INVESTIGATIONOFPLANARTERAHERTZPASSIVEDEVICESANDCOUPLING METHODSFORON-WAFERAPPLICATIONS By JoshuaCarlMyers ADISSERTATION Submittedto MichiganStateUniversity inpartialentoftherequirements forthedegreeof ElectricalEngineering{DoctorofPhilosophy 2015 ABSTRACT INVESTIGATIONOFPLANARTERAHERTZPASSIVEDEVICESANDCOUPLING METHODSFORON-WAFERAPPLICATIONS By JoshuaCarlMyers Inrecentyears,developmentshavepushedthecutfrequenciesoftransistorsnear1 THz,enablingforthetimethedesignoflargebandwidthtransmit/receivemodules. Whiletherehasbeenatinterestintheresearchcommunitytoimplementthese devices,manychallengeshaveslowedsuchprogress.Primarily,thesechallengesstemfrom thehighdielectricandmetallossesmanymaterialsdisplayintheTHzspectrum.However, toimplementwafer-levelintegratedcircuitsintheTHzspectrum,tpassivedevices thatareintegrationcompatiblemustbedeveloped.Foranyintegratedsystem,manyofthe mostimportantpassivebuildingblocksofthesystemarereducedtotwaveguiding, andcouplingbetweenanyactivecomponents,necessarymeasurementsystems, andinputsources.Inthisdissertation,tpassiveterahertzcomponents,including waveguides,s,andinputcouplers,aredeveloped. First,amethodoftlycouplingTHzradiationbetweencommercialquasi-optical THzsystemsandintegrationcompatibleTHzcomponentsisintroduced.Theprimary methoddevelopedistheuseofhigh-densitypolyethylenefocusingprobeswhichcanbeeasily fabricatedsothattheyarecompatiblewithcommercialTHzsystems.Theofthe probesaretheninvestigatedwhenusedwithasimplesilicon-baseddielectricwaveguide. Next,dielectricridgewaveguidesmadeofsiliconareinvestigatedforlowlossTHzwave propagation.Atheoreticaleindexmethodisappliedtodeterminethemodalprop- agationpropertiesofthewaveguidesaswellastheattenuationofthestructures.FEM simulationisalsocarriedouttoverifytheseresults.Variousridgewaveguidesmadeon siliconwafersareinvestigatedthroughmeasurementanddeterminedtoprovidelow-loss waveguidingpropertiesintheTHzspectrum.Thefocusisthenshiftedtothedesignof integrationcompatibleTHzThesearedesignedwithmulti-objective evolutionaryalgorithmscoupledwithFEMmodeling.Bandwidth,stopbandcharacteristics, multi-resonance,andotherpropertiesofthearedevelopedandimprovedthroughop- timization.ThearemeasuredusingacommercialTHzsystem,andshowntomatch wellwiththeoptimizedexpectations. Finally,anotherwaveguidingstructureisintroducedwhichisbuiltwiththin-metalperi- odicstructuresonsubstrates.ThesestructurestlyguideTHzwavesalong thesurfaceofthetexturedmetalstructures.Withthesestructures,otherpassiveTHzcir- cuits,suchaspowersplittersandsensors,arealsodeveloped.Thewaveguidingstructures, aswellaspowersplitter,aremeasuredinconjunctionwiththedielectricfocusingprobes developedpreviously,andshowtoprovidehightransmissionpropertiesatspdesign frequencies. Throughoutthisdissertationtwaveguides,andcouplingmethodsarein- troduced.Thesemethodsarecompatiblewithcurrentsemiconductorfabricationtechniques, enablingdevicerealizationdirectlyon-wafer.Inaddition,allofthepassivedevicesthatare developedaresimpletofabricate,aswellaslow-cost.Throughtheworkpresentedinthis dissertation,therealizationofpassivebuildingblocksforon-waferactiveTHzcircuitsare developed,whichinturnprovidesthepossiblerealizationofactiveon-waferTHzcircuits. ACKNOWLEDGMENTS IwouldliketothankmyadvisorDr.PremjeetChahal.Sincemeetinghim inECE405asanundergraduate,IhavelearnedmorethanIthoughtpossibleaboutelec- tromagnetics.Althoughattimeshemaybeataskmaster,hiscreativeanduniquevisions haveinspiredmewithnumerousresearchideasthatneitherInoranyoneelsecouldhave envisioned.WithouthisresearchguidanceandassistanceIcantrulysaythatIdonotknow whatIwouldbedoingwithmylife.Inadditiontoallofthis,Iwouldliketothankhim greatlyforgivingmetheopportunitytocompletemygraduatedegreeandwelcomemeinto theElectromagneticsResearchGroupatMichiganStateUniversity. Second,IwouldliketothankDr.EdwardRothwellforallofthemeaningfulandinsightful conversationswehavehadnotonlyaboutthisresearch,butalsoaboutmanyotherareas inelectromagneticsandlife.Whilehissarcasmissometimesthick,Ihavehadnothingbut positiveexperiencesworkingwithhim.Althoughheisnotmyadvisor,hehastreatedme withthesamerespectandhelpfulnessthathetypicallyreservesonlyforhisstudents.I wouldalsoliketothankDr.NelsonSepulveda,notonlyforhisexcellentsoftballplaying, butalsohisassistanceinmyresearchandforservingonmycommittee.Inaddition,Iwould liketoalsothankDr.AlejandroDiazfortakingthetimefromhisbusyscheduletobeon mycommittee,aswellassitthroughour\marathonEMsessions". Iwouldliketoalsoacknowledgeallofmyexcellentco-workersandfriendsintheEM group.Inparticular,IwouldliketothankXianboYangnotonlyforhisfriendship,butalso forhisknowledgeandhelpfulnessinthecleanroom.Withouthim,Ihighlydoubtthisthesis wouldhavebeenpossible.Inaddition,IwouldliketosincerelythankDr.RaoulOuedraogo fortheuseofhisGAoptimizationcodethatisthebasisoftheoptimizerusedinthiswork. Further,IwouldliketothankBenjaminCrowgeyforhisfriendshipandourfrequenttalks aboutsportsthatsuccessfullydistractedmefromcompletingthisthesisatanearlierdate. IwouldalsoliketothankJunyanTangforhishelpinsolderingconnectors,aswellashis iv manytang-isms.Lastbutnotleast,Iwouldliketothankmyformerco-workerDr.Jose Hejasefornotonlyhishelpwithmyresearch,butalsohisendearingfriendship.Without JoseIwouldneverhavecametoworkwithDr.Chahal.Idon'tthinkIcouldhaveever foundabettermentorandfriend. Mostimportantly,IwouldliketothankmywifeMelissaMyersforallhersupportand lovethroughoutthisprocess.WithoutherIwouldhaveneverknownmybeautifuldaughter SunshineandmyamazingsonShane.ForthisIwillbeeternallygratefultoher.Additionally, Iwouldliketothankherparentsandbrothersforputtingupwithmealltheseyears.Iwould alsoliketothankmyparentsBarbaraandDarrylMyers.WithoutthemIwouldobviously notbehere.TheirloveandsupporthashelpedmoldmeintothepersonIam,andIam extremelyluckytobetheirson. v TABLEOFCONTENTS LISTOFTABLES.....................................viii LISTOFFIGURES....................................ix CHAPTER1IntroductionandBackground.......................1 1.1TerahertzOverviewandBackground......................1 1.1.1RealizationofIntegratedTHzCircuits.................7 1.2CurrentResearchTopicsinTHzTechnologies.................9 1.2.1THzWaveguides.............................9 1.2.2THzCouplingMethods..........................16 1.2.3THzFilters................................19 1.3DissertationOverviewandObjective......................23 CHAPTER2CouplingMethods.............................26 2.1DielectricFocusingProbes............................26 2.1.1ProbeDesignSimulation........................26 2.1.2ProbeV.............................30 2.1.3ImplementationwithCommercialTHzSystems............31 2.2ErrorAnalysisandDiscussion..........................38 2.3ConclusionsandDiscussion...........................38 CHAPTER3DielectricRidgeWaveguides.......................40 3.1IntroductionandProposedGeometry......................40 3.2TheoreticalAnalysis...............................40 3.2.1EIMSolution...............................41 3.2.21-DSlabAnalysis.............................42 3.2.2.1TEEvenModes........................46 3.2.2.2TEOddModes.........................47 3.2.2.3NumericalAnalysis.......................47 3.2.3CompositeRidgeAnalysis........................53 3.2.3.1LosslessRidgeAnalysis....................53 3.2.3.2LossyRidgeAnalysis......................54 3.3FEMModeling..................................63 3.3.1CurvesandPassiveCircuits.......................69 3.4FabricationandMeasuredResults........................72 3.5ErrorAnalysisandDiscussion..........................77 3.6ConclusionsandDiscussion...........................78 CHAPTER4OptimizationofTerahertzFilters...............83 4.1OptimizationTechniquesinElectromagnetics.................83 4.1.1Calculus-basedOptimizationMethods.................84 4.1.2EnumerativeOptimizationSchemes...................87 vi 4.1.3RandomSearchAlgorithms.......................87 4.1.4GeneticAlgorithmOptimization.....................87 4.1.4.1FitnessFunctionsandChromosomes.............88 4.1.4.2VariableSelection.......................88 4.1.4.3Population...........................90 4.1.4.4Selection............................90 4.1.4.5Mating.............................91 4.1.4.6Mutations............................91 4.1.4.7ConvergenceandFutureGenerations.............92 4.1.5Multi-objectiveOptimization......................95 4.1.5.1NSGA-II............................95 4.1.6ApplicationsofGeneticAlgorithmsinElectromagnetics........98 4.2HFSS-MATLABOptimizationInterface.....................99 4.3FilterDesignandImplementation........................102 4.4ImplementationTestofNSGA-IIAlgorithm..................105 4.5FEMSimulationandOptimizationResults...................108 4.5.1SingleObjectiveOptimization......................108 4.5.2Multi-ObjectiveOptimization......................110 4.5.2.1OptimizationofBandwidthandStop-band..........110 4.5.2.2Multi-resonantOptimization.................113 4.5.2.3FilterImplementation.....................113 4.6MeasurementandFabrication..........................118 4.7ErrorAnalysisandDiscussion..........................122 4.8ConclusionsandDiscussion...........................122 CHAPTER5Plasmonic-InspiredPeriodicWaveguideStructures...........123 5.1IntroductionandProposedStructures......................123 5.2SimulatedResponseofSeveralPeriodicStructures...............123 5.3TheoreticalFloquetModeAnalysis.......................128 5.4LinearWaveguideAnalysis............................131 5.4.1Array...................................132 5.4.2TerahertzWaveguides..........................136 5.5ApplicationsInPassiveElementDesign.....................141 5.6FrequencyTailorableStructures.........................147 5.7FabricationandMeasurementResults......................155 5.7.1FabricationMethod............................155 5.7.2MeasuredResults.............................155 5.8ErrorAnalysisandDiscussion..........................162 5.9ConclusionsandDiscussion...........................162 CHAPTER6ConclusionsandDiscussion........................164 BIBLIOGRAPHY.....................................166 vii LISTOFTABLES Table2.1Calculatedvaluesforwaveguidecouplingandprobeloss.........33 Table5.1UnitCellDimensions...........................124 Table5.2CutFrequencies.............................130 Table5.3ModalCots( 1%notshown)..................130 viii LISTOFFIGURES Figure1.1Microwavetovisibleopticsfrequencyspectrum............2 Figure1.2Diagramoffemtosecondlaser-basedTHzsystem............3 Figure1.3CommercialTHzsystemsforthe(a)time-domain(b)frequencydomain.5 Figure1.4SomeofthecomponentsnecessarytorealizeTHzintegratedcircuits.8 Figure1.5Typicalofadielectricwaveguidewithhighpermittivity claddings.................................12 Figure1.6Plasmonosculationsoccurringnearametal-dielectricinterface...13 Figure1.7SpoofplasmonictypewaveguideforTHzfrequencies.........15 Figure1.8Semi-circularplasmonicgrooveusedforcouplingTHzradiationto plasmonicwaveguides..........................17 Figure1.9RectangularwaveguidesusedascouplerstoTHzwaveguides.....18 Figure1.10Filterbasedonmultipledielectricstacks................20 Figure1.11Periodicwoodpilebased.....................21 Figure1.12Overallobjectiveofthisdissertation..................25 Figure2.1Proposedcouplergeometryandsetup..................28 Figure2.2Thesimulatedelectricementin(a)horizontaland(b) verticalplanesinthedielectricprobe..................29 Figure2.3OnefabricatedprobeplacedinaEmcoreTHzsystemopticalhead..34 Figure2.4Transmissionbetweeneachprobewithincreasedprobespacing....35 Figure2.5Waveguidemeasurementsetup......................36 Figure2.6Summaryoftherequiredmeasurementsforprobeandcouplingloss calculations................................37 Figure3.1Proposedgeometryofthedielectricridgewaveguide..........43 Figure3.2eindexmethod..........................44 Figure3.3One-dimensionaldielectricslabgeometry................45 ix Figure3.4One-dimensionalnumericalslabsolutions................50 Figure3.5 ! vs. plotforvaryingmodesinaone-dimensionalslab......51 Figure3.6ofslabheightonthepropagationcharacteristics........52 Figure3.7ofvaryingridgewidthonthepropagationcharacteristicsof theridgewaveguide............................55 Figure3.8ofvaryingridgeheightonthepropagationcharacteristicsof theridgewaveguide............................56 Figure3.9Theoreticalattenuationofridgewaveguideversusfrequency.....58 Figure3.10Theoreticalattenuationofridgewaveguideat250GHzwithvarying ridgeheight................................59 Figure3.11Theoreticalattenuationofridgewaveguideat250GHzwithvarying ridgewidth................................60 Figure3.12ectsofchanginglosslessridgeheightonattenuationofthewaveguide.61 Figure3.13Theoreticalattenuationat300GHzofsiliconridgewaveguidewith variousridgeheightandwidths.....................62 Figure3.14Fieldinridgewaveguidewithvaryingridgeheightat300GHz.64 