1 and 3.2.

Alternate configurations are shown in Figures 6.2 and 6.3. Figure 6.2 shows the
schematic of a transmitter that utilizes three optical channels with the data being
encoded on one wavelength while a timing pulse is sent on another spectral channel.

The logic chart or truth table for Figure 6.2 is shown in Table 6.3.

98

 

Optical Single-photon
Drivers Optical Emitters

>0 LJ
>_

 

V

 

 

V

 

 

 

V

 

 

 

 

 

V V

 

 

 

m1

Figure 6.2: This is a schematic of the three channel configuration. Here, the

 

 

V

 

emitter that is of wavelength 1 provides synchronization and a reference
polarization. This emitter has a fixed wavelength and polarization. The second set
of emitters is of a different wavelength than the sync emitter. The data is encoded
by the relative polarization of the emitter that is fired from the second wavelength
when compared to the reference emitter polarization. When the emitter of
wavelength 2 that is fired is the same polarization as the wavelength 1 emitter then
this encodes a zero bit. When the emitter of wavelength 2 that is fired has a

different polarization than the wavelength 1 emitter then this encodes a one bit.

 

 

 

 

 

Oscillator (Clock) Data Input Optical Output (A,
polarization)
0 any 0
1 0 9.] Vertical, 71.2 Vertical
1 1 3.1 Vertical, 2.2 Horizontal

 

 

 

Table 6.3: Truth table or logic chart for schematic shown in Figure 6.2. Light

emitters fire in pairs with complementary wavelengths and polarizations.

99

 

Optical Single-photon

Drivers Optical Emitters
l LiD-i—rD—rG *9

Output
Polarization
States

 

 

 

 

 

Figure 6.3: Schematic of the two channel configuration. In this case the data is
encoded using on / off keying. A ‘l’ is communicated by transmitting the
complimentary photons of the same wavelength and orthogonal polarizations. A
‘0’ is communicated by the lack of signal. This scheme requires the receiver to
compare the number of photon pairs received to a threshold to determine the bit

value.

6.2.2. Experimental Transmitter

The experimental version of the transmitter was built using commercial off the shelf
components. The components used were chosen with an emphasis on their potential to
eventually be incorporated into a very energy efficient monolithic device that is
appropriate for a miniature robot. For example laser diodes have been used along with
collimating optics limited to an aperture diameter of 1 cm. The lasers and optical
components of the transmitter are shown in Figure 6.4. There were 2 laser diode

sources at 669 nm and 2 at 673 nm. They were arranged so that one laser of each

100

wavelength was polarized vertically and the other was polarized horizontally. The
lasers were pulsed 10 times per bit and the pulse duration of the laser pulses was
approximately 10 to 20ns. This pulse duration is the lower limit of the commercially

available diodes and was slightly different for each individual laser.

Laser

/ llltltlt‘S

-1-1,

' liennr

_‘W

1 (ornlrining
/ ()pties

()utput
\llenuntion
I’illt‘l‘

 

Figure 6.4: Front view of the experimental transmitter. The four laser diodes are
utilized in the multiple configurations described previously. The output
attenuation filter is set so that an average of one photon per pulse is detected at the

receiver.

The electronic components of the transmitter are shown in Figure 6.5. The data source
is custom built specifically for these experiments. It has the option of using an internal
or external clock. The data bit period is programmable with dip switches and can be

varied from 1 to 256 microseconds. The data can either be alternating ones and zeros or

101

can be a preprograrnmed text message. The output of the data source gates a Berkeley
Nucleonics BNC 555 pulse generator. This pulse generator has four outputs that can
produce pulses of varying amplitude, duration and period. The outputs from the BNC

555 are used to trigger the laser diodes.

 

Figure 6.5: The electronic components of the transmitter consist of a custom built

data source (lower right) and a Berkeley Nucleonics BNC 555 pulse generator.

102

6.3 Receiver

A complimentary receiver for the transmitter described previously has been developed.
The receiver recognizes when photons are received within the coincidence window and
depending upon the wavelength and polarization of the coincident photons, the receiver
turns these coincident photon events into bit values. The optical components of the
receiver are functionally diagramed in Figure 6.6 and the receiver built for the
experiments is shown in Figure 6.7. The receiver has a 50.8 mm diameter telescope to
collect the photons and also collimate the received beam for the rest of the optical
system. Immediately after the collection optics is a bandpass optical filter, denoted 2.1,

that passes a 2 nm bandwidth centered at 669 nm. The filter reflects the 673 nm
photons which are guided to another 2 nm bandpass filter, denoted ’12, centered at 673

nm. With this set of filters the photons of wavelength 1 go to one set of photon
counting detectors and the photons of wavelength 2 to a separate set of photon
detectors. The photon counting detectors are Perkin Elmer Single Photon Counting
Modules that have about 70% quantum efficiency for 670 nm photons. These detectors
are actively quenched Geiger mode Avalanche Photodiodes which have built in cooling
and signal conditioning. After the filter, the photons of wavelength 1 are separated by a
Polarization Beam Splitter (PBS) into horizontal and vertical polarizations and then
detected by photon counters. The photons of wavelength 2 are likewise separated by

polarization and detected.

103

Transmitter Receiver

 

 

 

 

 

 

 

 

 

- . - \ Photon
Drrver ‘—-—> ' “$19“ Counter
>.

Photon
Counter

] Comcrdence (__

9 Electronics

A
A ‘ Photon
“" Counter

Photon
Counter

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 6.6: In this schematic the transmitter is shown working in conjunction with
a receiver. The internal optics of the receiver that sorts the received photons starts
with a telescopic front optic that collects and collimates the received photons.
After this there are two filters, one that passes photons in band 1 while reflecting
all other wavelength photons and a second that passes photons in band 2. Behind
the two filters are Polarization Beam Splitters (PBS) that have extinction ratios of
1000:] which they sort horizontally polarized photons from vertically polarized
photons. The front end optics therefore sorts the beams so that the photon

counters only see photons of a particular wavelength and polarization.

104

Single
l’lmton
('uunting
\ltrtlules
( \l’l)\)

Sorting
l-‘ilters

Reeeh in:

'l‘eleseupe

 

Figure 6.7 : Picture of the optical components of the receiver that is diagrammed

in Figure 6.6.

The coincidence electronics, pictured in Figure 6.8, determine which photon counters
fire at the same time and thereby decode the data in bits of ones and zeros. The
coincidence electronics have been built using a Field Programmable Gate Array
operating at 400 MHz and the coincidence time window is programmable between 3 ns
and 11.75 ns. When this circuit detects a coincidence a pulse is output to a logic

analyzer which logs the time the pulse occurred.

105

 

Figure 6.8: Custom built coincidence detector takes pulse outputs from two pairs
of photon counting detectors and determines if a pair of detectors fire within the
programmable coincidence time window. When a coincidence is detected the

circuit outputs a pulse to a logic analyzer which logs the time the pulse occurred.

The selection of the coincidence time window is influenced by the laser pulse duration.
It cannot be too small compared to the pulse duration or a photon fiom one source early
in the pulse will not be time coincident with another photon from its paired source late
in the pulse. The number of coincidences, rc, due to noise photons is directly
proportional to the coincidence time window, 5!, and is approximately equal to [Mandel

1965]

r, z Hr, 5H“l T [6-1]

n

where n is the number of channels used for coincidences, r, is the photon count for

channel n, and T is the bit period. The nominal coincidence window for the

106

experiments was 11.75 ns. Additional noise reduction would have been possible if a
coincidence time of 1 ns were used but this would have resulted in significant signal

loss because the laser pulses were of 10-20 ns duration.

6.4 Experimental Plan

As previously mentioned the experimental tests of the system were conducted in both
the laboratory and also in a hallway where longer ranged communication could be
tested. For each experiment run the quality of the transmitted information was
determined by measuring the Bit Error Rate for a transmitted message. The system
parameters that were varied during the experiment were the receiver aperture diameter,
transmitter optical pulse power, ambient light conditions, data rate and coincidence time
window. By varying the receiver aperture it is possible to simulate both how the system
will perform for different sized transmitter apertures or different ranges with a fixed
aperture. Varying the optical pulse power and ambient light are straightforward
measurements of the signal quality as a function of signal power and noise. The
experiment varying the coincidence time window will effect both the signal and noise
coincidences. The signal coincidences are reduced as the coincidence time gets smaller
than the pulse duration of the sources. Likewise the coincidences due to noise are
proportional to the coindidence time. Signal synchronization could be accomplished
with a number of different preamble signals, such as a clock, sync word or a unique

signal such as firing all sources at the same time but for these experiments a simple data

107

pattern of alternating ‘1’s and ‘0’s was used to make the synchronization

straightforward during the data analysis.