Figure3.15Fieldinridgewaveguidewithvaryingridgewidthat300GHz.65 Figure3.16Fieldinridgewaveguidewithvaryingdielectricbaseheightat 300GHz..................................66 Figure3.17Percentoftotalpowerleakedfromridgeasafunctionofthepermit- tivityoftheridgeat300GHz......................67 Figure3.18Simulatedattenuationofridgewaveguideat300GHzforvarying ridgeheightandwidths.........................68 Figure3.19Fieldinridgewaveguidecurveswithvaryingridgewidthat 300GHz..................................70 Figure3.20Fieldofcomplexridgewaveguidegeometriesat300GHz...71 Figure3.21Fabricationprocessforthesiliconridgewaveguide...........73 Figure3.22SEMphotographyofafabricatedridgewaveguide...........75 Figure3.23THzmeasurementsetupforsiliconridgewaveguides..........76 x Figure3.24Measuredtransmissionforridgewaveguideswith80 ridgeheight, withtwotridgewidths(normalizedpower)..........79 Figure3.25Measuredtransmissionforridgewaveguideswith40 ridgeheight, withtwotridgewidths(normalizedpower)..........80 Figure3.26Measuredattenuationofseveralridgewaveguides...........81 Figure4.1Localmaximumoffunctionf(x,y,z)..................85 Figure4.2Extendeddomainoffunctionf(x,y,z)showingmultiplemaximas...86 Figure4.3Samplediscretizedpixelgrid.......................89 Figure4.4Matingprocessinthebinarygeneticalgorithm.............93 Figure4.5Summaryofgeneticalgorithmoptimizationprocess.........94 Figure4.6NSGA-IIoptimizationprocess.....................97 Figure4.7GeneticalgorithmMatlab-HFSSinterfacewchart.........101 Figure4.8Proposedgeometry........................103 Figure4.9HFSSquetmodemodelingsetup...................104 Figure4.10AttainmentsurfacesfoundfromNSGA-IIalgorithm.........106 Figure4.11ConvergenceofNSGA-IItoZDT5testproblem............107 Figure4.12Progressionof j S 21 j throughGAgenerations..............109 Figure4.13SolutionsforP1objectivefunctionsafter30generations.......111 Figure4.14ProgressionofP1objectivefunctionsthroughGAiterations.....112 Figure4.15SolutionstoP2objectivefunctionsafter80generations........114 Figure4.16ProgressionofP2objectivefunctionsthroughGAiterations.....115 Figure4.17TwoparetofrontsolutionsfromtheP2objectivespace........116 Figure4.18TwoparetofrontsolutionsfromtheP1objectivespacecorresponding tomaximumtransmission(D1)andmaximumbandwidth(D2)...117 Figure4.19Fabricatedsamples.........................119 Figure4.20THzmeasurementsetupusedforthecharacterizationof...120 xi Figure4.21Measuredresults..........................121 Figure5.1Resonantunitcellstructures:a)circlestructure,b)dualcirclestruc- ture,c)crossstructure,d)minkowskifractal..............125 Figure5.2cotsofcircle-typeresonantstructures.......126 Figure5.3cotsofcross-typeresonantstructures........127 Figure5.4Designprocessofplasmonicwaveguides,progressingthrough(a)pe- riodicunitcell,(b)array,and(c)waveguide.......133 Figure5.5Powerwinboththex-andy-directionsalongthearray......134 Figure5.6Comparisonofpowerwinthey-directionof2x5and5x5circle arrays...................................135 Figure5.7SimulationtopologyanddesignprocessofTHzwaveguides......137 Figure5.8Powerwalongthesurfaceofthecrossandminkowskitypewaveg- uides...................................138 Figure5.9Powerwalongthesurfaceofthecirclestructuretypewaveguides.139 Figure5.10Angledependanceinboththe(a)cocientand(b)power wofthecircletypestructure.....................142 Figure5.11Bendingin(a)dielectricwaveguideat300GHz,(b)traditionalplas- monicwaveguideat300GHz,and(c)thinmetalbasedplasmonic waveguideat297GHz.Fieldtofapowersplitterisalso shown...................................143 Figure5.12Normalizedpowerwthrougheachsectionofthepowersplitter..144 Figure5.13Proposedsetupofthin-sampledielectricsensor.............145 Figure5.14Simulatedchangeinphaseoftransmissionthoughacircletypewave- guidewithvaryingsampledielectricconstant..............146 Figure5.15Geometryof(a)basiccirclestructure,(b)circlestructurewithholes (c)circlestructurewithmoreholes...................149 Figure5.16Recotsofthestructuresintroducedin5.15......150 Figure5.17Proposedstructureforoptimization..................151 Figure5.18Simulatedstructurewith(a)allpixelsonand(b)aselectedexample ofonetopologyafteroptimization...................152 xii Figure5.19Twooptimizedstructureswithresonancesat(a)120GHz,and(b) 275GHz.................................153 Figure5.20Recotofstructurespresentedin5.19.........154 Figure5.21Fabricatedwaveguide,powersplitter,andHDPEprobes.......156 Figure5.22Waveguidemeasurementsetup......................157 Figure5.23Measuredtransmissionspectraforcircletypewaveguidewith(a)fre- quencydomainsystem,(b)timedomainsystem............158 Figure5.24Measuredtransmissionspectraforcircletypewaveguidecompared withdielectricofsamedimensions....................159 Figure5.25Transmissionversuschangeinprobeplacementforthecircletype powersplitterat100GHz........................160 xiii CHAPTER1 IntroductionandBackground 1.1 TerahertzOverviewandBackground Theterahertz(THz)frequencyspectrumhaslongbeenoneoftheleastexploredsectionsof theelectromagneticspectrum.Typicallyfrom.1to30THz,theTHzspectrumlies inthefrequencygapbetweentraditionalmicrowavedevicesandoptics,asshowninFigure 1.1.Althoughsomeresearchersconsiderthelow-THzspectrum(100-300GHz)asmm-wave, inthisdissertation,100GHzandupwillbeconsideredthestartoftheTHzspectrum. Whiletherearemanyreasonsforalackofscienadvancementinthisarea,theabsence oft,eTHztechnologieshasbeenamajordetractorformanyyears[1]. Recently,therehasbeenatincreaseintheresearchcommunitytowardsdevel- opingTHzdevices[2]-[4].Thishasprimarilybeencausedbytheadvancesincommercially availableTHzsystemsandsourcesoverthelastdecade.Whileafewttypesof designtopologieshavebeendeveloped,thesesystemsareprimarilymadepossiblethrough thedevelopmentoffemtosecondlaserdevices.Byexcitingphotoconductivesemiconductor switcheswhichactasgateandpumplasers,mode-lockedfemtosecondlaserscanbeusedto generateTHzsignals[5]-[6]. Togeneratetime-domainTHzsignals,thelaserisincidentonabeamsplitterwhich 1 Figure1.1Microwavetovisibleopticsfrequencyspectrum. 2 Figure1.2Diagramoffemtosecondlaser-basedTHzsystem. 3 splitsthesignalbetweenamirror(thisactsasthepumplaser)andadelaytheoutput ofwhichactsasthegatelaser.Thepumplaserisusedtoexciteaswitchattheemitterofthe system,whichin-turngeneratesTHzradiationwhenthepumplaserison.Conversely,the gatelaserisusedtotriggerthereceiverswitchsothattheradiationcanbedetected.Avariety ofopticsandlensingcanbeusedattheemitterandreceivertogeneratefocused,collimated beam.Theblockdiagramofatypicaltime-domainTHzsystemintransmissionmodeis showninFigure1.2.Similarly,thesamesystemcanbeusedformeasurements withametalplaneplacedatthecorrectanglebetweentheemitterandreceiver.Typically, mostcommercialTHzsystemscanmeasurebetween100GHZand2.5THz.Bothfrequency andtime-domaincommercialTHzsystemsareshowninFigure1.3. ThankstotheseimprovementsinTHzsystems,thefrequencyspectrumhasdeveloped manycurrentandpotentialapplicationsinawidevarietyofareas.Thisspectrumisof- tenrichwithuniquematerialspectralts,makingitparticularlyadvantageousfor spectroscopy[7]andsensing[8].THzradiationisalsonon-ionizing,makingitsaferthan currentX-rayimagingtechnologiesforuseinmedicalapplications[9].Additionalareasof interestincludehighbandwidthcommunications[10],nondestructiveevaluation[11],and hiddenobjectdetectionforsecurityapplications[12]. SpectroscopyhashistoricallybeenaprominentapplicationoftheTHzregime[13].THz spectroscopyhasbeenusedforyearsinastronomytodiscoverthecompositionalmakeup ofstarsandothersolarsystems[14].THzspectroscopyhasalsobeenusedtoinvestigate proteins,DNA,andotherbio-moleculesbystudyingtheirfrequencyvibrationalmodes[15]. THzspectroscopyhasbeenusedheavilyinthepharmaceuticalindustry.Inparticular,[16] THzspectroscopyisusedforpolymorphicidenofdrugtablets.In[17],thecrys- tallinestructureofpharmaceuticalmaterialsisalsostudiedusingasimilartechnique.The temperaturedependanceofcarbamazepine(acommonanticonvulsant)isalsoinvestigated withpulsedspectroscopyin[18]. THzsensinghasalsobeenusedinmanyapplications.Duetothesmallwavelengthof 4 Figure1.3CommercialTHzsystemsforthe(a)time-domain(b)frequencydomain. 5 THzsignals,extremelysmallsamplesareabletobesensedaccurately.In[19],metamaterials operatingintheTHzfrequencyrangeareusedtodetectsamples.Additionally, THzsensinghasagainbeenusedinmanybiomedicalapplications,suchasdetectionofskin hydration[20],sensingincornealtissues[21],andmarker-freeDNAanalysis[22]. InadditiontothebiomedicalapplicationsofTHzsensing,THzimaginghasbeenwidely adoptedintissuecharacterizationandcancerdetection.Duetothenon-ionizingnatureof THzwaves,thesemethodsaresaferincomparisontoX-raysandcanthereforeberepeated asnecessary[23].Inparticular,duetothelowpenetrationdepthofTHzradiation,THz imagingiseasilyapplicabletotheskinandteeth.In[24],THzpulsedimagingisusedto detectcancerousgrowthinbreasttissue.Further,[25]usesTHzpulseimaging todetermineskincancergrowthintheupperlayerofskintissue.Inaddition,[26]uses 3Dimagingondentaltissuetodetermineattributesofteeth,suchasenamelthicknessand erosion. AnotherhugeareaofinterestintheTHzresearchcommunityistheuseofTHzdevices forhiddenobjectdetectionandsecurityapplications.Themostpopularoftheseapplications incurrentproductionisthemm-waveimagingboothsusedbytheTSA.mm-waveandTHz imagingisattractivefortheseapplicationsduetotheabundanceofmaterialsthataretrans- parenttoTHzradiation,suchaspaper,plastics,andmanyotherdielectriccomposites[27]- [29].ThisallowsTHzradiationtoessential'seethrough'concealingbarriers.Forexample, manyexplosives[30],[31],andillegaldrugs[32]havedetectablecharacteristicswhen exposedtoTHzradiation. Inadditiontohiddenobjectdetection,THzimaginghasbeenwidelyinvestigatedin thenon-destructiveevaluation(NDE)community.In[33],THzisusedforNDEofmetallic surfacestodeterminesurfaceroughness.Similarly,[34]usesTHzimagingforcorrosionof metalsbeneathpaintsurfaces. 6 1.1.1 RealizationofIntegratedTHzCircuits Intheprevioussection,theapplicationsofTHzradiationwasintroduced.Whilethese applicationsarenumerous,thereareserioussuccessfullyrealizingtTHz circuitsandsystems.Thisisduetoanumberofissues,butinparticularcurrentelectrical technologiesarenotcapableofcarryinglargefrequencysignalswithlowloss. Inaddition,currentTHzsystems,asshownintheprevioussection,arerelativelybulky andquasi-opticalinnature.ThismakestherealizationofcompactandtTHzcircuits torealize.However,theidealsolutionwouldbetocreatecompletelyintegrableTHz circuitsonthewaferlevelthataret,compact,andcostInorderforthis tobeaccomplished,anumberofbothactiveandpassivedevicesmustberealized. Manyactivedevicesmustberealized,suchastTHzdiodes,transistors, modulators,anddetectors,asshowninFigure1.4.However,beforethenecessaryactive devicesarerealized,tpassivebuildingblocksmustalsobedeveloped.Whileanumber ofpassivedevicesarenecessarytodevelopTHzintegratedcircuits,waveguidesandltering areofparticularimportance. Waveguidesin-particularareachallengeintheTHzspectrum,asmetalhas particularhighskin-depthlossesintheTHzspectrum.Thismakestraditionalwaveguides, suchasmicrostripsandstriplines,veryt.Therefore,THzwaveguidesmustbe basedondielectricorothernon-metalstructureswhichfurthercomplicatesthedesignpro- cess.Further,actuallycouplingTHzradiationintothewaveguides,especiallywithcurrent quasi-opticalTHzsystems,isespeciallycomplexandt.Thenextsectionofthis dissertationwillreviewsomeofthecurrentwaveguidingandtechniques,aswellas currentcouplingmethodsproposedintheliterature. 7 Figure1.4SomeofthecomponentsnecessarytorealizeTHzintegratedcircuits. 8 1.2 CurrentResearchTopicsinTHzTechnologies WhilethepreviousdiscussioncoverssomeofthemanyapplicationsofTHzradiationthat haverecentlybeenexplored,thissectionwilldelveintothreemoretechnicalaspectsofTHz researchthathavebeenpresentedintheliterature.Allthreeofthesesubsectionsareof particularimportanceintherealizationofmodernTHzcircuitsandsystems.First,THz waveguidesinthecurrentliteratureareexplored.Next,currentcouplingmethodsthatare usedtoexcitethewaveguidesusingmodernTHzsystemsarealsoinvestigated.Finally,mod- ernTHzareexploredaswellascurrentdesignmethodologiesandimplementations. 