Summary of Performed tests

1.

Identify how the system works with l, 2, 3 and 4 channels with varying
SNRs. The signal level was fixed and the noise level was varied. This
tests the affect of the noise level on system performance. This
experiment was conducted in the hallway.

The signal intensity was varied with 1, 2, 3 and 4 channels while leaving
the noise level fixed. This tested how signal intensity affects system
performance. This experiment was conducted in the hallway.

The coincidence time window was varied to 3 different settings with 2,
3, and 4 channels with a fixed signal level, noise level. This experiment
tested the affect of coincidence time on system performance. This
experiment was conducted in the hallway.

The bit rate was varied between 50 kHz and 1 kHz while keeping
average signal power per bit constant. This experiment examined what
affect the bit period has on system performance. This experiment was
conducted in the laboratory.

Vary the aperture of the receiver while keeping the signal, noise and
coincidence window constant. This experiment emulates the
transmission over multiple distances. This experiment was conducted in

the hallway.

108

6.5 Experimental Setup and Experiment Operation

The experimental setup diagram is shown in Figure 6.9. The test was conducted in a
hallway, shown in Figure 6.10, with the transmitter and receiver located next to one
another, shown in Figure 6.11. This allowed for the longest transmission distance and
also made aligning the two easier. A white paper screen, with a small hole in it to allow
for the transmitted beam to pass through, was placed in front of the transmitter. This
screen provided a uniform reflector so that the background light seen by the receiver
could be controlled by illuminating it with different brightness lights. In order to
achieve the highest ambient light levels a fiber optic light source was located next to the
beam path and directed towards the receiver. The screen and light sources are shown in

Figure 6.12.

The highest background light levels were similar to outdoors on a sunny day while the
lowest were similar to outdoors with heavy clouds. In this experiment the signal power
for all configurations was attenuated by neutral density filters so that for each channel
approximately 1 photon per pulse was detected at the receiver. When one system

parameter was varied all others were kept constant.

Multiple experiment configurations were tested. The baseline configuration was just a
single channel (no coincidence) that was used for traditional on/off keyed photon
counting communication. In the second configuration photons were transmitted in time

coincidence over 2 channels. A clock signal was transmitted and the bit values were

109

encoded by on/off keying. The third configuration used 3 channels and fourth used 4
channels. In this configuration the data was keyed as shown in Table 6.3 and 6.1
respectively. In general the transmitted power in the hallway experiments for the single
channel case was 180 pW, the 2 channel case was 360 pW, the three channel case 580

pW, and for the 4 channel case 760 pW.

The conditions of this hallway were not ideal. There was a very significant temperature
change between the room where the transmitter and receiver were located and the
hallway the mirror was in. There was also significant turbulence in the hallway from
the heating and cooling system. This caused a significant amount of beam wander, on
the order of 1.5 to 2 cm linear displacement, which was probably very similar to what
would be encountered outdoors. It was observed that the multiple beams did appear to
stay together as they moved which was expected since the beams were at nearly the
same wavelength. There were no active measures taken in the transmitter or receiver to
counteract this beam wander so it should be noted that this was a significant contributor

to the Bit Error Rate (BER).

110

Mirror ‘

 

 

 

 

  

 

 

 

36 Meters
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, ‘ ‘ 111'
Fiber optic ” I. ~ 1'11
light source ‘, ‘. , 1" .
White paper screer/ 75 /
/ _rl_

 

 

Transmitter
Receiver

 

 

 

 

 

 

Figure 6.9: This figure shows the configuration of the ranged experiment. The
experiment was performed in a hallway that allowed for a total of 72 meters of

distance between the transmitter and receiver.

111

 

Figure 6.10: This picture shows the hallway where the long range experiments
were conducted. The picture is taken from the location where the transmitter and
receiver is located and the mirror that reflects the beam back to the receiver can

be seen at the end of the hallway.

112

:mcvW' ' '

:‘x .

 

Figure 6.11: For ease of alignment the transmitter and receiver were located next

to one another. Both are pointed down the hallway at the top of the picture.

 

Figure 6.12: Front view of the transmitter and receiver with the white cardboard
to reflect the light sources located in front. The receiver was covered in black cloth
so that very little of the noise photons go directly to the photon counters but

instead reflect from the screen to the mirror and back to the receiver.

113

6.6 Summary

In this chapter the concept for the transmitter utilizing pairs of pulsed sources to
generate time coincidence photons has been presented along with the transmitter and
receiver that were built to test this concept. The experiments that were conducted were
likewise described along with the experimental setup and conditions. The results of
these experiments and a comparison of the predicted performance with measured

performance are the subjects of the following chapter.

114

CHAPTER 7
EXPERIMENTAL RESULTS AND DISCUSSION FOR COINCIDENT PHOTON

COMMUNICATIONS EXPERIMENT

7.1 Introduction

In this chapter the results from the experimental tests to determine the efficacy of the
time coincident photon communication system, as described in the previous chapter, will
be presented and discussed. The experimental results will also be compared to the
predicted results, which are calculated fiom the mathematical formulation described in
Chapter 3, to test how well the mathematical representation predicts the system
performance. The data processing and analysis of the time coincident photon
communication will be discussed first and then the results of the five different
experiments will be presented and discussed. After the discussion of the individual
experiments a general discussion of the overall experiment, covering the common results

and some general observations on this system will conclude this chapter.

7.2 Experimental Measurement and Data Analysis

The data acquired at the receiver for all of these experiments is a series of single photon

and coincident photon detection times. In the base line cases, where a single

transmitting channel was used, the photon an'ival times of that channel were recorded.

In the other cases where time coincident photon communications were utilized the

115

coincidence times for either one or two coincidence channels were recorded. This data

record was then transferred to a computer for post processing and analysis.

The processing of the data was accomplished using Mathcad programs which have been
provided in Appendices B and C. One of the programs processes on/off keyed data
(Appendix B) for the one and two channel data and a second program (Appendix C)

processes two state data for the three and four channel cases.

There were several sources of experimental error. A systematic error was caused by the
lasers not completely shutting off between pulses. The photons generated by the
partially on laser add a bias (non-zero off state) to the measured signal level. This bias
level was measured to be 24% of the overall signal level and is treated as a background
noise signal. Another source of error was caused by conditions in the experimental
environment (lab hallway) not being ideal. There was a very significant temperature
change between the room where the transmitter and receiver were located and the
hallway that the mirror was in. There was also considerable turbulence in the hallway
from the heating and cooling system. This caused a significant amount of beam wander,
on the order of 1.5 to 2 cm linear displacement, which is probably very similar to what
would be encountered outdoors. It was observed that the multiple beams did appear to
stay together as they moved which was expected since the beams were at nearly the
same wavelength. There were no active measures taken in the transmitter or receiver to
counteract this beam wander so it should be noted that this was a significant contributor

to the Bit Error Rate (BER).

116

7.3 Experiment 1: Effect of varying background noise

The data taken in these experiments has been tabulated and graphed in Figure l to show
the BER as a function of SNR. Three data sets consisting of approximately 10 Kbits of
data were transmitted through the system and the BER was measured for each data set.
In Figure 7.1, each data point is the average of the three BER measurements that were
taken for each condition point and the error bars show the maximum and minimum
values. SNR was measured by independently counting the number of noise photons
received by the individual detectors while the background lights were on and the
transmitter was off and also by counting the number of signal and noise photons
received when the transmitter and background lights were both on. The noise
measurement was subtracted from the signal with noise to give the signal photon count.
Then the SNR was determined ficm the ratio of the signal photon counts divided by the
noise photon counts. The background light was varied to 4 different levels that were
approximately equal for each configuration. The reason that the data points do not have
the same SNR for each configuration is because the laser power levels could not be
exactly matched and also by adding channels the amount of noise is increased linearly
with the number of channels. A significant reduction of the BER is shown for the 2
channel coincidence compared to the single channel baseline. The 4 channel
configuration also shows a significant reduction in BER from the baseline but the

improvement fiom the 2 channel case was not as significant.

117

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~10 -5 0 5 10
SNR(dB)

 

Lo Zuchannel . {channel—n 1 channel baselinel

 

 

Figure 7.1: In this figure a comparison of single channel photon counting
communication to time coincident photon counting communication for different
noise levels can be made. This graph directly compares the measured SNR to
BER. The variation in the magnitude between the maximum and minimum for the
different data points was caused by varying amounts of beam wander. The beam
wander would change because there was a large temperature difference along the
hallway where the experiment was conducted that was made worse by the building

heating system turning on periodically during the experiment.

In Figure 7.2 a sample of the raw data from the single channel (top) and two channel
(bottom) configurations is shown. The single channel data plots photon detections as
function of time. The two channel data plots photon coincidence detections over time.
The data rate was 100 Kbit/sec so there were 10 microseconds of ‘on’/ ’1’ bit with
photon pulses and 10 microseconds ‘off’ / ‘0’ bit without pulses. In the single channel
case it can be seen that there are 10 microsecond time periods with more photon counts

and periods in between with less but the contrast between these is not very strong. In the

118

2 channel case the 10 microseconds of coincidence counts are readily apparent as there
is almost no noise between them. The data clearly shows the noise immunity obtained
by using coincident photon communication. The data however also shows some periods
where the 2 charmel coincidence counts are low. For example, in the 2 channel data the
period between 30 and 40 microseconds there are only 4 coincidence counts. With some
low counts such as these it is apparent that signal loss due to beam wander was probably

one of the most significant sources of error.

 

 

 

 

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Figure 7.2: Top: A graph of photon detections as a function of time for the single
channel baseline. Bottom: A graph of photon coincidence detections as a function
of time for the 2 channel configuration. The bottom axis for both of these graphs is

in units of seconds. The dashed line shows the transmitted waveform for reference.

In order to more fairly evaluate the data shown in Figure 7.1, a second graph has been

generated in Figure 7.3 where the SNR is calculated in a way that compensates for the

119

deflated SNR that results from inflated noise levels caused by additional channels. Here
the signal is still the sum of the signal photons from each channel. The noise however is
now calculated as the single channel average number of noise photons, rather than the
sum of the noise photons from all channels. In Figure 7.3 it can be seen that again a
significant improvement comes from using the 2 channel photon coincidence as opposed
to a single channel photon counting system. A 5 to 7 db improvement has been
measured in these tests. The data however does not show an improvement of the 4
channel system over the 2 channel system. In this case the 4 channel system would
probably have to be coded with multiple bits, as in Table 6.2, for a given bit period to

see an improvement.

0.25T A +
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SNR(dB)

.2, Noise averaged “to 1 channel
o 2 channel A_ 4 M I 1__channel baseline _

 

 

 

Figure 7.3: In this graph the signal-to-noise ratio has been calculated with the
signal summed for all of the channels used in a particular configuration. The noise

however was calculated as an average for a single channel.

120

In order to test how well the equations derived in Chapter 3 [3—22, 23, 24, 27, 28, 29,
and 30] predict the system behavior, a comparison of the expected BER calculated from
those equations and the measured BER is shown in Figure 7.4. In this comparison it
should be noted that the bias caused by the laser not completely turning off has been
compensated by counting the laser photon counts outside of the pulses in the noise for
that detector. These compensated signal and noise photon counts for each individual
detector were then used, along with the BER equations, to obtain the calculated BER for
each condition. In this figure it can be seen that there is fairly good agreement between
the calculated BER and the measured BER. The two potential sources of the
discrepancies between the measured BER and the calculated BER are the beam wander
that dynamically changes the signal strength and also the fact that the photon counts
were measured independently from the data transmission. This independent
measurement, which was not taken from the data transmission record, took place a
couple of minutes before or afier the data transmission. This, along with the dynamics

added from beam wander, probably caused the majority of the discrepancies.

121

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SNR (dB)
7 I 1 channel measured 0 1 channel calculated i
a 2 channel measured 0 2 channel calculated |
I 4 channel measured :4 channel calculated , j

 

 

Figure 7.4: In this graph a comparison of the expected BER calculated from the
BER equations and the measured BER is shown. In this case the bias caused by the
laser not completely turning off has been compensated by counting the laser photon

counts outside of the pulses in with the noise for that detector.

Since the equations from Chapter 3 effectively predict the measured BER, they can be
used to further compare and contrast the difference between the one channel traditional
photon counting communication and two channel coincident photon communication.
Using these equations, and parameters that are close to those measured in the
experiment, the Bit Error Rate for the one and two channel systems for varying
background photon count per channel is calculated and shown in Figure 7.5. Here the
signal level for the one channel system has been doubled so the total signal photons are
the same as the two channel system and the threshold was kept at a constant level. In

the experiment the threshold level was optimized for each individual measurement to

122

produce the lowest BER. In this case that would have produced a curve that would have

had steps in it and so the threshold was held constant for better comparison.

 

 

 

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Background Photon Count per channel

 

_—_— BER 2 channel 97 BER 1 Channel I

 

 

Figure 7.5: In this figure the BER of the two channel system and one channel
system are directly compared for the following conditions. The signal is held
constant at one million photon counts per second for both cases. The one channel
system has a signal level equal to 1 million photons per second in the single channel
the two channel system has 500000 photons per second in each channel. The

threshold level for determining the bit value was held constant.

This graph produced from the simulated data shows that the single channel system
degrades much more quickly from noise than the two channel system does. This
further supports the conclusion that the coincident photon technique appreciably
suppresses noise and enables photon counting communications in the presence of

significant background noise.

123

7.4 Experiment 2: Effect of varying signal levels

In this experiment the affect of varying signal level on the coincident communication
system is studied. The signal level was varied by placing various neutral density filters
at the output of the transmitter. The noise was kept constant so that only the changing of
the signal level changed the SNR. In this experiment a single channel (traditional
photon counting) OOK baseline was obtained as well as data fi‘om 3 channel and 4
channel coincident photon counting with two state coding. A graph of the experimental
results is shown in Figure 7.6. In this graph several of the modifications mentioned in
the previous experiment have been used. Here the laser noise has been counted in with
the noise figure to obtain the calculated values. Also in this figure the calculated BER
from an independent measurement of the signal and background photon counts is
shown. The noise level in this experiment was 4 times higher per channel than the

maximum signal level per channel.

124

. I

T

Bit Error Rate
0
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01 O.)
l l
O
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ill 0

 

0.15 ~ I
I

 

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0 100000 200000 300000 400000 500000

Signal Photon Rate per Channel

 

 

(photons / S)
Ct I 1 channel measured 0 1 channel calculated I
I I 3 channel measured 0 3 channel calculated I
I I 4 channel measured 0 4 channel calculated I

 

 

 

Figure 7.6: In this graph the variability of the Bit Error Rate as a function of
Signal to Noise Ratio for the one, three and four channel configurations is shown.
In this case only the signal level was changed and all other parameters were kept
constant. The SNR in this case is the ratio of the signal to the average noise per
channel as discussed in the previous experiment. The error bars for the measured

data points are the maximum and minimum data values for that point.

There are two conclusions that can be taken from this data set. The first is that the
equations developed in Chapter 3 to calculate the BER for given conditions fairly
represent the measured data. Again the same sources of error, the independent
measurement of background and signal counts and also beam wander, probably account

for most of the discrepancy. The second conclusion is that the time coincident

125

communication system is much more susceptible to performance degradation when the
signal is reduced below a certain minimum level, which is around 10 coincidences per
bit. In this experiment the photon coincidences were below this level for all of the data
points. The average number of coincidences per bit was 5.5 at the maximum signal
level and at an average of about 1 coincidence per bit at the lowest signal level. This
conclusion regarding the performance degradation at low signal levels is also apparent
from a general analysis of the coincident photon communication technique that is similar

to the analysis for communication range in Chapter 3.

The coincident photon technique suppresses noise because for a narrow slice of time
ambient photons have low probability of arrival and a pair of them occurring is even
more improbable because, as they are independent probabilities, it is then equal to the
product of two of these low probabilities. As signal strength falls below a minimum
threshold, registering photon coincidences works against this technique because the
probability of there being a signal coincidence is the product of two declining signal
photon probabilities. This reduces the rate of signal coincidences more rapidly than the
individual channels signal photon count rate declines. Note that in this case the photon
probabilities are declining because of increased attenuation fi'om neutral density filters,

which is a good analog of lower power sources.