1.2.1 THzWaveguides Traditionalwaveguidingstructures,suchasmicrostriplinesand,striplines,andmetallic waveguideshavehighattenuationconstantsatTHzfrequencies[35].Thisleadstothe necessityforthedesignofTHzwaveguidesanddevicesthataremuchtthantheir RFandmicrowavecounterparts.DuetotheunavailabilityoftTHzwaveguidesand interconnects,THzcircuitshavebeenslowtodevelop. However,inrecentyears,anumberofalternativeTHzwaveguideshavebeenintroduced. Thesewaveguidedesignsrangefromtraditionalmetallic-typewaveguideswithuniqueaspects thatlowertheirattenuationconstants,tomuchmorenovelconceptssuchasmetamaterial andplasmonictypestructures.Inthissection,ageneraloverviewofmanydttypes ofTHzwaveguideswillbepresented,aswellassomeoftheproblemsassociatedwiththe currentlypresentedwaveguidedesigns. Initially,moretraditionalstructures,suchasthinwireswereinvestigated.Forexample, in[36]cylindricalwirewaveguidesareinvestigatedasTHzwaveguidesbyexcitingsurface wavesonthewire.Inthiscase,radiallypolarizedTHzradiationisincidentonthewire, withascatteringmechanismusedforinputcoupling. Anotherwirebasedmethodisshownin[37],whereTHzradiationiscoupledthroughonto 9 cylindricalwireswhichsupportloworderradialmodepropagation.Thesewaveguidesshow virtuallynodispersion,relativelylowattenuation,andarerelativelysimple.However,both ofthesewire-basedwaveguidesfrombeingtoimplement,andnotcompatible withintegration. Hollowcylindricalmetallicwaveguideswiththininnerdielectriccoatingshavealsobeen studiedforTHzwavepropagation,withthedielectriccoatingchosentobemuchsmaller thanawavelength[38]-[39].Thewaveguidesarecoatedwithdielectricsinordertoavoid someoftheskin-depthlossesthatthetraditionalmetalwaveguidesfromintheTHz region.Thewaveguideshowtheuseofbothsingleandmulti-layerdielectriccoatingsand aredesignedsuchthatthelow-losstransmissionofthe HE 11 propagatingmodeisexcited. Again,whilethesewaveguidesarecapableoftlytransmittingTHzradiation,theyare relativelybulkyandulttoimplement. Photonicbandgap(PBG)structureshavealsobeenstudiedindetailforTHzwavepropa- gation.In[40],twodimensionalPBGstructuresareimplementedwithTEMmodepropaga- tionwithinmetalparallelplatewaveguides.In[41],one-dimensionalphotonicmetalparallel platewaveguidesarepresented.Thewaveguidesaredesignedtooperateinaspectralregion of.5-3THz.Throughthisrange,thewaveguidehasahighthroughputwithupto40dBof dynamicrange. Othermetamaterialtypestructures,suchaselectronicbandgapmaterialsmadeofdi- electricstructureshavealsobeeninvestigated.In[44],concentriccylindricallyperiodicdi- electricsareusedtorealizelow-losspropagationintheTHzfrequencyspectrum.Inthiscase, mostofthepoweriscontainedwithintheaircoreregionofthecylinder,andapropagating TE 01 modeisexcited.AnotherEBGwaveguideisshownin[45],whereanall-dielectric waveguideisdevelopedthroughrapidpolymer-jetprototyping. Anotherrecentlyproposedsolutionisthedielectricribbonwaveguide.Dielectricribbon waveguideshavebeenshowntobetcarriersofTHzwavesbycontainingpropagating THzradiationprimarilyintheairabovethedielectric[49].However,ribbonwaveguides 10 largelossesatbendsorcurvesduetothenementoftheinthesurrounding area,makingthemnon-idealcircuitsandsystemswhichrequiresharpbendsorcomplex geometries.Recently,therehavebeenpromisingresultscoatingthedielectriccorewithhigh permittivitydielectricsinordertobettercontaintheinthecenterofthewaveguide [50].Figure1.5showsthegeometryandUnfortunately,includingthecladdingregionstends toincreasethefabricationcomplexityofthewaveguides. RibbonwaveguideshavealsobeeninvestigatedforTHzwavepropagationwhenmadeof semiconductormaterials.Typically,theseribbonwaveguidesdonotrequireextracladding materialsduetothehighpermittivitybetweenthesemiconductorandsurrounding air.Asanexample,in[51]-[52]highlyresistivesiliconisusedonaglasssubstratetocreate low-lossribbonwaveguidesupto500GHz. AnotherpromisingapproachforguidingTHzwavesisthroughsurfaceplasmonics.Sur- facePlasmons(SPs)arecoherent,wave-likeoscillationsoffreecharges,whichoftenresideat thesurfaceofmetal-dielectricinterfaces,asshowninFigure1.6.SPshavebeenexploitedat opticalwavelengthsfornumerousapplications[47]-[48].TheSPphenomenaisobservednear theplasmafrequencyofamaterial,whichinthecaseofametal,typicallyliesintheUV spectralregion.ThismakesSPsveryweaklytometalsintheTHzfrequencyspec- trum.However,theplasmafrequencyofmetalscanbealteredbyperiodicallytexturingthe surfaceofthemetal[60].Texturedmetalsurfaceshavebeenstudiedingreatdetailforthe designofTHzwaveguidesin[53]-[55].Thesemetal-dielectriccompositestructures supportso-called spoofplasmons . Acommonmethodoftailoringtheplasmafrequencyofametalinvolvesdrillinganarray ofholesalongthesurface,providedthattheperiodicitybetweentheholesismuchlessthan awavelength.ThistypeofplasmonicwaveguidehasbeenstudiedextensivelyintheTHz region[56]-[59].Thegeometryofsuchawaveguideisshownin1.7.Theeplasma frequencyofthetexturedstructurecanbedesignedbasedontheresonanceoftheindividual apertures[58].Infact,theresonanceofonecavitycanbeshowntobeexactly 11 Figure1.5Typicalrationofadielectricwaveguidewithhighpermittivitycladdings. 12 Figure1.6Plasmonosculationsoccurringnearametal-dielectricinterface. 13 equaltotheplasmafrequencyofthecompositestructure[60].Whiletheoperatingfrequency ofthesecompositemetalstructurescanbetailoredtoadesiredfrequency,theirpractical applicationislimited.Commonly,thesewaveguidesarebuiltdirectlyfrommetalsubstrates, whichdoesnotmakethemeasilyintegratedinTHzcircuits.Also,theassociatedfabrication requirementstocreatethesedevicesareexpensiveandnotreadilyavailable. WhilemanyoftheseproposedTHzwaveguideshavebeenshowntotransmitTHzra- diation,mostareeithertcomparedwithtraditionalRFmethods,orare toimplementwithintegrationlevelpackaginginTHzcircuits.Inthecaseofthemetallic wiretypewaveguides,itisrelativelyclearthatsimplewirescannotbeimplementedinmod- ernTHzsystems.WhilethehollowcylindricalwaveguidesintroducedalsoshowgoodTHz propagationcharacteristics,theyarerelativelybulky,andwouldalsobetoimple- mentinintegratedsystems.Similarly,PBGandEBGtypestructurescouldbeimplemented on-wafer,butthecurrentlyproposedstructuresaremostlybasedonmetallicwaveguides. Otherintroducedwaveguides,suchasthedielectricribbonwaveguide,andtheplasmonic typewaveguides,fromavarietyofproblems,suchascomplexfabricationrequirement andcurvaturelosses.ThisleavestheTHzresearchcommunityindireneedofintegration compatible,low-losswaveguidesandinterconnects. 14 Figure1.7SpoofplasmonictypewaveguideforTHzfrequencies. 15 1.2.2 THzCouplingMethods WhiletherehavebeenmanyadvancesinTHzwaveguides,actuallycouplingradiationef- tlyintowaveguideshasnotbeenwellexplored.TypicalTHzmeasurementsystems arequasi-opticalinnature,withhighspeederopticsandreceiver/transmittedheads. Thismakesthetransitionbetweenthemeasurementsystemanddesiredwaveguide especiallywhenthewaveguideisplanarorintegrated. ManyofthecurrentlyproposedTHzwaveguidesaretoimplement,inconvenient, orcomplexcouplingmethods[62].Infact,manycurrentlyproposedwaveguideshavesimply non-existentcouplingmethods,andareinvestigatedonlytheoreticallyorthroughsimulation, andthenmeasuredatmuchlowerfrequenciestobeusedforaproofofconcept[63]-[64].For example,in[63],plasmonicTHzwaveguidesareinvestigatedatTHzfrequencies,andthen scaledtomuchlowerfrequenciesofoperationandmeasuredwithsimpleSMAconnectors. Othercouplingmethodshavebeensuggested,butingeneralhavebeenverycomplexand mostlyt.In[56],aplasmonicsemi-circlegrooveisusedtotocoupleincomingTHz radiationontoasimilarlyconstructedplasmonicwaveguide.Thesignalisthenmeasured alongthesurfaceofthewaveguidewithaZnTecrystaldetector.Thismethodonlyprovides aonewaycouplingmethod,asthesignalispickedupwiththedetector.Also,thismethod istoimplementandveryt.Theoverallsetupofthecouplingmethodis illustratedinFigure1.8. Anothermethodisshownin[51],wheresilicondielectricwaveguidesaremeasuredin thelowTHzfrequencyrange.Thewaveguidesaremeasuredusingacombinationoftwo metallicrectangularwaveguidesactingasthelaunchpoints,withthedielectricwaveguide placedinthemouthofeachwaveguide.Whilethistlyactsasacouplingmechanism tothedielectricwaveguide,itisrelativelytoimplementinareal-worldsystem.The overallsetupofthiscouplingmethodisshowninFigure1.9. 16 Figure1.8Semi-circularplasmonicgrooveusedforcouplingTHzradiationtoplasmonic waveguides. 17 Figure1.9RectangularwaveguidesusedascouplerstoTHzwaveguides. 18 1.2.3 THzFilters AnadditionalcomponentofgreatinterestintheTHzresearchcommunityareelectromag- neticInthiscase,avarietyofarenecessary,includinghigh-pass,low-pass, andband-passHowever,typicalTHzareprimarilybasedonopticsdesigns. Thismakesthemrelativelybulky,tomeasure,andnotintegrationcompatible.In thissection,somecommonopticalbasedandothercurrentlyproposedTHzare reviewed. ManytypesofltershavebeendemonstratedtoworkwellabovetheTHzfrequency rangeinavarietyoffashions.Typicaloptics-basedrelyonstackedlayersofdielectric toachieveadesiredresponse[65]Forexample,glasspiecesstaggeredbyaquarter wavelengthbetweenlayerscanbeusedtocreatebandpassThepropertiesofthe reprimarilybythethicknessofeachglasslayer,aswellthedielectricconstantof thematerial.TheimplementationofthisisshowninFigure1.10. Anotherpopularlyusedopticalstructureisa3Dphotoniccrystalbasedwithacomplete bandgapatthemicronscalewasdesignedin[66].Thisstructureissimplyaseries ofstackedlogsintdirections,calledawoodpile.Thegeometryofsuchastructure isshowninFigure1.11.Basedonthethicknessofthelogs,thematerialtheyarecreated from,andtheamountoflogsinthestack,thepropertiesofthestructurecanbeusedto createaringmechanism.ThishasbeenexploredrecentlyintheTHzspectrumaswell. In[67],a3Dprintedwoodpilestructureiscreatedwhichactsasastrongbandstop Thepotentialforthetoalsobeusedasasensorbychangingthedielectricconstant insidethewoodpileisalsodiscussed. In[68],aTHzbasedonacompositemetal-dielectric-metalstructureisintroduced. Theareprimarilyusedfortheirstop-bandcharacteristicsintheapplicationofband- passDuallayerstructuresarealsoinvestigatedtoimprovetheproperties. Thisisstudiedprimarilythroughsimplecascadinganalysis,andtuningofthe 19 Figure1.10Filterbasedonmultipledielectricstacks. 20 Figure1.11Periodicwoodpilebaseder. 21 bandwidthandcenterfrequencyisinvestigatedbymodulatingtheparametersofthestruc- ture. Theworkpresentedin[69],atriple-channelTHzisintroducedwhichiscapableof multi-resonanceintheTHzspectrum.Theisbasedonasiliconmulti-cavityresonant systemthatisexperimentallyinvestigatedusingabackwardwaveoscillator.Thethree resonancepeaksintheareanalyzedandtheisdeterminedtocomefromaFabry- Perotresonancecausedbythickcavitiesinthestructure,whiletheothersarecausedby couplingintothetwocentralcavities. OthermoreexoticsolutionsforTHzhavealsobeendeveloped.Similartothe waveguidesshownearlier,plasmonicbasedstructureshavealsobeenshowntoactase intheTHzregion[70]-[72].Forexample,In[73],aplasmonichighpassis designedbyengineeringthedielectricpropertiesofathin-wirelattice.Inthiscase,thehigh- passpointoftheisdesignedtobethetransitionpointbetweenapositiveandnegative dielectricconstant,knownastheplasmafrequency.Atthisfrequency,asharpchangeofthe andtransmissioncotsmakethestructureahigh-passThisallowsthe authorstoachievehigh-passcharacteristicswellabove0.7THz,withatwodimensional cubiclattice. In[74],amulti-bandTHzisproposedbyutilizingthepositiveandnegativerefractive indicesofaphotoniccrystalprism.Inthiscase,apassbandisimplementedwitha prismformedfroma2Dhexagonalarrangementofmetallicrods.Theisabletooperate overanapproximatebandwidthof250GHz,startingat1THz. MetalholearrayshavealsobeenstudiedtoprovideverylargebandwidthTHz whenstackedinmultiplelayers.In[75],aTHzwidebandbasedonadoublelayerof metalholesisdeveloped.Thisiscreatedbysimplyperforatingametallayerwithcircular airholes.Thetransmissioncharacteristicsofthearedeterminedbytheaccumulation ofscattingandplasmonpolarations.Overall,thehasacenterfrequencyof.8THz, witharelativelywidebandwidthof400GHz. 22 TunableTHzltershavealsobeeninvestigatedintheliterature[79]-[80].In[81], anopticallycontrolledTHzispresentedwhichexploitstheelectron-holepairsina semiconductorquantumwelltoattenuateTHzfrequencycontent.Thisisaccomplishedin amixedGaAS/AIAsmultiplequantumwellsample.Inthiscase,thetransmissionspectra isabletobecontrolledoverawidefrequencyrangefortunable Anothersolutionisshownin[82],whereathermallytunablebasedonasimplepho- toniccrystalstructureispresented.Theisbasedonasmalltransmissionband,which originatesfromasmalldefectmodethatappearsinoneofthecrystals.Thisallows fortuneabilityofapproximately20%overawiderangeintheTHzfrequencyspectrum. However,alargetemperatureswingisrequiredtotunethetertly. Whiletheaboveltersworkwellasstandalonecomponents,theyrequirecomplexfabri- cationstepsanddesignprocedures.Spe,theyarerelativelybulky,andwouldnotbe compatiblewithintegrationlevelprocessingatthewaferlevel.Whiletherehasbeensome movementintheresearchcommunitytocreateTHzcomponentdesignsthatarecompati- blewithwafer-levelintegration[76]-[77],aresptoachieve.Thisis primarilybecausethTHzinthecurrentliteraturedonotdisplayaslargeofa rejection/acceptanceband,norhavetheybeenshowntobeaseindesign[78]. 1.3 DissertationOverviewandObjective Torealizeanymodernintegratedelectricalsystem,anumberofpassivecomponentsare necessary.Inparticular,waveguidesareneededtoactasinterconnectsbetweenmanyof theactivecomponentswithinthesystem.Inaddition,amethodofcouplinganexcitation intothewaveguidescientlyisnecessary,weatheritisasimpleSMAconnectoratlower RFfrequenciescouplingintoamicrostrip,oralasercouplingintoaeropticscablein theopticalspectrum.Finally,anumberofhigh-,low-,andband-passarenecessary bothforeliminationofnoise,butalsotocontrolunwantedharmonicsandotherEMCissues. 