126

7.5 Experiment 3: Effect of varying coincidence time windows on system

performance

In this experiment the effect that varying the coincidence time window has on the
coincident photon communication system was examined. In this experiment the only
parameter that was varied was the coincidence time setting for the receiver coincidence
circuit. This setting affects both the number of signal and noise coincidences that are

detected. The results of the experiment are shown in Figure 7.7.

 

 

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Coincidence time (ns)

I 3 channel calculated

AA,. A_______ .

 

o 3 channel measured

 

 

Figure 7.7: In this figure the performance of the 3 channel system is shown for
various coincidence times. In this case only the coincidence time in the receiver
coincidence circuit was changed and all other parameters were kept constant. The
fixed parameters were: Aperture Diameter: 4.5 cm, Data Rate: 100 KBit/sec,

Average Signal Counts per Channel: 500,000, Average Noise Counts per Channel:

127

985,000 and Average SNR: -2.88. The calculated data points in this case are made
from signal and noise rates that have laser noise counted with the noise as discussed
in the Experiment 1. The error bars for the measured data points are the

maximum and minimum data values for that point.

This experiment was performed with a high noise level. The laser noise compensated
signal to average channel noise level was measured for each data point and varied
between -2.3 dB and -3.6 dB. The nominal coincidence time for all other experiments
performed with this system was 11.75 ns, which was the maximum coincidence time of
the circuit. In this experiment the coincidence time was varied from 11.75 us down to 5

ns.

In Figure 7.7, it is best to examine the data from the nominal operating point, which is at
the end of the graph, and go backwards from there. In going from 11.75 ns coincidence
time down to 9.9 ns the BER is decreasing. This is because the dominate affect is that
the noise level is being reduced by the shorter coincidence times. For progressively
shorter coincidence times below this point the noise level continues to be reduced but
the BER is increasing. This is because not only is the noise level being reduced but also
the signal coincidences are being reduced. The reason the signal coincidences are being
reduced is because the pulse widths of the particular lasers used in the experiment can
only be made as small as about 14 ns. If one detector counts a photon at the beginning

of the pulse and the other coincident detector does not detect a photon until the end of

128

the pulse, a coincidence will not be registered if the coincidence time is less than time
between photon events. So with laser pulses being as long as 14 as it is apparent that the
signal must be significantly degraded as the coincidence time gets significantly smaller
than 14 ns. The drop in signal coincidences therefore dominates between 9.9 ns and 5 ns
and the performance degrades even though the coincident noise level continues

dropping.

7.6 Experiment 4: Data rate effect on system performance

In this experiment the affect that varying data rate has on system performance is
examined. Only the three channel configuration was tested in this case. As in the
previous experiments, all other parameters were held the same and only the data rate was
varied. The lasers were still pulsed 10 times per bit in order to get a significant number
of signal coincidences for each bit. Also the pulse durations were kept to 14 ns, but the

time between pulses was increased to decrease the data rate.

The results from this experiment are shown in Figure 7.8. Some parameters that help to
explain the operation of the system follow. Even though the signal level was not
purposely adjusted, the number of measured signal coincidences did change a little
throughout the experiment. They were an average 5.25 signal coincidences for the
shortest bit period and these decreased to about 4.1 for the longer bit periods. This was
probably caused by differences in the lasers pulse power with different time between

pulses. This however was not the largest contributor to the increasing error rate. The

129

increased error rate was due to the noise level increasing as the bit period increased. A
longer bit period leads to proportionately greater accumulation of noise coincidences, as
can be seen from Equation [3-30]. It was found the average noise coincidences per bit
increased from 0.1 for the shortest bit period to 1 for the longest. This is an increase of
10 times the noise level for an increase of 16 times greater bit period. The increase in
noise coincidences should have been the same as the increase in the bit period. The
discrepancy in this case was caused by a 32% reduction in noise photons as the
experiment progressed. This reduction of noise photons completely accounts for the
discrepancy. The noise reduction was caused by a lower number of noise photons from
the lasers due to changes in operating parameters required ti operate the lasers with more
time between pulses. There was also a slight change in the noise photons fiom the noise

lamps as the experiment progressed.

The threshold level was not changed in this experiment to consistently optimize the
BER. It was instead held constant at a level of 1. It is readily apparent that at the
longest bit period the probability of a ‘0’ bit being incorrectly interpreted as a ‘1’ bit is
about 50 % when the average noise coincidences are approximately equal to the
threshold value. The potential of the ‘1’ bit value being incorrectly interpreted as a ‘0’
is very small in this case so the average of the two error probabilities is about 25%. The
error probability measured for the longest bit period was about 20%. The difference
between what is expected and what was measured is because in this implementation
when the number of coincidence measured was equal to the threshold the bit was

arbitrarily assigned a ‘0’ bit value.

130

 

0.4 T TTT
0.35 T
0.3
0.25 4'
0.2 ~
0.15 -
0.1 ,

0.05 1

Bit Error Rate

 

 

 

 

0 50 100 150 200 250 300
Bit Period (us)

I 2 channel measured -—2 channel calculated _T

 

 

 

 

Figure 7.8: In this figure the performance of time coincident communication
system at multiple bit periods is shown. In this case only the transmitter bit period
was changed and all other parameters were kept constant. The calculated data
points in this case are made from signal and noise rates that have laser noise
counted with the noise as discussed in the Experiment 1. The error bars for the

measured data points are the maximum and minimum data values for that point.

The calculated data in Figure 7.8 gives a fairly good approximation of the measured
data. The discrepancy at the 160 microsecond bit period is also due to the operating
parameters shifting as the experiment progressed. If each calculated data point was

individually calculated there would have been better agreement, but the curve would not

131

have been shown and it was decided that it was more valuable to show the general trend

of the experiment.

7.7 Experiment 5: Effect of (Simulated) range on system performance

This experiment was performed to simulate how transmitting at further ranges will affect
the performance of the coincident photon communication system. It was not feasible to
transmit at longer ranges because of space limitations so instead the size of the receiver
aperture was varied. By varying the receiver aperture the amount of the transmitted
beam that is captured is reduced. This simulates how with increasing range less of the
transmitted beam is captured by a fixed aperture because the transmitted beam spreads
as it propagates. The size of the receiver aperture was varied by placing a variable
aperture in front of the telescope and taking measurements as the aperture diameter is
reduced. In this experiment three different configurations were tested. The single
channel baseline and 2 channel coincident photon configurations were tested using OOK

bit coding. Also the three channel configuration was tested using two state bit coding.

The laser beam diameter did not fill the entire receiver aperture and so reducing the
aperture did not exactly simulate increased range until the aperture was closed to a
diameter of 2 cm. To help illustrate this situation, the noise and laser (signal) photon
detection counts for one representative detector (C) are graphed in Figure 7.9 for the
different aperture settings. In this figure it can be seen that the photon counts from the

laser remain constant until the aperture diameter is decreased to 2 cm while the noise

132

photon counts steadily decrease as the aperture diameter is decreased. This is because
the noise uniformly illuminates the receiver aperture while the laser beam has a diameter
of only 2 cm. So the data points that correspond to the 2 cm or less aperture do
simulate an increased range, or at least they simulate increased range with a spatially
limited background noise source. Note that if the background noise source extended
beyond the field of view the noise would remain constant for a fixed aperture receiver
were moved to greater distances. While the other data points do not simulate increased
range they are helpful in that this experiment provides another situation, like Experiment
3, where noise is initially decreased and then the noise and signal are decreased
concurrently. So the results here will be a nice comparison to the results for Experiment

3.

 

 

 

5 1,500,000 . ___- _fi - . .. fl
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i 9 1,000,000 .
o g 1
a 3 i
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9- a
a l i
0 l ‘l T 7 l h -_ F’Hl

 

5.00 4.00 3.00 2.00 1.00 0.00
Reciever Aperture Diameter (cm)

+ C LaserCounts + C Noise Counts

 

 

 

Figure 7.9: In this figure the noise and laser (signal) photon detection counts for
one representative detector (C) are graphed for the different aperture settings.