23 Asshownintheprevioussections,manyTHzandwaveguideshavebeendeveloped. However,theyarenoteasilyfabricated,measured,oraretheyintegrationcompatiblewith modernsemiconductorwaferlevelfabrication. InthisDissertation,THzwaveguides,andcouplingmethodsaredevelopedwhich arecompatiblewithmodernsemiconductorwaferlevelintegration.Thisoverallobjectiveis illustratedinFigure1.12.Chapter2introducesmethodsoftlycouplingTHzradiation betweencommercialquasi-opticalTHzsystemsandintegrationcompatibleTHzcomponents. Thesemethodsincludeover-modedwaveguidecouplers,couplingbetweenwaveguidingstruc- tures,anddielectricfocusingprobes. Chapter3investigatestheuseofdielectricridgewaveguidesmadeofsilicon.Atheoretical eindexmethodisappliedtodeterminethemodalpropagationpropertiesofthe waveguidesaswelltheattenuationofthestructures.FEMsimulationisalsocarriedout toverifytheseresults.Variousridgewaveguidesmadeonsiliconwafersareinvestigated throughmeasurementanddeterminedtoprovidelow-losswaveguidingpropertiesinthe THzspectrum.Chapter4thenfocusesonthedesignofintegrationcompatibleTHz Thesearedesignedwithmulti-objectiveevolutionaryalgorithmscoupledwith FEMmodeling.Bandwidth,stopbandcharacteristics,multi-resonance,andotherproperties oftheThearemeasuredusingacommercialTHzsystem,andshowntomatch wellwiththeoptimizedexpectations. Finally,chapter5introducesanotherwaveguidingstructurebuiltwiththin-metalperiodic structuresonsubstrates.ThesestructurestlyguideTHzwavesalongthe surfaceofthetexturedmetalstructures.Withthesestructures,otherpassiveTHzcircuits, suchaspowersplittersandsensors,aredeveloped.Thewaveguidingstructures,aswellas powersplitter,aremeasuredinconjunctionwiththedielectricfocusingprobesdevelopedin chapter2,andshowtoprovidehightransmissionpropertiesatspdesignfrequencies. 24 Figure1.12Overallobjectiveofthisdissertation. 25 CHAPTER2 CouplingMethods Inthischapter,methodsofcouplingbetweenmodernTHzsystemsandthewaveguidesand otherdevicespresentedwithinthisthesisareestablished.Amethodofcouplingbetweena THzsourceandwaveguideisimplementedbytheuseofdielectricfocusingprobesplaced betweenthetransmitterandreceiversofthesystemandthewaveguides.Theprobesare theoreticallyinvestigatedthroughsimulation.Inaddition,themeasuredcharacteristicsof theprobesareinvestigated,andtheprobesareshowntoworktlyinaTHzwaveguide measurement.Theseprobesarethenusedthroughouttherestofthisdissertationtocouple intootherdevices,particularlyinchapter3and5. 2.1 DielectricFocusingProbes 2.1.1 ProbeDesignSimulation ThedielectricprobesproposedinthisworkaremadeofHighDensityPolyethylene(HDPE). HDPEpossessesverylowlosspropertiesintheTHzspectrum,withatypicaldielectric constantof r =2 : 4andtan =0 : 01at300GHz[117].Theprobedesignbuildsupon thedemonstrationofwidebanddielectricprobein[ ? ].Theprobesarecomprisedofthree primarysections:aplano-convexlens,cylindricalfocusingregion,andtaperedcone.The 26 sectionoftheprobe,theplano-convexlens,ensuresproperwavepolarizationandfocuses thewavetoapointinthesubsequentcylindricalregion.Thecylindricalfocusingregionis followedbythetaperedcone.Thetaperingoftheconeisprimarilyresponsibleforthe focusingoftheprobeatitstip.Basedonthetaperdesign,thefocalpointofthe probecanbeadjusted.SincetheprobesareintendedtobeusedascouplersbetweenaTHz systemandwaveguide,theprobesaredesignedsothatthefocalpointisdirectlyatthetip. Figure2.1showsthegeometryofasampleprobeaswellastheproposedsetupwhenused toprobeaTHzwaveguide. Toensuretheiswellwithintheprobeandthatthefocalpointoftheprobe isnearthetip,asmallsectionoftheprobeencompassingtheregionclosesttothetipofthe probeissimulated.Inthiscase,thecommercialFEMsolverHFSS15.0isused.Only asmallsectionissimulatedastheentireprobeismanywavelengthslong,andtherefortoo largetobefullymeshed.Theinboththelateralandverticaldirectionsthroughoutthe probeandthesurroundingareaisshowninFigure2.2.Clearly,theiswellto theprobeinboththeverticalandhorizontalplanes,withtheonlypenetrationnearthe tipoftheprobe.Also,theishighlylocalizednearthetipoftheprobe,that thefocalpointisdirectlyatthetip. 27 Figure2.1Proposedcouplergeometryandsetup. 28 Figure2.2Thesimulatedelectrictin(a)horizontaland(b)verticalplanes inthedielectricprobe. 29 2.1.2 ProbeV Aquasi-opticalTHzmeasurementsetupisusedtocharacterizetheprobes.TheTHzsignal isgeneratedusinganEmcorePB-7200commercialfrequencydomainsystem.Thissystem ismadeupofreceiver(Rx)andtransmitter(Tx)headsthatareinterfacedwithsources througher-optics.ThesystemiscapableofmeasuringtransmissionbetweentheRxand Txheadsfrom0.1to2THz,withafrequencyresolutionof100MHz.TheRxandTxheads arecapableofbeingmovedonarailingsystemseparatingeachopticalhead.Theprobes arefabricatedbytakingalongHDPErodandmachiningthegeometryoftherodtothe probedesign.Theprobesarethenfurthersharpenedusingsandpaperalongthetapered conesection.Anadapterisalsofabricatedusing3-Dprintingsothattheprobecanbe directlyintotheTHzsystemreceiver/transmitterhead.Thefabricatedprobeinsertedinto thecouplerandinterfacedwiththereceiveroftheTHzsystemisshowninFigure2.3. Toensuretheprobesbehaviormatchesthatpredictedbysimulation,thetransmission betweeneachprobeismeasuredatvariousdistances.TheTHzsystemmeasuressignal powerinarbitraryunitsbetweentheTxandRxopticalheads.Therefore,theexactpower transmittedthroughthesystemisunknown,butcomparisonsbetweenmeasurementscan bemade.First,theprobesarealignedtip-to-tip,suchthatallthepowerisdirectlycoupled througheachprobe.Theprobesarethenslidalongtherailingandthetransmissionis recordedwithspacingsof1,2,and3cmbetweentheprobetips.Figure2.4showsacontinuous measurementoftheprobe-to-probetransmissionofthesystemateachprobespacingfrom 100to300GHz.Clearly,whentheprobesareplaceddirectlytip-to-tip,thetransmission throughthesystemislargest.However,whendistanceisintroducedbetweentheprobetips, thesignalisdecreased.Thisthatthefocalpointoftheprobesisdirectlyatthe tip,asexpected,giventhatpowerfallswithincreaseddisplacement. 30 2.1.3 ImplementationwithCommercialTHzSystems Now,toinvestigatethepotentialoftheprobesinwaveguidecoupling,thesystemis withaprobeinboththeRxandTxheads.Theprobesarethenalignedwiththewaveguide suchthatthetipsaredirectlytouchingthewaveguideedges.Inthiscase,asimpledielectric ribbonwaveguideisusedastheTHzwaveguide.Thiswaveguideismadefromsilicon,with athicknessof250 andawidthof1mm.Moredetailsonthedesignofsimilarribbon waveguidesfortheTHzspectrumcanbefoundin[92].Theoverallmeasurementsetupof thewaveguideprobingsystemisshowninFigure2.5. Inordertocharacterizethewaveguidecouplingmethod,thelossduetothecouplers,as wellasthelossduetothecouplingintothewaveguide,areofparticularinterest.Tothe lossesassociatedwiththeseanumberofTHzmeasurementsmustbetaken.First, areferencemeasurementwithnothingbetweentheTxandRxheadistaken.Thedistance betweentheheadsaswillbeneededtocontainbothprobesandthedielectricwaveguide wasused,yieldingthetotalsystempower P t .Next,ameasurementofbothprobesinthe tip-to-tipisperformed,whichproducesthetotalpowerofthesystemwithboth probesinplace,called P pr .Finally,ameasurementwithbothalongandshortdielectric waveguideisperformed,whichcanbeusedtocalculatethelossesofthewaveguidewith noneofthecouplingrefereedtoas P WL and P WS ,respectively.Inthiscase,a waveguidelengthof1and2cmisused.Asummaryofthesefourmeasurementsisshown inFigure2.6. Eachoftheabovemeasurementsisnecessaryinordertoperformaseriesofcalculations todeterminethelossofthesystemcoupledwiththeprobesandawaveguide.Assumingthe totallossofthesystemisonlyduetothelossintheprobes,thelossinthewaveguide,and thecouplingloss,thetotallossofthesystemcanbewrittenas: L t = L pr + L W W l + L CL (2.1) 31 where L t isthetotalloss, L pr isthelossduetothetwoprobes, L W isthewaveguide loss(inloss/distance), W l isthewaveguidelength,and L CL isthelossduetocoupling. Sincethemeasuredpowerisinarbitraryunits,thementionedlossescanonlybefound asapercentageofthetotalpower.FromthemeasurementsetupsshowninFigure2.6, eachlosscanbedeterminedfromtherelativepowerreadings.Theprobelosscanbefound fromdividingthepowerwiththeprobesinplacebythetotalpower,whichisshownin equation2.2. L pr =1 P pr P t (2.2) Thisyieldstotwowayprobeloss,meaningthatthelossduetoeachprobeisactuallyhalf of L pr .Thelossduetothewaveguidecanbefoundbydividingthetransmissionthrough the2cmwaveguidebythetransmissionthroughthe1cmwaveguideasfollows. L W =1 P WL P WS (2.3) Thisleavesthewaveguidelossinpercentimeter,asthecebetweenthewaveguide lengthswas1cm.Thetotallossinthesystemwithboththewaveguideandcouplersin placecannowbeastheshorterwaveguideisexactly1cmlong.Thetotallossof thesystemisthen P WS dividedbythetotalsystempower. L t =1 P WS P t (2.4) Thetwo-waycouplinglosscanthenbefoundbysubstitutingequations2.2-2.4back intoequation2.1andsolvingfor L CL .Again,thecorrespondingone-waycouplerloss canbefoundbydividingthisvaluebytwo.Table2.1showsthevariousarbitrarypower measurementsandlossesdiscussedabovefor100,200,and300GHz.Clearly,atthelower frequenciesthetotallossisrelativelylow,withonlya14%lossduetotwowaycoupling,and alowlossforboththeprobesandwaveguide.However,asthefrequencyisincreased,the 32 Table2.1Calculatedvaluesforwaveguidecouplingandprobeloss. f(GHz)100200300 P t 1x10 7 7.21746x10 7 5.12385x10 7 P pr 7.96358x10 7 5.57332x10 7 3.75581x10 7 P WL 4.42376x10 7 1.07248x10 7 1.21856x10 7 P WS 5.63175x10 7 1.712496x10 7 2.07195x10 7 L W 21.45%37.37%48.18% L pr 20.36%22.78%26.70% L cl 13.95%16.12%20.63% waveguidelossisgreatlyincreased,butthecouplingandprobelossarerelativelystable.In thiswork,weareprimarilyinterestedinthecouplingandprobeloss,andnotthewaveguide loss,asonlyasimpledielectricribbonwaveguidewasusedinthiswork.Itisalsoobserved thatallotherlossesnotincludedinthewaveguideandprobesareessentiallybuiltintothe couplingloss.Theselossescouldincludelossduetomisalignment,andmany otherfactors.Therefore,thereportedcouplinglossisactuallyhigherthantheactualloss duetothewaveguidecoupling. 33 Figure2.3OnefabricatedprobeplacedinaEmcoreTHzsystemopticalhead. 34 Figure2.4Transmissionbetweeneachprobewithincreasedprobespacing. 35 Figure2.5Waveguidemeasurementsetup. 36 Figure2.6Summaryoftherequiredmeasurementsforprobeandcouplinglosscalculations. 37 2.2 ErrorAnalysisandDiscussion ForthismethodofcouplingTHzradiationbetweenthecommercialopticalsetupusingdi- electricfocusingprobes,someerrorwilloccurduringthemeasurement.Whiletherehas beensomediscussionofTHzmeasurementerror[93],duetothecomplexsetupofthemea- surementsystemandprobes,someerrorisexpectedtooccur.Manyfactorscancontribute tothis,beginningwiththealignmentofthefocusingprobestotheTHzoptics.Fornearly everymeasurement,somealignmenterrorisexpected.Thealignmentoftheprobetipswith themeasureddevice(inthiscase,thedielectricribbonwaveguide)isalsotoquantify. Additionally,thefrequencydomaintestsetupusedintheseexperimentshassomeerror withinthesystem.Thisprimarilycomesfromtheheatingandcoolingofthelaser,which controlswhatfrequencytheoutputTHzradiationoccurs.Inthiscase,asthelaserisheated, thefrequencyisincreased,andasitiscooled,itisdecreased.Theproblemoccurswhen multiplemeasurementsaretaken,thetemperatureofthelaserwillnotbeexactlythesame asitwasinthepreviousmeasurement,makingthefrequencynotidenticalandintroducing someerrorintotheresults.Overall,theexpectederrorbetweenmeasurementsislikelyto benogreaterthan10%,whichiswithintheexpectationssetinthecurrentliterature. 2.3 ConclusionsandDiscussion Inconclusion,thischapterexploredthedevelopmentofanexperimentalmethodofcoupling betweencommercialTHzmeasurementsystemsandcommonTHzwaveguidesusingdielec- tricfocusingprobes.TheprobebehaviorisvalidatedboththroughFEMsimulationaswell asmeasurement.Overall,themethodproducesaone-waycouplinglossintoadielectric ribbonwaveguideaslowas7.2%,andatwowaycouplinglossof21%.Thesevaluesshow relativelylowlosscouplingmaybeachievedevenintheTHzspectrum,withpotentialappli- cationsinnearlyeverypassiveTHzsystemthatrequireswaveguiding.Thischapterswork 38 willbeusedthroughouttherestofthisthesiswhenmakingTHzmeasurements,especially forwaveguidingapplications. 39 CHAPTER3 DielectricRidgeWaveguides 3.1 IntroductionandProposedGeometry Awaveguidewhichisplanaraswellasdirectlycompatibleinon-waferintegrationwould beverydesirableintheTHzfrequencyspectrum.ApossiblemethodofguidingTHzwaves onwaferwouldbetodirectlyfabricatethewaveguideonthewaferitself.Thiscanbe accomplishedwithridgeorribwaveguides,whichhavebeenusedextensivelyintheoptical frequencyspectrum,containingabulkdielectricwithathintoplayerridge[83]-[86],show ininFigure3.1.Typicallymadeofglassorotherdielectricmaterials,ridgewaveguidesdo notrequireanyofthedielectriclayerstobemuchthinnerthanawavelength.However, ridgewaveguideshavebeenlittleexploredintheTHzspectrum,outsideofverysp applications,suchasquantumcascadelasers[87]-[89].Inthischapter,ridgewaveguidesare evaluatedthroughtheoreticalcalculations,simulation,andmeasurementfortheirapplication asTHzwaveguides. 3.2 TheoreticalAnalysis Unfortunately,theboundaryconditionscannotbeanalyticallyfortheridgewave- guide,meaningananalyticaltreatmentofthisproblemisnotpossible.However,approx- 40 imatesolutionsforproblemsofthistypehavebeenwellexploreintheliterature[90]-[91]. Inthiscase,theeindexmethod(EIM)willbeusedtoapproximatethesolutions oftheridgewaveguide.TheEIMhasbeenwidelyexploredintheopticalregion,however, therearecertainassumptionsthatmustbemadebeforethismethodisapplied.Thebulk oftheassumptionscontainedwithintheEIMmethodisthatatwo-dimensionalstructure mustbeapproximatedasaseriesofone-dimensionalstructures.Intheopticalspectrum, mostoftheexploredstructuresaremuchlargerthanawavelength,makingthisassumption valid.However,inthecaseoftheridgesizesthatwillbeusedinthisanalysisfortheTHz spectrum,theridgedimensionsareclosertotheorderofawavelength. Therefore,theEIMsolutionisonlyusedtoobtainageneralunderstandingoftheprop- agationcharacteristicsofthewaveguide.Thisincludestheattenuationofthewaveguideas wellasthe ! propagationcharacteristics.Beforetheconclusionsaretakenfromthe EIMsolutions,thesecharacteristicsareandcomparedto3-DFEMsimu- lationtoensuretheassumptionscontainedwithintheEIMsolutionisstillvalidatthese frequencies. 3.2.1 EIMSolution Theeindexsolutionmethodcanbeusedtosolvemanydielectric-basedwaveguide problems.Inthismethod,theproposedwaveguidegeometryisreducedtoanumberof 1-Ddielectricslabswhichcaneasilybeanalyzedusingconventionalmethods.Thee refractiveindex(ordielectricconstant)canbededucedfromeach1-Dwaveguidefromthe propagationconstantoftheslab.Then,theeparametersareusedasparametersfor a1-Dslabwhichconstitutestheesystem.Inthecaseofthedielectricridge waveguide,thegeometryisbrokendowninto4one-dimensionalslabs.Twoslabscorrespond totheareasontheedgeoftheridge,andonecorrespondstotheridgeitself.Thee indicesofthesethreeregionsarethenusedtoformacomposite1-Dslab,whichtakesinto accountthewidthoftheridge.TheoverallprocessandgeometryissummarizedinFigure 41 3.2. 3.2.2 1-DSlabAnalysis Inthissection,theone-dimensionalanalysisofaslabwaveguideispresented.Theslabis madeofacoreandcladdingsection,withpermittivityof C and CL ,respectively.Theslab hasathicknessofh,withtheoriginplacedatthecenteroftheslab.Figure3.3showsthe geometryofthe1-Ddielectricslab.Assumingtheslabisinthey-andz-directions, withthewavepropigationoccurringinthez-direction,thedependanceoftheEandH inthey-directionisnegligible( d=dy =0).Thewaveequationinthiscaseisthen ( r 2 + ! 2 ) ~ E =0(3.1) forTEpolarization,theelectriconlyhasay-component,leadingtothefollowing expressionfortheelectric ~ E = E y ( x;y;z )^ y = E y e jz ^ y (3.2) ThemagneticeldisfoundthroughtheMaxwell'sequation r X ~ E = j! ~ H (3.3) r X ~ H = j! ~ E (3.4) whichgivesthefollowingrelationforthemagnetic ~ H = 1 0 ( jE y ^ x + dE y dx ^ z ) e jz (3.5) Byplacingtheoriginatx=0,thesymmetryofthestructureisexploitedtoeven andoddmodesolutionsforthe 42 Figure3.1Proposedgeometryofthedielectricridgewaveguide. 43 Figure3.2eindexmethod. 44 Figure3.3One-dimensionaldielectricslabgeometry. 45 3.2.2.1 TEEvenModes TheelectricdfortheTEevenmodescanbeexpressedas E y ( x )= 8 > > > > > > < > > > > > > : C 0 e y ( x h= 2) ;x h= 2 C 1 cos( y x ) ;h= 2 x h= 2 C 0 e y ( x + h= 2) ;x h= 2 (3.6) where C 0 and C 1 areunknownconstants.substitutingthesesolutionsbackintoequation1, yieldsthefollowingrelation. 2 y + 2 = ! 2 0 0 n 2 f = ! 2 c 2 n 2 f = k 2 0 n 2 f (3.7) 2 y + 2 = ! 2 0 0 n 2 cl = ! 2 c 2 n 2 cl = k 2 0 n 2 cl (3.8) Applyingtheboundaryconditionsontheedgeoftheslab(continuityoftheEandH yields C 0 = C 1 cos( y h= 2)(3.9) y 0 C 0 = y 0 C 1 sin( y h= 2)(3.10) settingtheseequationstozeroyieldsatranscendentalequationintermsofthepropagation constantasfollows. y = y tan( y h= 2)(3.11) 46 3.2.2.2 TEOddModes TheelectricdfortheTEoddmodescanbewrittenasthefollowing. E y ( x )= 8 > > > > > > < > > > > > > : C 0 e y ( x h= 2) ;x h= 2 C 1 sin( y x ) ;h= 2 x h= 2 C 0 e y ( x + h= 2) ;x h= 2 (3.12) Applyingtheboundaryconditionsandeliminatingfor C 0 and C 1 yieldsasimilartran- scendentalequationforthepropagationconstantasinthepreviousanalysis,shownbythe following. y = y cot( y h= 2)(3.13) 3.2.2.3 NumericalAnalysis Thepropagationconstantscannowbefoundnumerically,butifequation6and7are subtractedandmultipliedby( h= 2) 2 ,thefollowingrelationshipisfound. ( y h= 2) 2 +( y h= 2) 2 = ! 2 0 0 ( n 2 f n 2 cl )( h= 2) 2 =( k 0 h= 2) 2 ( n f n cl ) 2 (3.14) Thisequationcanbewrittenintheformofacircle,withnormalizedcoordinates X = y h= 2, Y = y h= 2.Therefore, ( X ) 2 +( Y ) 2 ==( k 0 h= 2) 2 ( n f n cl ) 2 = R 2 (3.15) where R = k 0 h= q n 2 f n 2 cl .Theintersectionpointsbetweenthiscircleandequations12 and10willthengivethepropagationconstantsoftheslabforTEoddandevenmodes, respectively. 47 Figure3.4One-dimensionalnumericalslabsolutions. 48 Figure3.5 ! vs. plotforvaryingmodesinaone-dimensionalslab 49 Figure3.6ofslabheightonthepropagationcharacteristics. 50 Figure3.4showsthegraphicalrepresentationoftheintersectionsbetweentheabove circleandthecharacteristicequationsfortheTEoddandevenmodes.Forthisslab,aslab thicknessof h =3 mm , c =2 : 56and c l =1areused.Clearly,theintersectionpointsvary dependingontheinputfrequency.However,thesamecanbesaidwhenthethicknessofthe slab,orthepermittivityoftheslaborsurroundingstructureischanged.Inaddition,the modesexcitedwithintheslabwillvarydependingonthesameparameters.Inthiscase,at thehighestfrequency(40GHz)onlythe m =0and m =1modesareexcited. Withthisgraphicalsolution,thepropagationandattenuationconstantsaresolvedfor inthey-direction.However,thepropagationinthez-directionisdesired.Usingasimple dispersionrelation 2 z = 2 C 2 y = ! 2 C C 2 z (3.16) orintermsoftheattenuationconstant 2 z = 2 y + 2 0 = 2 y + ! 2 0 0 (3.17) where C isthepropagationconstantinthedielectricregion.Usingthedatafromthe graphicalintersectionsandequation15,thepropagationconstantinthez-directionfora 1-Dslabcanbefound.Usingthesevalue,thepropagationcharacteristicsoftheslabcan bededucedintheformofan ! vs plot.Figure3.5showssuchaplotforaslabwitha thicknessof4 mm , C =2 : 56,and CL =1.Thepropagationwithintheslabiscontained withintwolightlines,onerepresentingawavepropagatinginfreespace,aswellasanother representingawavepropagatinginauniformmaterialofthesamepermittivityoftheslab. Thepropagationcharacteristicsofeachmodeshowthatthewaveiscloselyto freespacepropagation,butasthefrequencyisincreasedthepropagationconstantsslowly convergetothatoftheslab. Thesecharacteristicsintuitivelymakesense,aswhenthefrequencyisincreased,the 51 wavelengthwilldecrease,causinglessofthewavetopropagateinthecladdingregions. Changingthethicknessoftheslabprovidesachangeinthepropagationcharacteristicsof the ! vs plot.Figure3.6showsthe ! vs plotwithvaryingslabthickness.Inthis case,theslabisvariedbetween100 and2mm.Astheslabthicknessisincreased,the propagationcharacteristicsconvergetothatoftheuniformslabofdielectricconstant C morequickly. 3.2.3 CompositeRidgeAnalysis 3.2.3.1 LosslessRidgeAnalysis Inthissection,theabove1-Danalysisisusedtoanalyzearidgewaveguidemadeof4 composite1-DslabsusingtheEIM.Inthiscase,eachslabismadeofalosslessmaterial witharelativepermittivityof11.9(similartosilicon).Similartotheprevioussection, ! vs plotsarederivedforvariousparametersofthewaveguide.Inthiscase,therearethree primarygeometricalparametersdescribingtherib(andeachslab).ReferringtoFigure3.2, theheightoftheridge, h 1 ,theheightoftheedge h 2 ,andthewidthoftheridge,W. Figure3.7showsthepropagationcharacteristicsofalosslessridgewaveguidewithvarying ridgewidthupto300GHz.Inthiscase,thelightlinesnowcorrespondtothepropagation characteristicsoftheslabswhichrepresenttheedgeregionsoftheridge,aswellastheridge itself.Clearly,asthefrequencyisincreased,thepropagationcharacteristicsconvergetothat oftheridgeportionofthewaveguide.Figure3.7alsoshowstheofchangingthe widthoftheridge.Asonewouldexpect,iftheridgewidthisincreased,moreofthewave propagationiscontainedwithintheridge,causingconvergencetothelightlineoftheridge tobeatlowerfrequencies. AsimilarisshowninFigure3.8forvaryingridgeheights.However,nolightlines aredisplayedastheywouldchangewitheachtridgeheight.Again,thepropagation constantincreasesmorequicklywithfrequencyastheridgeheightisincreased.Whilethis 52 analysisisusefulforvisualizingthepropagatingmodesintheridgewaveguide,inreal-world materialstherewillbeloss,andthepropagationconstantwillnolongerbepurelyreal.In thiscase,theimaginaryportionofthepropagationconstantwillbeduetotheattenuation ofthewaveguide. 3.2.3.2 LossyRidgeAnalysis Inthissection,theofusingacomplexpermittivitytorepresentportionsoftheridge waveguideareinvestigated.Whenintroducingacomplexvalueintotheaboveanalysis,a graphicalmethodofsolvingforthepropagationconstantisnolongerfeasible. 53 Figure3.7ectsofvaryingridgewidthonthepropagationcharacteristicsoftheridge waveguide. 54 Figure3.8ofvaryingridgeheightonthepropagationcharacteristicsoftheridge waveguide. 55 Therefore,arootsolvingalgorithmwhichcansolveforcomplexrootsmustbeused.In thiscase,asimplenewtonsmethodisused.Eachslabismodeledwithtypicalproperties ofsilicon,including r =11 : 9+ j: 07.Eachslabissolvedgraphicallyforthelossless caseathelowestfrequencyofinterest,whichisthenusedasaninitialguessforthenewtons method. Figure3.9showstheattenuationofaridgewaveguidewith h 1 =300 , h 2 =200 , andawidthof400 .Aswouldbeexpected,theattenuationoftheridgeisincreasingwith frequency.At250GHz,thewaveguidehasanattenuationofapproximately.5dB/mm. Thesameanalysisisperformed,butwithvaryingridgeheightandwidth,at250GHz. TheattenuationduetotheseparametersisshowninFigures3.10and3.11.Clearly,the attenuationisincreasedwhentheridgeparameters(widthandheight)arealsoincreased. Thisintuitivelymakessense,asiftheareaofthelossymaterialisincreased,moreofthe propagatingwavewillattenuatethroughit.Mathematically,equation14showsthatthe radiusoftheintersectingcircleisdirectlyproportionaltotheheightoftheslab,aswellas thepermittivityofthecladdingandcorelayers.Therefore,ifoneofthesepermittivitesis complex,whentheheightoftheslabisincreasedtheimaginaryportionwillbeincreased, leadingtoahigherattenuation.Figure3.13alsoshowstheattenuationcharacteristicsfor bothincreasingridgewidthandheightat300GHz. Totheseassumptions,asimilaranalysisisperformedwithjustoneoftheridge regionsmodeledaslossless.Inthiscase,theslabrepresentingtheridgeheightismodeledas alosslessmaterial,whiletheotherslabsarestilllossywiththesameparametersmentioned above.Figure3.12showstheofchangingtheridgeheightinthelosslessregiononthe overallattenuationoftheridgewaveguide.Now,whenthelosslessregionisincreased,the overallattenuationisdecreased.Thistheaboveassumptions,andvalidatesthatif alossymaterialisincreased,theoverallattenuationwillalsobeincreased. 56 Figure3.9Theoreticalattenuationofridgewaveguideversusfrequency. 57 Figure3.10Theoreticalattenuationofridgewaveguideat250GHzwithvaryingridgeheight. 58 Figure3.11Theoreticalattenuationofridgewaveguideat250GHzwithvaryingridgewidth. 59 Figure3.12ctsofchanginglosslessridgeheightonattenuationofthewaveguide. 60 Figure3.13Theoreticalattenuationat300GHzofsiliconridgewaveguidewithvariousridge heightandwidths. 61 3.3 FEMModeling Three-dimensionalFEMmodelingisalsousedtoanalyzethewaveguidesandthe theoreticalresults.Inthiscase,thecommercialFEMmodelerANSYSHFSS13.0isused. Again,siliconisusedasthematerialforthebasedielectricandtheridge,withthesame electricalpropertiesasusedinthetheoreticalanalysis.First,theinsidethe ridgewaveguidesareinvestigated.Theinsidetheridgearesampledonaverticalplane placedinsidethewaveguide. TheinsidethewaveguideforthreeseparatecasesareshowninFigures3.14-3.16. Figure3.14showstheofchangingtheheightoftheridge,whilekeepingthebaseand ridgewidthconstant.Astheheightoftheridgeisincreased,theismore withintheridge,andthespreadwithinthebasedielectricregionisalsodecreased,the latterctisobservedespeciallyneartheedgesoftheridge,astheheightisincreased. Figure3.15showstheofincreasingtheridgewidthontheeldcontainedwithinthe waveguide.Similartoincreasingtheridgeheight,increasingthewidthalsoincreasesthe concentrationintheridge.However,insomecases,moreoftheisspreadtothe basedielectriclayer.Finally,Figure3.16showstheofincreasingthedielectricbase height.Theseresultsshowitisimportantthatthedielectricbaseheightisnottoothin, ascaneasilyleakoutofthebase.Ifthethicknessislargeenoughtheismore towardsthecenteroftheridge/baseregion.Overall,thereisagreatonthe twithinthewaveguidebasedonthedimensionschosenfortheridge. Asshowninthesomeamountofpowerwillleakoutofthewaveguide astherearenometallicboundaries.Theamountofpowerleakedfromtheridgecanbe calculatedfromtheFEMsimulationsbycalculatingtheaveragepowerintworegions.First, theisintegratedovertheregioncorrespondingtotheareaoftheridge.Next,the intheareasurroundingtheridgeisintegratedtondthetotalpowerintheridgeandthe surroundingarea.Subtractingthesetwoaveragedpowersleavesjustthepowerinthe 62 Figure3.14Fieldinridgewaveguidewithvaryingridgeheightat300GHz. 63 Figure3.15Fieldinridgewaveguidewithvaryingridgewidthat300GHz. 64 Figure3.16Fieldinridgewaveguidewithvaryingdielectricbaseheightat300GHz. 65 Figure3.17Percentoftotalpowerleakedfromridgeasafunctionofthepermittivityofthe ridgeat300GHz. 66 Figure3.18Simulatedattenuationofridgewaveguideat300GHzforvaryingridgeheight andwidths. 