This figure shows that the laser beam had a beam diameter of about 2 cm and so all

133

aperture settings larger than 2 cm affected only noise while all aperture settings

smaller than 2 cm affected noise and signal.

As the aperture is decreased from 4.5 cm to 2 cm the SNR for all three configurations
improves as the noise is decreased. This is shown in Figure 7.10 where the SNR as a
function of aperture diameter is graphed. After reducing the aperture below 2 cm the
SNR begins to drop for all three configurations. These trends of SNR provide further
insight into the relative affect that noise and signal changes have on system

performance.

 

'2.00 » ~- T— ~ ~ TTT .
1.00~ 1
0.00 ~
-1.00Al ‘V
-2.00 ~
-3.00 —
-4.oo ~
-5.00 ~
-6.00 ----TT~T . ~- . - . TTT
o 100 200 300 400 500 600 700 800
Simulated Range (m)

 

 

dB)

V

SNR

 

 

 

 

+ 3 channel g

" +1 channel +2 channel

 

Figure 7.10: In this figure the laser noise compensated signal to noise ratio for each
configuration is graphed according to the simulated range. The points greater than
200 m simulate the affect of greater range. Below 200 m it does not successfully

simulate increased range because the SNR is increasing.

The system performance results of the simulated range experiment for all three

configurations are shown in Figure 7.11. In interpreting this graph it is helpful to begin

134

at the shortest range. Initially the two and three channel systems have a lower BER than
the one channel system. As the noise level is decreased, for the first 4 data points, the
one channel system performance improves but the two and three channel systems remain
the same. The two and three channel systems are very insensitive to the change in noise
level. This finding further supports the conclusions in experiment 1 that the coincident
photon communication has significantly less sensitivity to noise than traditional photon

counting communication.

0.3 1;

Bit Error Rate

    

1
1
o -——» --T—~-——--

0 200 400 600 800
Simulated Range (m)

 

+1 channel measured "’ ” T
—-— 2 channel measured
+ 3 channel measured

 

Figure 7.11: This figure shows the experimental results that different simulated
ranges (inverse receiver aperture diameters) have on system performance. These
results show that the coincident communication systems (2 and 3 channel) are more
sensitive to changes in signal, but less sensitive to changes in noise, than the single
channel traditional photon counting system. The error bars are the maximum and

minimum data values for that point.

135

After the first five data points the closing of the aperture begins to roughly simulate
greater range. For the next two data points, which are for simulated distances of 171 m
and 228 m, the signal-to-noise ratios approximately level out for all three configurations.
The BER for the single channel system increases only slightly. The BER for the 2 and 3
channel systems however increases substantially. This is because the signal was at a
low level to begin with and the loss of signal affects the coincident photon
communication system more than the single channel system. This supports the
conclusions in Chapter 3 regarding the relative affect of range on the two different
systems, which was that the coincident communication system dropped at l/R‘, where R
is range, and the traditional system dropped off at UK2 when beyond the range at which
the laser beam is entirely captured by the receiver collection optic. The conclusion of
experiment 2 is also supported by this data The single channel system BER nicely
follows the trend in SNR for that system. However, the coincident communication
system is more affected by signal strength and so this system more closely follows

trends in signal strength.

7.8 Discussion

The general conclusion of all these experiments is that the coincident photon
communication system is a photon counting communication technique that is effective
even with significant ambient noise. The second conclusion is that the coincident
photon counting technique is very sensitive to signal strength, in general more sensitive

than traditional photon counting communication. This is to be expected and can be

136

explained by comparing the equations for SNR for the 1 channel case to the 2 channel
case. The SNR, in terms of photon counts registered by the receiver, for the one channel

system, with an ideal detector that has 0: =1, is equal to

SNR] = — [7-1].

In this case changes in noise level affect the SNR in a way that is directly proportional to
the noise level. The SNR for the two channel case is derived from the equations for
average signal count per bit for a one bit [Equation 3-27] and average noise count per bit

for a zero bit [Equation 3-30]. This SNR, again with ideal detectors, is represented by

[R132]

R T
SNR2 = ___” P

[’1 '2]

 

[7-2].

These equations are more readily comparable if we assume the signal rates and the pulse

rate are all the same and also all of the noise rates are the same, and they simplify to

 

SNR] = E [7'3]
r
.5;
_ Tp
SNRz — 2 [7-4].

137

In the case where the signal photons are equal to the background photons the SNR for
one channel is equal to 1 while the SNR for the 2 channel case is the ratio of 1 over the
pulse time divided by the background noise count. If the background noise count is 1
million photons per second and the pulse time is 10 nano seconds then the SNR is 100 as

shown here

__1_
10‘8

6 =102 [7-5].
10

SNR2 =

 

Since these rates and pulse widths are representative of the numbers found in the
experiment we can see that error in the communications has more to do with the signal
than it does from the noise. Keep in mind that a SNR of 100 can still produce a high
BER if the signal is on the order of 5 coincidences per bit and the noise is .005 because a
Poisson distribution with an average of 5 will have quite a few zeros, and so there will
be quite a few bits with no signal. In the data taken for these experiments the numbers
of coincidences for the 2, 3 and 4 channel cases were in general in the single digits per
bit, so even without any noise there would have been a BER of at least 10'5 just because
of a fraction of bits having no signal. Any reduction of signal, when the signal is

already low, therefore significantly impacts system performance.

The experiments performed here demonstrate the potential for this technique for a very
low power system. The bit error rates achieved are not those that would be required for

a planetary mission. In that case the BER would have to be in the range of 107. While

138

that hasn’t been demonstrated with this experimental system there is significant potential
to reach this level. Improvements in the transmitter and receiver to reduce the pulse
time to 1 ns and the coincidence time to lns would significantly improve the BER.
Also increasing the number of pulses to 15 or 20 would significantly improve the BER.
Also it is possible that Pulse Position Modulation could be used to further decrease the

power per bit and Forward Error Correction coding could likewise improve the BER.

To illustrate how improvements in the system can affect overall performance Figure
7.12 was created. In this figure the performance of a two state 4 channel system is
presented for three different situations. The data points were calculated using Equations
[3-22, 23, 24, 27, 28, 29 and 30] and the Mathcad worksheet shown in Appendix D. The
first data series is denoted as ‘Experiment Configuration’ and these data points represent
the system performance of the experimental system with transmission loss neglected.
The second curve is denoted as ‘Coincidence / pulse time 1 ns’ and this shows
improvement in system performance by reducing the coincidence time and laser pulse
width time to 1 ns. The third curve, denoted as ‘Shorter coincidence time with 15 pulses
per bit’, shows how the overall system performance is improved by both reducing the

pulse width / coincidence time and increasing the number of pulses to 15 per bit.

139

0.1

 

0 Experiment

0.01 e g» __, -~— w Configuration
M”

90...... . . . . .
o o I Councldencelpulse

0.001 . -— - - time1 ns

(I
LU
MIIIIIIIIII I I I I I

 

 

A Shorter coincidence
0.0001 HAM-1' ——~ w *- lime and 15 pulses per

M bit
MAAAAA A 4)

0.00001 . r
—6.00 4.00 -2.00 0.00

SNR

 

 

 

 

Figure 7.12: In this figure the system performance is graphed for the experimental
configuration (diamonds), an improved system with a 1 ns pulse width and
coincidence time (squares) and a further improved system that uses 15 pulses

instead of 10 (triangles).

Figure 7.12 shows that reducing the pulse width of the lasers from 14 ns to Ins and also
reducing the coincidence time from 11.25 ns to 1 ns produces an order of magnitude
reduction in BER. By further improving the system by increasing the number of pulses
per bit from 10 to 15 the BER is reduced by another order of magnitude. With these two
improvements the system has better than a 10'4 BER and the radiated power would still
be less than 1 nW. The technique has demonstrated significant noise immunity in the
presence of background noise and with fiirther system refinement such as these and with
the inclusion of standard coding and modulation techniques it has significant potential to

enable free space communication for miniature sensor stations.

140

7.9 Summary

In this chapter experiments testing the low power optical communication system has
been presented. In contrast to traditional photon counting the system is made
significantly immune to background noise by only counting photon coincidences.
Experiments conducted with this system have shown that a signal of just 360 pW can
have an effective range of 70 meters even in the presence of ambient light levels similar
to what can be expected outdoors. The experiment, while not optimized, has
demonstrated low error communication at significantly lower signal to noise ratios than
is possible with traditional photon counting. Previously this type of coincident photon
communication method has been accomplished using non linear systems to generate
quantum entangled photons. The system presented here has been developed because it
can more readily utilize the smallest high efficiency sources that tend to have low total
power levels. With sources such as these, the transmitter electrical energy can be as low
as a billionth of a watt, which would overcome a significant hurdle for miniature

planetary sensor platforms.