67 surroundingarea,thisissummarizedintheinsetofFigure3.17.Theofchangingthe dielectricconstantofthewaveguideonthepowerleakedfromthewaveguideisshownin Figure3.17.Clearly,whenthedielectricconstantofthewaveguideisincreased,thepower thatisleakedoutsideofthewaveguideisdecreased.Therefore,adielectricmaterialwitha highdielectricconstant,suchassilicon,isidealtoconstructthesewaveguidesandreduce thepowerradiated. Theattenuationofthewaveguidescanalsobefoundthroughsimulation.Thisisaccom- plishedbycalculatingthetransmissionpropertiesforwaveguidesoftwotlengths andsubtractingtheresults.Thisleavesjusttheattenuationthroughthewaveguide,as anycouplinglossesareremoved.Figure3.18showsthesimulatedattenuationwithvarious ridgeheightsandwidths,withaconstantbaseheight.Thesimulatedattenuationmatches relativelywellwiththetheoreticalresults,withtheattenuationincreasingwithincreased ridgeheightandwidths.Inthesimulatedcase,duetothethree-dimensionalnatureofthe simulations,theattenuationisslightlyhigherthaninthetheoreticalinvestigation. 3.3.1 CurvesandPassiveCircuits Overall,theridgewaveguidesshowrelativelylow-losspropagationover300GHz.However, whiletheattenuationofthewaveguideiscomparabletootherTHzdielectricwaveguides, duetotheextraridgearea,thesewaveguidesdisplayslightlyhigherlosses.Whiletheridge waveguidesdisplaylargerattenuation,theyhaveotheradvantagesovertypicaldielectric waveguides(suchasthedielectricribbonwaveguide).Outsideoftheintegrationcompatibil- ityadvantages,thesewaveguidesalsohavemanyapplicationsincomplexcurvedstructures thatwouldbetorealizeusingotherdielectricwaveguides. 68 Figure3.19Fieldinridgewaveguidecurveswithvaryingridgewidthat300GHz. 69 Figure3.20Fieldofcomplexridgewaveguidegeometriesat300GHz. 70 Asmentionedintheprevioussection,thewidthandheightoftheridgesimpactthe attenuationofthewaveguide.Iftheridgeistoonarrownearthebendofacurvethe powerisradiated,asdisplayedinFigure3.19,wheretheonacurvemadefromaridge waveguideisshownwithvaryingridgewidths.Clearly,astheridgewidthisincreased, moreofthepowerisacceptedintotheridge,withlessradiatedatthebend.Therefore,for curvedwaveguidingapplications,thereisabetweentheincreasedattenuationof thewaveguideduetoawiderridgeandthebeingmorewithintheridge. Inadditiontosimplecurves,othermorecomplexstructurescanbeimplementedwith theridgewaveguides.Figure3.20showssamplesoftwomorecomplexstructures,a powersplitterandamulti-curvestructure.Forthepowersplitter,theiswellcontained withinthecenterportion,andtheisapproximatelysplitbetweenthetwobranchesas wouldbeexpected.Additionally,themulti-curvestructureshowsthatwhilesomepoweris lostinthebend,thesignalisstilltlytransmitted. 3.4 FabricationandMeasuredResults Severalsilicon-basedridgewaveguideswerefabricated,withtheightandwidths.In thiscase,thesiliconridgewaveguideswerefabricatedusingn-typesinglesidepolishedsilicon waferswithresistivityofapproximately cm ,andatotalwaferthicknessof500 .The waveguideswerefabricatedusingastandardopticallithographyandwetetchingprocess. Thesiliconwaferwaspreparedbyremovingthenativeoxideusingaeredhy- acid(HF)solution.Atitaniumofproximately2 wasthendepositedon thefrontandbacksideofthesiliconwaferusinge-beamevaporation.Here,thetitanium wasusedasthemaskfordeepanisotropicetchingofthesiliconwaferduetoitsexcellent adhesionproperties.Thisisfollowedbypatterningandetchingofthetoptitaniumlayer onthepolishedsideofthewaferusingHF: H 2 O 2 : H 2 O=1:1:100,whileprotectingthe titaniumonbacksidewithphotoresist.Next,theetchingofthesiliconwasperformed 71 Figure3.21Fabricationprocessforthesiliconridgewaveguide. 72 usinga30%PotassiumHydroxide(KOH)solutionat75 C for1hourforaridgeheight ofapproximately50 .Finally,thetitaniumwasremovedusingHF: H 2 O 2 :H 2 O= 1:1:100torevealtheridgestructureswithinthesilicon.Theoverallfabricationprocessis summarizedinFigure3.21.Foraridgewaveguidewithalargerheight, SiO 2 deposited usingplasmaenhancedchemicalvapordeposition(PECVD)wasusedasahardmask,with patterningachievedusingaoxideetchant(BOE6:1).Figure3.22showsSEM imageofoneofthesiliconridgesunderAridgeisclearlydevelopedwithin thesilicon,althoughtheridgedoesnothaveacleanverticalwallduetotheetchingprocess. Therefore,twoseparatewidthsareassociatedwiththeridge. Theridgewaveguidesaremeasuredusingaquasi-opticalTHzmeasurementsetup.The THzsignalisgeneratedusingaEmcorePB-7200commercialfrequencydomaintestsystem. Thissystemismadeupofreceiver(Rx)andtransmitter(Tx)headsthatareinterfacedwith sourcesthrougher-optics.Thesystemiscapableofmeasuringtransmissionbetweenthe RxandTxheadsfrom100GHzto2THz,withafrequencyresolutionof100MHz.The ridgewaveguidesamplesareinterrogatedwithdielectricfocusingprobesmadeofHDPE introducedinchaptertwo,thataredesignedtooperateupto500GHz.Ametallicwindow isalsoplacedonthebackendoftheRxprobesothatanyexcessprobe-to-probecoupling isreduced.Figure5.22showstheoverallmeasurementsetup. Tomeasureasamplewiththeabovesetup,areferencemeasurementisrequired.Forthe ridgewaveguidesamples,areferencewastakenbyde-couplingtheprobesformthesilicon waferbyasmalldistancesuchthatnosignalistransmittedintothesilicon.Water,astrong absorberofTHz,isalsoplacedonthesurfaceofthewaveguidetofurtherensurethatno signalistransmittedduringthereferencemeasurement. 73 Figure3.22SEMphotographyofafabricatedridgewaveguide. 74 Figure3.23THzmeasurementsetupforsiliconridgewaveguides. 75 Multipleridgeheightsandwidthswereetchedontosiliconwaferstobemeasured.For thiswork,twotridgewidthsaremeasuredeachhavingtwoseparateheights.The tworidgeheightsusedinthiscaseareapproximately H 1 =40 and H 2 =80 .Thetwo sampleridgewidthsare W 1 =460 ,and W 2 =750 .Figures3.24and3.25showthe transmissionbetweenfourtridgewaveguideswithtridgeheightandwidth combinations.Thewaveguideshaveawidetransmissionspectra,from100to500GHz. Additionally,asexpectedfromthetheoreticalandsimulationresults,thewaveguideswith thethinnerridgesdisplaytheleastamountofloss. Themeasuredattenuationofthewaveguidesisalsocalculatedbyusingtwoseparate lengthwaveguideswiththesameridgewidthandheight.Thetransmissionofbothwaveg- uidesisthensubtractedandconvertedtoanattenuationinunitsofdB/mm.Themeasured attenuationofthewaveguideisshowninFigure3.26.Here,theattenuationoffourwaveg- uidescorrespondingtoridgeheightsof H 1 and H 2 ,aswellasridgewidthsof W 1 and W 2 isdisplayed.Theseresultsmatchrelativelywellwiththepredictedattenuationfromthe theoreticalandsimulatedresultsintheprevioussections.Overall,thelowestmeasured attenuationofaridgewaveguidewitharidgewidthof460 andaheightof40 is approximately0.4dB/mmat100GHz,or0.5dB/mmat300GHz. 3.5 ErrorAnalysisandDiscussion Inthischapter,themeasurementofsiliconbaseddielectricridgewaveguidesispresented. Similartothelastchapter,errorsintheprobingandcouplingareexpectedduetothenature oftheTHzsystem.Again,thealignmentoftheprobeswiththesampleiscritical,butvery toquantify.Anotherfactorwhichoccursinthemeasurementoftheridgewaveguides directlyonsiliconwafersisthatthewafersarenotperfectlydicedevenlybetweensamples. Thisleadstoslightlyttransmissionandcouplingcharacteristicsbetweensamples duetotheontheedgeofthewafer.Formorediscussionontheerrorsinvolved 76 withprobecoupling,refertothepreviouschapter. 3.6 ConclusionsandDiscussion ThischapterdisplaysthepotentialfordielectricridgewaveguidesforTHzon-waferappli- cations.Thewaveguidesshowrelativelylow-lossevenathighfrequencies( > 300 GHz ). ThisisthroughboththeoreticalapproximationsaswellasFEMsimulation.The waveguidesalsohaveverywidebandsingle-modepropagationatfrequencieswellintothe THzregion.Thesimulatedandtheoreticalattenuationforvariousridgeheightandwidths arecompared,withattenuationaslowas0.45dB/mmat300GHz.Finally,amethodof fabricatingandmeasuringthewaveguidesispresented.Thesemethodsallowforsimpleand 77 Figure3.24Measuredtransmissionforridgewaveguideswith80 ridgeheight,withtwo tridgewidths(normalizedpower). 78 Figure3.25Measuredtransmissionforridgewaveguideswith40 ridgeheight,withtwo tridgewidths(normalizedpower). 79 Figure3.26Measuredattenuationofseveralridgewaveguides. 80 tcouplingbetweenwafer-levelwaveguideandcurrentquasi-opticalTHzsystems.The measuredattenuationalsoshowsrelativelygoodagreementwiththe0.4dB/mmat200GHz. Overall,thedielectricridgewaveguidespresentaverypromisingsolutiontothecomplex problemofhighfrequencyinterconnectsthatarecompatiblewithon-waferapplications. 81 CHAPTER4 OptimizationofTerahertz Filters Inthischapter,thedesignofTHzcomponentsusingsingleandmulti-objectiveevo- lutionaryalgorithmsisintroduced.EachstructureisoptimizedthroughaHFSS-MATLAB interfacewithperiodicboundaryconditionsandplanewaveincidence.First,ter- ahertzband-stopareinvestigatedbasedonadual-crossstructure.Theare optimizedforrejection,bandwidth,andmulti-resonantproperties.Abandwidthofapprox- imately45GHzwith-25dBofrejectionat300GHzisobserved,aswellasmulti-resonant at250and300GHz. 4.1 OptimizationTechniquesinElectromagnetics Anumberofproblemsinelectromagneticsbecometosolvewithconventionalan- alyticequations.Mostoftheseproblemscanbesolvedusingnumericalmeans,however,a numberofproblemsexistthatrequireverycomplexstructureswithmanypossiblevariables. Optimizationcanbeusedtosolvethesetypesofproblems,andiswidelyusedinmanyarea ofelectromagneticssuchasantennadesignandmaterialcharacterization,alongwithoth- ers.Therearethreeconventionalcategoriesofoptimizationandsearchmethodsusedinthe 82 currentliterature.Thesethreemethodsincludecalculus-based,exhaustivesearch,andran- domsearchmethods[94]-[95].Allofthesemethods,aswellasnon-traditionaloptimization methodbasedonnaturalselection,aresubsequentlyintroducedinthissection. 4.1.1 Calculus-basedOptimizationMethods Calculus-basedmethodsarewidelystudiedthroughoutavarietyofresearchareas.These methodsinvolveseekinglocalmaximaandminimabysolvingthegradientofthedesiredob- jectivefunctionsetequaltozero.Givenasmoothobjectivefunction,acorresponding peakinvolvescalculatingderivativesinalocalareaandwheretheyconvergetozero. Whilethismethodislocalinscope,forafunctionsimilartotheoneshowninFigure4.1the peaklocationandvalueoftheobjectivefunctioncanbeeasilyfound.However,thismethod isextremelydependentonthelocationoftheinitialguessforthesearch.Dependingon theguess,theremaybenowaytotellifthemaximumoftheobjectivefunctionisalocal maxima,oraglobalmaxima.Thismeansthatthesolutionthemethodconvergestomaynot betheoptimal,orevenbest,solutionavailable.Forexample,ifthedomainofthefunction showninFigure4.1isextendedasshowninFigure4.2.Thecurrentmaximaisrevealed tonotbetheglobalmaximainthearea,meaningabettersolutioncouldbefoundwitha tinitialguess.Inaddition,thesemethodsdependupontheexistenceofwell derivativeswhichmaynotalwaysbeavailable. 83 Figure4.1Localmaximumoffunctionf(x,y,z). 84 Figure4.2Extendeddomainoffunctionf(x,y,z)showingmultiplemaximas. 85 4.1.2 EnumerativeOptimizationSchemes Theideaofanenumerative(alsoknownasexhaustive)searchispossiblythemoststraight forwardmethod.Withinasearchspace,thealgorithmwillevaluatethedesiredob- jectivefunctionatallpossiblepointswithinthespace.Thesimplicityofthissearchisvery attractive,andforsmallsolutionspacescanbee.However,formorecomplexprob- lems,thesemethodslackthenecessary.Searchingalargesamplespaceelement byelementsimplytakesfartolong. 4.1.3 RandomSearchAlgorithms Randomsearchalgorithmshavebeenshowntobeeformanyproblems.Thesesearch methodsinvolverandomlyselectingpointsalongthedesiredsolutionspace,asopposedto anexhaustivesearchsearchingeverypoint.Thesetechniquesalsohavesomeoftheshort comingsoftheexhaustivesearches.Onceagain,theofsuchasearchcanbefar toolowforverycomplexproblems.However,formanydesiredsolutionspaces,arandom searchisabletosatisfactoryresults. 4.1.4 GeneticAlgorithmOptimization Thegeneticalgorithm(GA)isanoptimizationandsearchtechniquebasedontheprinci- plesofnaturalselection.Thesealgorithmsarewidelyusedinmanytengineering applicationsinawiderangeofAGAallowsapopulationcomposedofmanyin- dividualsto"evolve"undersprulesinordertomaximizeadesiredorcost, functionassociatedwiththecurrentproblem.GAoptimizationhasmanyadvantagesover theoptimizationtechniquesdescribedpreviously.Forexample,theGAcanoptimizewith continuousordiscretevalues,althoughinthisworkonlythediscretebinaryGAisused.In addition,thismethoddoesnotrequireandderivativeinformation.GAscanalsosimultane- ouslysearchawiderangeofobjectivefunctionsanddealwithalargenumberofvariables. 86 Inaddition,alocalminimumormaximumasopposedtoaglobaloneisnotanissue withaGA,meaningthatextremelycomplexobjectivefunctionscanbeevaluated.Finally, GAsalsoworkverywellwithnumericallyorexperimentallygenerateddataasopposedto analyticfunctions.Theseadvantagesprovideaninterestingoptimizationapproachthatcan solvemanyproblemstheprevioussearchandoptimizationmethodscannot.Athorough explanationoftheprocessesoftheGAoptimizationtechniqueispresentedinthesection, witheachcomponentexplainedseparately.Inaddition,somecurrentapplicationsofGA optimizationinelectromagneticproblemsarepresented. 4.1.4.1 FitnessFunctionsandChromosomes Afunction(sometimescalledacostfunction)representthedesiredsolutionspace thattheGAwillattempttominimize(sometimesmaximize).Thisfunctiongeneratesan outputfromasetofinputvariables.TheseinputvariablesintheGAarereferredtoasa chromosome.TheGAbeginsbyachromosomearraytobeoptimized.Ifthelength ofthechromosomeis N bits ,andeachelementofthechromosomearegivenby P Nbits ,then achromosomecanbewritteninthefollowingway. chromosome =[ P 1 ;P 2 ;::::::;P Nbits ](4.1) 4.1.4.2 VariableSelection AsthevariablesoftheGAarerepresentedasbinary,theactualmeaningofthevariables mustbetranslatedintobinarybits.Toillustratethisconcept,asheetdiscretizedintosquare pixelswithequalsidesofalengthisshowninFigure4.3.Eachpixelcanbeintwopossible states,onorInthiscase,a1canbethoughtofasanonstate,anda0canbethoughtofas anstate.Thegridhas10rowsand10columns,andtheoverallgeometryisrepresentative ofachromosomeof100bitlength.Forexample,thethechromosomerepresentingthe 87 Figure4.3Samplediscretizedpixelgrid. 88 geometryofthegridcanbewrittenasberepresentedasinequation1.3. chromosome =[1110101101 :::: ](4.2) Withthisdiscretization,thebinarybitsareabletoberepresentedinthegeometrywewish tooptimize. 4.1.4.3 Population ThecollectionofallthechromosomeswithintheGAisknownasthepopulation.The populationhas N pop chromosomesandeachchromosomehas N bits sothepopulationwill beanmatrixof N pop by N bits insize.InordertobegintheGAoptimizationprocess, aninitialpopulationmustbegenerated.Theinitialpopulationisfoundbyperforminga randomsearchandthepopulationwithrandomonesandzeros.Thisinitialpopulation isthenpassedintothefunctiontobeevaluated. 4.1.4.4 Selection Fromtheevaluationoftheinitialpopulation,thebestchromosomesareselectedbythe GA.Thisisdonebyrankingthechromosomesfrombesttoworseaccordingtothe desiredfunction.Fromhere,onlythebestchromosomesarekeptandtheothersare discarded.Thenumberofchromosomestobekeptareselectedbasedontheselectionrate, X rate ,whichrepresentedthefractionofthe N pop chromosomesthatarekept.Thenumber ofchromosomesthatarekeptaregivenby N keep = X rate N pop (4.3) Selectionoccursateachiteration(knownasageneration)ofthealgorithm.Decidinghow 89 manychromosomesarekeptdependsontheapplication.However,keepingtoofewwilllimit theavailabilityofgenesintheKeepingtoomanychromosomescouldbringintoo manybadperformersfromthepreviousgeneration. Twochromosomesarethenselectedfromtheremainingchromosomes N keep toproduce twonewuntilthediscardchromosomesarereplaced.Whilethereareanumberof techniquesusedfortheselectionofthenewchromosomes,atournamentselectionmethodis usedthroughoutthisthesis.Tournamentselectioninvolvesrandomlypickingasmallsubset ofchromosomesfromtheremainingpool,andthechromosomewithinthisselectionwiththe bestischosentobecomeaparent.Thetournamentrepeatsuntileveryparentneeded toregeneratethepopulationofchromosomesarefound.Thismethodworksespeciallywell forlargepopulationsbecausethereisnoextrasortingnecessary. 4.1.4.5 Mating Matingisthecreationoffromtheparentsfoundintheselectionprocess.The mostcommonformofmatinginvolvestwoparentswhichcreatetwoAcrossover pointbetweentwoparentsischosenrandomlybetweentheandlastbitofbothparents chromosomes.Theparentwillpassitsbinarycodetotheleftofthecrossoverpoint totherstThesecondparentalsopassesitsbinarycodetothesecond fromtheleftofthesamecrossoverpoint.Thebinarycodetotherightofthecrossoverpoint oftheparentisthenpassedtothesecondwhilethebinarybitstotheright ofthecrossoverpointforthesecondparentarepassedtotheThisleavesus withtwowiththegeneticmakeupofbothparents,whichareusedtoreplacethe twoparentsselectedfor N keep .ThisprocessissummarizedinFigure4.4 4.1.4.6 Mutations Randommutationsarealsousedtoaltertheapercentageoftheremainingpopulationmatrix. Mutationintroducesanotherelementtotheoptimizationprocessbyintroducingtraitsinto 90 thepopulationthatwerenotinitiallypresentintheselectedparentsandInthe binaryGA,mutationcanbeassimpleaschangingasinglebitinachromosomefroma1 toa0,orviceversa.MutationisimportantfortheGAprocessasitintroducestraitsnot foundintheselectedparentsandtothepopulation.Withoutmutation,theGA mayconvergetooquicklytoananswerthatdoesnotincludeotherpossiblecombinations. Thenumberofmutationsaregivenbyequation1.5,where rate isthedesirednumberof mutationsfortheentirepopulation. mutations = rate ( N pop 1) N bits (4.4) 4.1.4.7 ConvergenceandFutureGenerations Afterthemutationstakesplaceandthefunctionsassociatedwiththegare calculated,theresultsarecomparedwithastoppingcriteria.Ifthestoppingcriteriaisnot met,thealgorithmtakesthecurrentpopulationandbeginstheselectionprocessagainin anewgeneration.Ifthecriteriaismet,thealgorithmwillstopandtheresultswillbe exported.TheoverallGAoptimizationprocessisshowninFigure4.5. 91 Figure4.4Matingprocessinthebinarygeneticalgorithm. 92 Figure4.5Summaryofgeneticalgorithmoptimizationprocess. 93 4.1.5 Multi-objectiveOptimization theGAhasbeenprimarilystudiedasasingle-objectivealgorithm,andinthepastwas widelybelievedtobeincompatiblewithmulti-objectiveproblems[97].Inrecentyears, however,anumberofpromisingmulti-objectiveGAshavebeenestablished,includingthe paretoevolutionaryalgorthm(SPEA)[98],themulti-objectivegeneticalgorithm(MOGA) [99],andthenon-dominatedsortingalgorithm(NSGA)[100].Inparticular,anelitistbased versionofNSGA,calledNSGA-II,hasbeenextremelypopularformanymulti-objective optimizationapplications[101]. 4.1.5.1 NSGA-II Whendealingwithmultipleobjectives,therawvalueofeachobjectivedoesnotde- scribenecessarilythebestsolution.Whentwoormoreobjectivesareconsidered,apareto optimalfrontisformedbetweeneachsolutionrepresentingthebetweeneachob- jective.Therefore,thegoalofsuchanoptimizationprocedureistosolutionsas closeaspossibletotheparetotfront(thebestpossiblesetofsolutions),aswellas maximizethenumberofpossiblepointsalongtheparetofront. Tohandlethemulti-objectivenatureoftheproblem,NSGA-IIisusedoptimizemultiple characteristicsoftheNSGA-IIprimarilyfromthesingle-objectiveGAshown inFigure4.5bytheevaluationoftheofeachobjective.Inthiscase,theof eachobjectiveiscalculatedforeachmemberofthepopulation.Anewpopulationis thencreated, R t .Thispopulationcontainstheofeachobjectivefortheprevious generation(knownastheparents),aswellasthepreviousgenerationafterselection,muta- tion,andcrossover(knownasthechildren)suchthat R t =[ P t Q t ],where P t istheparent population,and Q t isthechildpopulation. R t isthendividedintonon-dominatedfrontswhichareusedtosortthetrade-oof eachobjective.Thebestfrontsarechosenandkeptinthenextgenerationofthealgorithm, 94 referredtoas P t +1 ,whichisofthesamesizeastheinitialpopulation.Therefore,the membersoflow-rankingfrontswillbediscarded,onlyleavingthebestsolutions. However,therewillmostlikelybesomeoverlapbetweenasinglefrontattheborderofthe forthenextgeneration.Membersofthisfrontarechosenforthenextgeneration basedofthedistancebetweentheirlocationandthelocationofthenearestpointonthe front.Thepointswiththemaximumdistancefromotherpoints(knownasthecrowding distance)arechosenforthenextgeneration.Inthiscase,theendpointsarealwayspreferred andassignedancrowdingdistance.Thisallowsfornotonlythebestsolutionstobe presentinthenextgeneration,butalsoensuresthemostdiversesolutionsarealsopreserved. TheoverallprocessoftheNSGA-IIalgorithmisshowninFigure4.6. 95 Figure4.6NSGA-IIoptimizationprocess. 96 4.1.6 ApplicationsofGeneticAlgorithmsinElectromagnetics GeneticalgorithmsareusedasanoptimizationtoolinawidevarietyofElectromagnetics problems.In[102],geneticalgorithmsareusedtosynthesizelight-weight,broadbandmi- crowaveabsorbers.Theabsorberisintendedtobeaslight-weightaspossible,whilebeing thinandmulti-layered,backedwithaPECconductor.Eachlayeroftheantennaisop- timizedwithafrequencydependentmaterial,whilethepermittivityandpermeabilityare varied.Theyofthearrayisoptimizedwhilechangingthematerialsinthearray- stack,whilekeepingthestackasthinaspossible.Awiderangeoffrequencyabsorbersare designed,withrecotsrangingfrom.2-8GHz. Thesealgorithmshavealsobeenusedinthedesignoffrequencyselectivesurface(FSS) structures[103].Inthiswork,theFSSstructuresaredesiredtobeusedaswaveguide Asthecharacteristicsdependupontheshapeandsizeoftheindividualelements,as wellasthenumberofelementlayers,bothareoptimizedwiththeGA.Verystrongbandpass andbandstopersareshowninthiswork,atfrequenciesashighas25GHz. GAsarealsowidelyusedinantennaarraydesign.In[104],thesidelobelevelsofan antennaarrayaredecreasedbythinningorremovingtheelementsthatmakeupanarray. Thisisdonebyrepresentingtheelementswithabinarynumber,andturningthemtoeither a1or0basedoniftheelementisonorExtremelylowsidelobelevels,aslowas-22dB, arereported.Refrence[105]usesthegeneticalgorithmtooptimizealinearantennaarray toshapethemainbeamoftheradiationpattern.Inthiscase,thegoalistoselectaset ofamplitudeandphasecotsfortheantennatoachieveanarrowbeamatasp location. Optimizationhasalsobeendoneextensivelyonsingleantennaelements.In[106],a patchantennaisoptimizedsothatthebandwidthoftheantennaistlywiderthan atraditionalpatch.TheGAiscoupledwithamethodofmomentssothatabinarystring couldrepresentthepresenceorabsenceofasubsectionofmetalinthepatch.Withthis 97 method,thebandwidthofonepatchwasabletobeincreasedbyapproximately20%.The GAoptimizationmethodhasalsobeenrecentlyusedtominiaturizeantennas. In[108],apatchantennaisminiaturizedbyplacingSRRsbetweenthetoplayerofthe antennaandthegroundplane.ThegeometryoftheSRRsareoptimizedwithaGA,while thefunctionisdesignedtominimizethecotoftheantenna.Agood impedancematchandradiationcharacteristicsaremaintainedwiththeoptimization,and onestateisshowntoachieveaminiaturizationofapproximately1/16ththesizeofthe originalpatch.[107]presentsaloopantennathatisminiaturizedusingabinaryGA.The loopantennaisprintedonaplanardielectric,withapixelizedsheetdirectlyaboveit.Each pixeliscontrolledwiththebinaryGAandthefunctionischosentominiaturizethe cotatadesiredfrequency. Anotherminiaturizationmethodispresentedin[110].Inthiswork,amonopoleantenna issurroundedbyametallicpixelizedgridcontrolledbyabinaryGA.Thepixelgridisused tominiaturizetheantennathroughcontroloftheGA.Theradiationcharacteristicsofthe monopolearewellmaintainedthroughouttheminiaturization,andanoverallminiaturization of 0 = 26isachieved.AllthreeofthesemethodsareimplementedusingaHFSS-matlab interface,whichwillbediscussedindetailinthefollowingsection. 4.2 HFSS-MATLABOptimizationInterface InordertoimplementtheGAoptimizationsuccessfullywithanelectromagneticsproblem,a numericalsolutionmethodmustusuallybeimplemented.Whilesomesimpleproblemscan besolvedthroughanalyticequations,mostrequireapproximatesolutions.Therearemany numericalsolutiontechniquesthatcanbeused,however,perhapsthemostpopularmethod isintheuseofcommercialelectromagneticssolvers.OnesuchcommercialsolverisAnsys HighFrequencyStructuralSimulator(HFSS),whichisbasedonaelementmethod. ThissolverhasaCADlikeinterfacewhichcanbeeasilyusedandcanimplementanumber 98 ofsolutionmethodsinboththefrequencyandtimedomain. ImplementingaGAtosolveaproblemiterativelyisunfortunatelynotavailableinHFSS. However,HFSScommandsareabletobeexecutedthroughsimplemacroscriptsthatcan beimportedandruninrealtime.ThesemacroscanbeexecutedthroughMATLAB,and compiledintoascriptwhichcanbeimportedtoHFSS.Thisallowsfortheautomatedcreation ofgeometry,boundaryconditions,andexcitationsinHFSS.Thisallowsthegeometrytobe alteredaftereveryiterationofaparameter,meaningaGAcanbeusedtooptimizestructures withaninterfacebetweenHFSSandmatlab. Anoverallwoftheoptimizationprocessisasfollows.First,matlabislaunchedand theGAparametersareinitialized.Thegeometryisthencreatedfortheiterationof theGA.ThescriptisthenassembledandHFSSislaunched.ThescriptispassedtoHFSS, andthegeometryisdrawninrealtime.Thestructureisthensimulated,andtherelevant resultsareexportedbacktomatlabforpostprocessing.Iftheseresultsmeetthedesired requirements,thentheGAisstopped.However,iftheresultsdonotmeettherequirements desired,theoverallprocessisrestartedwithanewgeometryandthenextiterationofthe GAisperformed.TheoverallwchartforthisprocessisshowninFigure4.7. 99 Figure4.7GeneticalgorithmMatlab-HFSSinterfacewchart 100 4.3 FilterDesignandImplementation ThegeometryofthesuggestedTHzgeometryisshowninFigure4.8.Theim- plementedhereisbasedonadualcrossunitcellstructure.However,thecrossesarebroken intosmallsubsections,similartothepixelgridexamplegivenintheprevioussections.This allowsthetopologytobeoptimizedtoproducecertaindesiredresults. Inthiscase,AnsysHFSSisusedalongwithperiodicboundaryconditionswithafunda- mentalquet-modeincidencetothedesiredpropertiesoftheThesetupofthe boundaryconditionsfortheisshowninFigure4.9.Furtherinformationpertainingto thequetmodeanalysisispresentedinthechapter5.Theoverallunitcellsizeisgivenby Y p = X p =550 ,withaoutercrosslengthof425 andinnercrosslengthof300 .The crossesaresplitintosmallsquarepixelsubsectionswith a =25 sides.Thelterisbuilt ona250 polyethyleneterephthalate(PET)substrate,with r =3 : 4and = : 001, foundfromthecharacterizationin[117]at300GHz. 101 Figure4.8Proposedgeometry. 