141

Chapter 8 Conclusion

This work has been focused on further developing low power optical communications
based on the utilization of both Quantum Entangled (QE) photons and also pulsed pairs
of photons. In this final chapter the new knowledge and accomplishments of this work
are summarized. Also, a comparison of the results of this work with State-Of-the-Art
(SOA) low power communication systems is made. The chapter, and this work, is
completed with a discussion of the next steps that might be taken in developing

miniature low power optical transmitters.

8.1 Dissertation accomplishments:

When this work began a list of planned accomplishments was created. These
accomplishments were generated to further define the scope and significance of the
work. The list is repeated here and how these accomplishments have been met is also

included with each accomplishment.

1. Develop two state error probapilities and build a 2 state tra_r_r_smitter

utilizing quantum entangled photons.

 

The error probabilities for both the Quantum Entangled (QE) and the pulsed
coincident photon communication systems for the two state bit coding were
developed in Chapter 3. In Chapter 5 calculated BER values using the

equations for the QE system were compared to experimental values and they

142

had very good agreement. Likewise in Chapter 7 calculated values for the
coincident photon system were compared to experimental results and had

good agreement.

A transmitter based on quantum entangled photons was built that has two
states, one for each bit value. One bit value was coded by sending photons
of like polarization and the second bit value was coded by sending photons
with orthogonal polarizations. The transmitter and receiver designs for this
system were described in Chapter 4 and an experiment testing the system
was described in Chapter 5. The findings from this accomplishment were:
The system successfully transmitted data at a remarkably low power level, a
received optical power of l Pico joule per bit, in the presence of significant
background noise. As mentioned, this experiment had very good agreement
to the theoretical prediction and so it confirmed the method for two state

BER calculation developed in Chapter 3.

2. Contrast Ratio Calculation

The contrast ratio calculation, which is the ratio of the average of the ‘1’ bit
value to the ‘0’ bit value - similar to SNR, was completed and described in
Chapter 3. This calculation showed that the QE based communication
system can produce much higher bit contrast ratios in very high noise
environments, up to -20 dB SNR, than is possible with traditional photon

counting systems.

143

3. Modify Probabilistic Mathematical Model to account for solid state
gaasmitter instead of existing OE based transmitter

The method for calculating the average number of received photon pairs for
the system based on coincidently pulsed source is described in Chapter 3.
This method was adapted from the previously developed formulation for QB
photon pairs [Man 1984, Hon 1985]. Once the average numbers of photon
pairs can be determined, the BER can be calculated by analyzing the
Poisson probability functions generated from these averages. The BER
calculation for on / off keying was directly taken from the previous work for
the QE system. The BER calculation for the two state keying was
developed as part of this work and also appears in Chapter 3. This
calculation is applicable to both the QE system and the coincidently pulsed

SOUI‘CCS system.

4. Develop energy efficient traasmitter concept anj build an experimental
transmitter and receiver and test the concept

The transmitter concept was completed and described in detail in Chapter 6.
This concept was considered to be very novel and so the National
Aeronautics and Space Administration has filed for a patent on it in May
2006. Both the transmitter and receiver were built to test the pulsed photon

pair concept and they were described in Chapter 6.

144

This concept was tested in several experiments and the results of these
experiments were described in Chapter 7. The experimental results
confirmed that the technique does indeed allow for photon counting
communications in the presence of significant background noise. They also
confirmed that the mathematical model developed in this dissertation does
accurately predict BER. The final finding, and potentially most significant,
from this accomplishment is that the system was able to achieve a BER of
2"‘10'3 while having a data rate of 100 Kbits/ sec, transmitting over a
distance of 70 meters with a background level that was above the signal
level (received SNR was -0.7) using only 760 pW of transmitted power.
This translates to only 7.6 femto watts of transmitted power per hit. This
confirms the low power optical communications concept that was the goal

of this work.

One final accomplishment that deserves mention was unplanned. This accomplishment
was the calculation in Chapter 3 regarding the differences in performance, as a function
of range, between a QB based system and a system that is based on pulsed pairs of
sources. It was assumed when this work began that the issue of range was solved, as it
had been reported in the publication by Jackson et.al. [Jackson 2002]. The QE system
however has been shown to have the potential for a significantly greater effective range

than the system based on coincidently pulsed sources. These calculations have shown

145

that the QE system can have an effective range hundreds of times greater than the pulsed

pair system [Lekki 2008-1].

8.2 Comparison of general results from QE, coincident photons and SOA

communication methods

The QE based system, coincidently pulsed sources system, the SOA optical and Radio
Frequency systems all have some advantages and disadvantages for low power
communication applications. The SOA has been covered in Chapter 2 so the advantages

and disadvantages of the two techniques will only be discussed here.

The SOA miniature RF systems have several advantages. They have already been
operated at 100 uw of electrical power and are Omni-directional, so pointing and
tracking are not issues. The chief disadvantage of a miniature RF system is that it has a
range of generally only 10 meters when operating at the 100 uw power level. For
optical communication, the most promising systems for low power transmission are
photon counting systems that use Geiger mode detectors. The advantages of these
systems are that the receivers are extremely sensitive, as they can detect single photons,
and they have very low noise, in the hundreds of counts per second. The optical sources
can be made to be very small and also very energy efficient. Also, because small optical
transmitters are more directional than RF transmitters of the same size, the photon
counting system has greater range than the RF system. The directionality however does

introduce issues with pointing and tracking problems for mobile stations. These SOA

146

optical systems have been used to achieve nearly 1 photon per bit fi'ee space
communication, but the chief disadvantage is that they have, until now, been limited to
situations with “little or no background noise” [Maj 2008]. The advantages of photon
counting communications and this specific disadvantage, is the essential motivator for

developing the time coincident photon pair communication techniques.

The QE system has two chief advantages. The first is that a QB source intrinsically
produces photons nearly simultaneously and so the receiver can have very short
coincidence times. This would be very important in a situation with very high
background light levels. The second advantage of a QB system is that because of the
momentum entanglement it is possible to have hundreds of times further range than a
pulsed pair system. The chief disadvantage of the QE system is that it is not energy
efficient to produce QE photons. Without a more efficient method of producing QE
photons this disadvantage may make it impossible for the QE system to be utilized in a
miniature low power station. If the energy efficiency is increased then there are
significant opportunities for this system to be implemented for long distance low power

communication.

The system based on coincidentally pulsed sources has significant advantages. It has all
of the advantages of a traditional photon counting communication system with the
further advantage that it is a photon counting technique that can work in the presence of
significant background noise. This system also has better range than the RF system as it

has been demonstrated to 70 meters and a simulated range of about 175 meters. This

147

was achieved with a signal power of 760 of picowatts. Even with very low electrical to
optical energy efficiency ~1%, an optimized optical system utilizing this technique
would still only use 76 nw of electrical power. This is a three orders of magnitude
power improvement over the RF device while achieving greater range. The chief
disadvantage to this system is that the signal falls off proportional to l/R4 beyond the

point where most of the beam is captured by the receiver.

Since the QE based system can have significantly greater effective range than the pulsed
coincident source system and the QE system has lower energy efficiency it is not clear at
this point which one will be more effective in the future. For shorter ranges the
coincidently pulsed sources is clearly better. For ranges beyond that several questions,
such as how much can the energy efficiency of QR sources be improved and also can the
longer range transmissions by QE systems be realized, before a clearly preferred

technique is determined.

8.3 Future Work

The accomplishments in this work can be expanded upon in numerous areas. Both the
system based on Quantum Entanglement and the coincident photon communications
systems have significant improvements that can be made. There are also areas in bit
coding and error correction that can be applied to both these systems that can
significantly enhance the system performance. Finally, pointing, tracking and

synchronization techniques need to be implemented and tested for these systems.

148

For the QE based system firrther work towards improving the efficiency of spontaneous
down conversion and work to confirm the increased range possible with QE photons are
both reasonable next steps. The efficiency of spontaneous down conversion can be
increased by placing the non linear crystal in an optical cavity. The cavity will increase
the number of times that the pump photons passes through the crystal and will therefore
increase the potential that a pump photon will down convert into two QE photons,
thereby improving the energy efficiency of the system. Also, building and testing a QB
transmitter that recombines the beams in a geometrically symmetric fashion would make
it possible to test the conclusions in Chapter 3 regarding the improvement that can be

realized at long ranges when utilizing the QE system rather than a pulsed pair system.

The next step for the pulsed pair system would be to improve the light sources so that a
shorter pulse width can be achieved. The pulse width has lots of room for improvement
as the sources used in this work could only generate pulse widths down tol4 ns. A
source with pulse widths of a fraction of a nano second would allow for the coincident
time of the receiver to like wise be reduced to a fiaction of a nano second. This will
reduce the noise coincidences by at least a factor of ten and will significantly improve

the BER of the system.
The BER for both these systems can be improved by utilizing error correction

techniques. This will come at a loss of bandwidth and increase in the energy per bit, but

the overhead is probably necessary to achieve BERs on the order of 107, which is the

149

general minimal requirement for planetary missions. Further work in bit coding can
reduce the energy per bit. The 3 and 4 channel systems could be encoded so that they
would have 3 and 4 bit states respectively. This would allow the 4 channel system to
send twice the information of the two channel system. The number of channels and the
number of states could like wise be increased beyond 4 by adding sources of different
wavelengths. Even more out of the ordinary, Orbital Angular Momentum states could
be used to add additional channels. The benefit of OAM states is that they are mutually
orthogonal and so it is straight forward to add channels by simply increasing the OAM
of the photons. This is highly speculative however because the OAM modes have there

own range limitations based on the size of the aperture.

Finally, work in pointing, tracking and synchronization are other future steps that are
necessary. Traditional tracking and synchronization techniques for optical
communications would be applicable for systems such as these and so work in applying
these techniques should be undertaken in the future. To initiate correct pointing, the low
power transmitter can work in cooperation with larger higher power relay stations.
These higher power stations can transmit higher power communication signals to the
low power stations to give them a beacon to orient towards. The relay station will have
to in turn listen for the low power transmissions as it scans an area with its receiver.
This scanning may not be difficult as the small low power stations will probably have
limited mobility and so the area that needs to be scanned may not be very large once the

sensor has been initially localized.

150

8.4 Concluding Remarks

A concept for low power communication has been demonstrated to allow
communication up to 70 meters utilizing Pico watts of radiated power. There is
significant potential for improvement beyond this, as has been described in the previous
section. This work has led to the potential of building firture miniature planetary
explorers that can communicate with nano watts of power. This is a power level that is
readily ‘scavenged’ from the environment. It is therefore possible that robotic explorers,
utilizing a communication technique such as this, might work as self sustaining swarms
to study an area from many vantage points and collect a wealth of information in places

we so very much want to explore.

151

APPENDIX A
MATHCAD WORKSHEET FOR CALCULATING BER FROM EXPERIMENT

COINCIDENCE DATA

Mathcad ll worksheet for calculating the Bit Error Rate of 2 state quantum
entangled photon communication. Created: 11/9/2007 by John Lekki.

N 1 := 55.66 Number of 1 state coincindences measured when '1' bit
transmitted

N 01 := 23.28 Number of 0 state coincidences measured when '1' bit
transmitted

N 0 := 53.95 Number of 0 state coincindences measured when '0' bit
transmitted

N 10 := 23.67 Number of 1 state coincidences measured when '0' bit
transmitted

20

3
P10 := Z en (N10+N0)[1‘l_1(_)_]2 -,In(z 2 /N10 N0)

2:]

P10 = l.8l3x 10‘4

z
20 — N +N N01 2

P012: 2 e ( 01 ”[W] 'ID(Z,2’N01N1)
z=0

P01 = 1.219x10-4

P +P
BER:= 10 01

BER = 1.516x10_ 4

152

APPENDIX B

COMMUNICATION DATA ANALYSIS FOR ON / OFF KEYED DATA

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APPENDIX D

BIT ERROR CALCULATION FOR TIME COINCIDENT PHOTON
COMMUNICATION

Mathcad 11 worksheet for calculating the Bit Error Rate of 2 state time coincident
photon communication. Created: 11/9/2007 by John Lekki.

R1 2: 50000(
R2 2: 500000

R3 2: 500000

R4 := 500000
r1 := 500000
r2 := 500000
r3 := 500000
r4 := 500000
a 1 := 07
a2 := a1

(1.3 I: (11
a4 := 0.]

St = 11.5-10'9
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T8 := 2x IO—5
Rp .= IO

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N1 := R1'°‘2"%ETS+ [[(1- a2)R1r2 +(1— a1)R2r1+ r1 ~r2]-8t:|-TS

Number of 1 state coincidences measured when '1' bit
transmitted
N01 2: 1'3 '1'4'OI'TS

Number of 0 state coincidences measured when '1' bit
transmitted

N0 := R304}? TS+ [[(1 - a4)R3 r4 +(1— a3)R4r3 + r3-r4J-5tJ-TS

Number of 0 state coincidences measured when '0' bit
transmitted

N10 2: 1'1 T2°OI°TS

Number of 1 state coincidences measured when '0' bit
transmitted

N1 = 5.459
N01 = 0.058
N0 = 5.459

N10 = 0.058

175

Z
2

20
P10:= Z e—(N10+N0)[_:;:] .1n(z,2 /N10'N0)

2:]
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2
2

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1.01.: X e_(N01+Nl)[iNol_1] .m(z,2m)

z=0

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P +P
BERz= 10 01

 

BER = 2.97x .o- 3

176

REFERENCES

Abouraddy, A. F., Saleh, B. E. A., Sergienko, A. V. and Teich, M. C., “Role of
Entanglement in Two-Photon Imaging”, Physical Review Letters 87(12), 123602 1—4
(2001).

Alde, D. M., Dyer, P., Luther, G. G., Morgan, G. L. and Schauer, M., “Quantum
Cryptography”, Los Alamos National Laboratory Publication LA-UR-95-806.

Andrews, L. C. and Phillips, R. L., Laser Beam Propagation through Random Media,
SPIE Optical Engineering Press, Bellinham, Washington (1998).

Arakawa, Y., “Connecting the Dots”, OEMagazine, January, 18-20 (2002).

Amon, 8., “Effects of atmospheric turbulence and building sway on optical wireless-
communication systems”, Optics Letters 28(2), 129-131 (2003).

Atkin, G. E. and Fung, K. L., “Coded Multipulse Modulation in Optical
Communication Systems”, IEEE Trans. on Comm. 42(2/3/4), 574-582 (1994).

Banaszek, K., Dragan, A., Wasilewski, W. and Radzewicz, C., “Experimental
demonstration of entanglement-enhanced classical communication over a quantum
channel with correlated noise”, Phys. Rev. Letters 92(25), 257901 1-4 (2004).

Barnett, S. M., Phoenix, S. J. D., “Information theory, squeezing and quantum
correlations”, Phys. Rev. A 44(1), 535-545 (1991).

Bouwmeester, D., Ekert, A. and Zeilinger, A., The Physics of Quantum Information,
Springer, Berlin (2000).

Bumham, D. C. and Weinberg, D. L., “Observation of Simultaneity in Parametric
Production of Optical Photon Pairs”, Phys. Rev. Letters 25(2), 84-87 (1970).

Dmitriev, V. G., Gurzadyan, G. G. and Nikogosyan, D. N., Handbook of Nonlinear
Optical Crystals 3'“. edition, Springer, Berlin (1999).

Eckardt, R. C., Masuda, H., Fan, Y. X. and Byer, R. L., “Absolute and Relative
Nonlinear Optical Coefficients of KDP, KD*P, BaBzO4, LiIO3, MgO: LiNbO3, and

177

KTP Measured by Phase-Matched Second-Harmonic Generation”, IEEE J. Of
Quantum Electronics 26(5), 922-933 (1990).

Friberg, 8., Hong, C. K., and Mandel, L., “Intensity Dependence of the Normalized
Intensity Correlation Function in Parametric Down-Conversion”, Optics
Communications 54(5), 31 1-316 (1985).

Gourley, P., “N anolascrs”, Scientific American Magazine; March 1998, p. 56-61.

Grant, K. J ., Corbett, K. A., Clare, B. A., Nener, B. D., Boettcher-Hunt, A., and
Davies, J. E., “Dual Wavelength Free Space Optical Communications”, Proceedings
of CLEO / QELS / Phast Conference, Baltimore, Md. (2005).

Haight, F., Handbook of the Poisson Distribution, New York, New York (1967).
Hecht, E., Optics (3“ Edition), Addison-Wesley, New York (1993).

Hong, C., F riberg, S. and Mandel, L., “Optical communication channel based on
coincident photon pairs”, Applied Optics 24(22), 3877-3882 (1985).

Jackson, D., Hockney, G. and Dowling, J ., “Quantum communication noise rejection
using correlated photons”, Journal of Modern Optics 49, 23 83-23 88 (2002).

J oobeur, A. and Saleh, B. E. A., “Spatiotemporal coherence properties of entangled
light beams generated by parametric down-conversion”, Phys. Rev. A 50(4), 3349-
3361 (1994).

Karim, M. A., Electra-Optical Devices and Systems, PWS-Kent, Boston (1990).

Kim, I. I., Hakakha, H., Adhikari, P., Korevaar, E., and Majumdar, A. K.,
“Scintillation reduction using multiple transmitters,” Free-Space Laser
Communication Technologies IX, Proc. SPIE 2990, 102-113 (1997).

Kim, I. 1., Stieger, R., Koontz, J. A., Moursund, C., Barclay, M., Adhikari, P.,
Schuster, J ., Korevaar, E., Ruigrok, R., and DeCusatis, C., “Wireless optical
transmission of fast Ethernet F DDI, ATM and ESCON protocol data using the
Terralink laser communication system”, Opt. Eng. 37(12), 3143-3155 (1998).

Kimble, M., Anderson, E., Jayne, K., and Woodman, A., “Micro-Tubular Fuel Cells”,
NASA Tech Briefs, April 2004.

Kurtsiefer, C., Oberparleiter, M. and Weinfiirter, H., “High efficiency photon pair
collection in type II parametric fluorescence”, Phys. Rev. A 64(2), 023802 1-4 (2001).

178

Kwiat, P. G., Mattle, K., Weinfurter, H., Zeilinger, A., Sergienko, A. V., and Shih,
Y., “New High-Intensity Source of Polarization-Entangled Photon Pairs”, Phys. Rev.
Letters 75(24), 4337-4341 (1995).

Lee, H. and Kim, J ., “Quantum teleportation and Bell’s inequality using single-
particle entanglement”, Phys. Rev. A 63, 012305 1-5 (2000).

Lekki, J. D., Nguyen, Q., Nguyen, B. and Hizlan, M., “Quantum Optical
Communication for Micro Robotic Explorers”, Proceedings of the AIAA
Infotech@Aerospace Conference, Arlington, Va., September (2005).

Lekki, J. D., Nguyen, Q., and Nguyen, B., “An Extremely Low Power Quantum
Communication Link for Autonomous Robotic Explorers”, Proceedings of AIAA
Infotech@Aerospace Conference, Rohnert Park, Ca, May (2007).

Lekki, J ., “Quantum entanglement enables low-power Optical communication to
orbital ranges”, Optical Engineering 47(1), (2008).

Lekki, J. D., Nguyen, Q., and Nguyen, B., “An extremely low power quantum optical
communication link for miniature planetary sensor stations”, Journal of Aerospace
Computing, Information and Communication, (Submitted March 2008).

Majumdar, A. and Ricklin, J ., Free Space Laser Communications: Principles and
Advances, Springer, New York 2008, p 184.

Mandel, L. and Wolf, E., “Coherence Properties of Optical Fields,” Rev. Mod. Phys.
37,231(1965)

Mandel, L., “Proposal for almost noise-free optical communication under conditions
of high background”, J. Opt. Soc. Am. B, Vol 1, March (1984), p. 108-110.

Mao, S. S., “Nanolasers: Lasing from Nanoscale Quantum Wires”, Int. J. of
Nanotechnology 1(1/2), 42-85 (2004).

McEliece, R. J ., “Practical Codes for Photon Communication”, IEEE Trans. on
Information Theory 27(4), 393-398 (1981).

Miyazawa, T., Tatebayashi, J ., Nakaoka, T., Ishida, S., Iwamoto, S., Takatsu, M.,
Arakawa, Y., Hirose, 8., Takemoto, K., Usuki, T. and Yokoyama, N.,
“Electroluminescence from a Single Quantum Dot at Telecommunication
Wavelength”, Proceedings of CLEO / QELS conference, Baltimore (2005).

179

National Science and Technology Council, Committee on Technology, Subcommittee
on Nanoscale Science, Engineering and Technology, “National Nanotechnology
Initiative: The Initiative and Its Implementation Plan”, July 2000, Washington DC,
p. 61-62.

Nielsen, M. and Chuang, 1., Quantum Computation and Quantum Information,
Cambridge University Press, Cambridge (2000).

Nordholt et Al., “Present and Future F rec-Space Quantum Key Distribution”, SPIE
Conference: F rec-Space LASER Communications Technologies XIV, 20-25 JAN
2002, San Jose, CA

Nordholt, J. E., Hughes, R. J ., Morgan, G. L., Peterson, C. G. and Wipf, C. C.,
“Present and future free-space quantum key distribution”, Los Alamos National
Laboratory Publication LA-UR-01-681 7 (2002).

Oberparleiter, M. and Weinfurter, H., “Cavity-enhanced generation of polarization-
entangled photon pairs”, Optics Communications 183, 133-137 (2000).

Ortiz, G., Sandusky, J ., and Biswas, A., “Design of an Opto-Electronic Receiver for
Deep-Space Optical Communications”, T MO Progress Report 42-142, August
(2000).

Pierce, J. R, “Optical Channels: Practical Limits with Photon Counting”, IEEE
Trans. On Communications 26(12), 1819-1821 (1978).

Pittman, T. B., Shih, Y. H., Strekalov, D. V. and Sergienko, A. V., “Optical imaging
by means of two photon quantum entanglement”, Phys. Rev. A 52(5), 3429-3432
(1995).

Polishuk, A., “Communication performance analysis of microsatellites using and
optical phased array antenna”, Opt. Eng. 42(7), 2015-2024 (2003).

Rabaey, J ., Amer, J ., Karalar, T., Li, S., Otis, B., Sheets, M., Tuan, T., “PicoRadios
for Wireless Sensor Networks: The Next Challenge in Ultra-Low-Power Design,”
Proc. of the Int’l Solid-State Circuits Conf., San Francisco, CA, February 3-7, (2002).

Rarity, J. G. and Tapster, P. “Experimental Violation of Bell’s Inequality Based on
Phase and Momentum”, Phys. Rev. A 64(21), 2495-2498 (1990).

Rarity, J. G. and Tapster, P. R., “Quantum Communications”, Appl. Phys. B 55, 298-
303 (1992).

180

Rarity, J. G., “Getting Entangled in Free Space”, Science 301, 604-605 (2003).

Rarity, J. G., “Quantum communications and beyond”, Phil. Trans. R. Soc. Land. A
361, 1507-1518, (2003).

Saleh, B. E. A. and Teich, M. C., Fundamentals of Photonics, Wiley-Interscience,
New York (1991).

Shannon, C. E., “A Mathematical Theory of Communication”, The Bell System
Technical Journal 27, 379-423 & 623-656 (1948).

Siegrnan, A. E., Lasers, University Science Books, Mill Valley, California (1986).

Sklar, B., Digital Communications Fundamentals and Applications, Prentice Hall,
New Jersey (2000).

Stephens, D. R., Phase-locked Loops for Wireless communications: Digital, Analog
and Optical Implementations, Kluwer Academic, New York (2002).

Strickland, B. R., Lavan, M. J ., Woodbridge, E. and Chan, V., “Effects of fog on the
bit-error rate of a free-space laser communication system”, Applied Optics 38(3),
424-431 (1999).

Takeuchi, S., “Beamlike twin-photon generation by use of type II parametric down
conversion”, Optics Letters 26(11), 843-845 (2001).

Vilnrotter, V. and Lau, C. W., “Quantum Detection Theory for the Free-Space
Channel”, IPN Progress Report 42—146, (2001).

181

 

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