102 Figure4.9HFSSquetmodemodelingsetup. 103 4.4 ImplementationTestofNSGA-IIAlgorithm FirsttheNSGA-IIalgorithmistestedtoensureconvergenceanddiversityamongitssolu- tions,aswellastoensurethealgorithmisperformingcorrectly.Manymulti-objectivetest problemshavebeenintroducedthroughouttheyears[111]-[114].TheZitzler-Deb-Thiele (ZDT)testfunctionshavebeenparticularlyusefulsincebeingintroducedin[115].The ZDTtestproblemsconsist(atleastinitially)of6functionswhichtesttheconvergenceand complexityofamulti-objectiveoptimized.Sincethemulti-objectivealgorithmusedhereis abinaryNSGA-IIasopposedtoarealcodedversion,thetestproblemZDT5isusedasit isparticularusefulintestingbinarycodedGAs.TherepresentativeequationsforZDT5are showninequations2-5. f 1 ( x )=1+ u ( x 1 )(4.5) g ( x )= 11 X i =2 V ( u ( x i ))(4.6) h ( f 1 ( x ) ;g ( x ))= 1 f 1 ( x ) (4.7) V ( u ( x i ))= 8 > < > : 2+ u ( x i ) u ( x i ) < 5 1 u ( x i )=5 (4.8) TheNSGA-IIalgorithmisrunwithapopulationof500,10%mutation,and1000 generations.TheresultsfortheNSGA-IIalgorithmareshowninFigures4.10-4.11.Figure 4.10showstheattainmentsurfacesfoundfor5runscomparedwiththeglobalparetooptimal front.Figure4.11alsoshowsthebestrunversustheglobalparetooptimalfront.TheNSGA- IIalgorithmconstructedinthisworkshowsgoodagreementwithZDT5,especiallyafter f 1 isgreaterthanthree. 104 Figure4.10AttainmentsurfacesfoundfromNSGA-IIalgorithm. 105 Figure4.11ConvergenceofNSGA-IItoZDT5testproblem. 106 4.5 FEMSimulationandOptimizationResults 4.5.1 SingleObjectiveOptimization First,asingle-objectiveGAisusedtooptimizetheband-stopcharacteristicsoftheat 300GHz,describedbyminimizingthefollowingfunction F = j S 21 j (300 GHz )(4.9) where S 21 isthetransmissioncotoftheat300GHz.Thesingle-objective GAusedinthisoptimizationprocessisinterfacedthroughMATLABwiththeEMsolver HFSS13.0.Asingle-bitmutationrateof10%,alongwithsingle-bitcrossover,aninitial populationof240,and115totalpixelsareusedasGAparameters.Thisarrangementleaves theGAoptimizationprocesswithapproximately2 115 possiblecombinationstochosefrom. InHFSS,theismodeledasaneriodicunitcellusingmaster/slaveboundary conditionsandanincidentTEpolarizedplanewavenormaltothesurfaceofthestructure. Theresultsofthreeseparatesingle-objectiveGArunsover50generationswiththeobjec- tivetominimizeEquation1aredisplayedinFigure4.12.Aminimum S 21 ofapproximately -24.68,-24.92,and-24.31dBarefoundforeachrun,respectively.Thelowvalueofthe transmissioncontsuggeststhatthedescribedgeometryandoptimizationtech- niquearesuitabletocreateastopbandlikeresponseatadesiredfrequency.Inaddition,the resultsofeachrunconvergetoapproximatelythesamevalue,showingthatthealgorithmis repeatable. 107 Figure4.12Progressionof j S 21 j throughGAgenerations. 108 4.5.2 Multi-ObjectiveOptimization Whilethesingle-objectiveresultsshowpromiseintherejectioncharacteristicsofthestruc- ture,otheraspectsofaarealsodesirable.However,asimplesingle-objectiveGAwill notworkwhenmorethanonecharacteristicisdesiredtobeoptimizedsimultaneously. 4.5.2.1 OptimizationofBandwidthandStop-band Themulti-objectivedesignisamin-maxproblem,describedwiththefollowing functionsdescribedbyP1. P 1= 8 > < > : Minimize F 1=20log 10 ( S 21 (225:325 GHz )) Maximize F 2= f H f L (4.10) where f H isthehighfrequency-3dBpointand f L isthelowfrequency-3dBpointwith respecttothecenterfrequencyofthestopband.Therefore,F2representsthebandwidthof thestopband,andF1representsthemaximumrejectionoftheTheresultsofNSGA- IIareshowninFigure4.13forafrequencyrangefrom225to325GHz.Aparetofrontis formedshowingabetweensolutionswithamaximumrejectionofapproximately-25 dBandamaximumbandwidthof44GHz.Keepinginmindthatthisisforasinglelayer structure,abandwidthof44GHzisrelativelylarge(andcoulddrasticallyincreased withmultiplelayers).Inaddition,theminimum S 21 ofapproximately-25dBmatcheswell withthesingle-objectivecase,showingconvergencebetweenthesingleandmulti-objective GAs.Figure4.14alsoshowstheprogressionofthebestofeachobjectiveduringthe NSGA-IIprocessover30generations. 109 Figure4.13SolutionsforP1objectivefunctionsafter30generations. 110 Figure4.14ProgressionofP1objectivefunctionsthroughGAiterations. 111 4.5.2.2 Multi-resonantOptimization Next,themin-minproblemoftheoptimizationofrejectionatmultiplefrequencypointsis consideredwithNSGA-IIusingthefollowingobjectivefunctions. P 2= 8 > < > : Minimize F 1=20log 10 ( S 21 (300 GHz )) Minimize F 2=20log 10 ( S 21 (250 GHz )) (4.11) Inthiscase,P2describestherejectionoftheatthetwofrequencies300and250 GHz.ThebetweentheseobjectivesisshowninFigure4.15after80generationsof NSGA-II. Clearly,abetweenthetwoobjectivesisformed,and5paretofrontmembersare foundwhichdescribeabetweentheresonancesateachfrequency.Figure4.16shows theprogressionofeachobjectiveasthegenerationsoftheGAareincreased.Again,itis worthnotingthatF1clearlyconvergestothesingle-objectivecasedisplayedat300GHzof approximately-25dB. 4.5.2.3 FilterImplementation Fourfoundintheaboveanalysisrepresentingtheidealamongeachobjec- tiveareevaluatedovertheirfullfrequencyspectrumsusingHFSS.Figures4.17and4.18 displaythe S 21 fortwofromthemulti-resonantoptimizationdescribedbyP2andthe bandwidthoptimizationdescribedbyP1,respectively.Thetransmissionthrougheach clearlymatcheswellwiththeexpectedresultsfromtheGAoptimizationprocess.Inthe caseofthemulti-resonantoptimization,theshowgoodoutofbandacceptancewith theexpectedrejectionpropertiesattheoptimizedfrequencies.Figure10showssolutions correspondingtothehighesttransmission,andthehighestbandwidth.Inthiscase,thehigh- estbandwidthsolutionisatapproximately240GHz,whilethelowesttransmissionsolution isat320GHz.Thesevaluesmatchwellwiththeexpectedresultsfromtheoptimization procedure,withabandwidthofapproximately45GHzandmaximumrejectionof-20dBfor 112 Figure4.15SolutionstoP2objectivefunctionsafter80generations. 113 Figure4.16ProgressionofP2objectivefunctionsthroughGAiterations. 114 Figure4.17TwoparetofrontsolutionsfromtheP2objectivespace. 115 Figure4.18TwoparetofrontsolutionsfromtheP1objectivespacecorrespondingtomaxi- mumtransmission(D1)andmaximumbandwidth(D2). 116 thehighestbandwidthsolution,andabandwidthofapproximately25GHzandrejectionof -25dBforthelowesttransmissionsolution. 4.6 MeasurementandFabrication Threefromtheaboveanalysisarechosenforfabricationandmeasurement.These correspondtoD1,D2,andD3showninFigures4.17and4.18.Thearefabricated on250 thickPETsubstrates,with1 ofsputteredcopper.Simplelithographyandwet- etchingisusedtopatternthemetal,withaminimumfeaturesizeofapproximately25 . ThefabricatedareshowninFigure4.19,withaU.S.dimeincludedforscale. InordertocharacterizetheaEmcorePB-7200THzfrequencydomaintestsystem isused.Themeasurementsystemconsistsoftworigidreceiverandtransmitterheads,with afrequencyrangefrom100GHzto2THz,andasamplingresolutionaslowas10MHz.To measurethesample,areferencemeasurementisrequiredinordertoisolateanynoisefrom theresult.Inthiscase,ablankPETlayerwiththesamethicknessastheisusedas areferencemeasurement.ThePETlayersareplacedina2cmmetallicwindow,designed toblockoutalltransmissionbetweenthereceiverandtransmitterotherthanthroughthe sampleplacedinthewindow.TheoveralltestsetupisshowninFigure4.20. Eachismeasuredoverafrequencyrangeof225to350GHz,withastepresolution of250MHz.Theresultingtransmissionspectraofeachcomparedwiththereference measurementisshowninFigure4.21.Themeasuredresultsmatchrelativelywellwith theexpectedsimulatedandoptimizedresults.D2showsmulti-resonantbehavioratthetwo optimizedfrequenciesof250and300GHz.D3hasthewidestbandwidthamongthesamples asexpected,andisshiftedinfrequencybyapproximately25GHz.D1stillshowsastrong resonance,however,thefrequencyisshiftedbyapproximately50GHz. Overall,themeasuredresultsthattheband-stopcharacteristicsofthecan beoptimizedthroughaGAtoachieveadesiredresponseintheTHzfrequencyspectrum. 117 Figure4.19Fabricatedsamples. 118 Figure4.20THzmeasurementsetupusedforthecharacterizationof 119 Figure4.21Measuredresults. 120 However,someofthedesignsmatchbetterwiththeirsimulatedcounterpartsthan others.Thisismostlikelyduetofabricationtolerances.Toimprovethefabrication,a thinnertoplayermetalthatiscompatiblewithtechniquescouldbeutilizedtoachieve precisepatterningofthemetalstructure. 4.7 ErrorAnalysisandDiscussion Inthischapter,theerrorsobtainedforthemeasurementsofthearenotasdrastic asthepreviouschapters,asthereisnocouplingmethodnecessarybetweenthesystemand themeasuredHowever,thesameproblemswiththeTHzfrequencydomainsystem heatingandcoolingarerelevanthere.Inaddition,theexactalignmentbetweentheTxand Rxheadsandthesampleistoquantify.Anothermajorcontributingfactortothe erroristheresolutionofthepatterning.Also,thethicknessofthemetalisapproximately andthusthelossesareexpectedtobehigher. 4.8 ConclusionsandDiscussion Inthischapter,multipleTHzcomponentsaredesignedthroughtheuseofsingleand multi-objectiveevolutionaryalgorithms.THzband-stopareinvestigatedbyoptimizing thebandwidthandtransmissionrejection,aswellasthemulti-resonantpropertiesofthe Threewerefabricatedandmeasured,showinggoodagreementbetweenthe optimizedresultsandmeasurements.Overall,theoptimizationprocessdevelopedinthis workisshowntoyieldcientintegration-compatibleTHzcomponentswithavarietyof applications. 121 CHAPTER5 Plasmonic-InspiredPeriodic WaveguideStructures 5.1 IntroductionandProposedStructures Inthischapter,metal-backedperiodicstructuresareinvestigatedforthedesignof integrationcompatibleTHzcircuitelements.Thesestructurescanbedesignedtohaveeither absorbingproperties,orsupportsurfacewavepropagation,dependingonthecharacteristics ofthetop-layermetal.Ifahighlyconductivemetalisused,thestructuresareusablein guided-waveapplications,withpotentialtorealizemanypassiveTHzelements. 5.2 SimulatedResponseofSeveralPeriodicStructures Tobegin,four2Dperiodicmetal-backedstructuresareexaminedinthissection.Each resonantstructureismodeledwithcopper,andbuiltona50 mthickdielectricsubstrate with r =3.5andadielectriclosstangentof =0.01.Eachunticellisalsocoveredwitha solidcopperbacking.ThefourperiodicstructuresareshowninFigure5.1,alongwiththeir dimensionsinTable5.1.Theperiodicstructuresintroducedherecanbesortedintotwo primarygroups.ThegroupconsistsoftwocirclestructuresshowninFigure5.1(a)and 122 (b).ThisstructureissimplyacircleofradiusR,whilethesecondisacombinationoftwo circles,oneofthesameradiusasthealongwithanotherofradius R s .Theresonance spectrumforthesestructuresisprimarilycharacterizedbymultiple,narrowresonances. Byincludingthesecondcircle,thefrequencyspectrumisexpandedfromtheadditional resonances. ThesecondgroupconsistsoftheresonantstructuresofFigure5.1(c)and(d),across typeresonantstructure,aswellasaMinkowskifractal,whichisthegeometriccompliment ofthecross.Thefrequencyspectrumofthesesstructuresareverytfromthe groupofresonators.Asopposedtomultiplenarrowresonances,thesestructuresprovidea single,butwidebandfrequencyspectrum. Eachstructureissimulatedina3DFEMsolver(AnsoftHFSS)asa2Dperiodic unitcellwithquetboundaryconditionsandplanewaveincidence.Theplanewaveisz- directedandTMpolarized,andthestructureisinitiallyexcitedatnormalincidence.The cotsaredisplayedforbothtypesofresonantgroupsinFigures5.2and5.3. Duetothemetalbackingoneachunitcell,itwouldgenerallybeexpectedthateach structurewillhavealloftheincidentpowerected.However,itisclearfromthe cotsthateachstructurehasaresonancecorrespondingtoalackofioncentered aroundadesiredfrequency. Table5.1UnitCellDimensions R( )L( )x p ( )y p ( ) (a)Circle400-864864 (b)Circle/Small400/100-864864 (c)Cross-400354354 (d)Minkowski-114276276 123 Figure5.1Resonantunitcellstructures:a)circlestructure,b)dualcirclestructure,c)cross structure,d)minkowskifractal. 124 Figure5.2ncotsofcircle-typeresonantstructures. 125 Figure5.3ioncotsofcross-typeresonantstructures. 126 Anumberoffactorscouldbeassumedtocontributetothis,suchasdielectricloss, absorption,surfacewavepropagation,orhigherordercouplingintoevanescentmodes.While someofthepowercouldbelostindielectricorothertypesoflosses,alinearlosswhich increaseswithfrequencywouldbeexpected.Inthiscase,itisclearthatpatterningofthe topmetallayerchangesthecharacteristicsoftheioncot,rulingouttraditional loss.Inthenextsection,thecharacteristicsofthequetmodeinteractionarestudiedto determineifhigherorderevanescentmodesareresponsibleforthisphenomena. 5.3 TheoreticalFloquetModeAnalysis Atheoreticalquetexpansioncanbeappliedtodeterminetheoverallcharacteristicsof thecouplingintotheperiodicstructuresatthefrequencieswherethecots displayaresonance.Whenatimeharmonicplanewaveisobliquelyincidentona2Dperiodic structurewithperiodicity x p and y p ,thescatteredelectriccanbewrittenas: ~ E s ( x;y;z )= ~ E s ( x + x p ;y;z ) e jk i x x p ; x-direction(5.1) ~ E s ( x;y;z )= ~ E s ( x;y + y p ;z ) e jk i y y p ; y-direction(5.2) wherethewavenumbersoftheincidentwaveineachdirectionare k i x = k 0 sin i cos ˚ i ;k i y = k 0 sin i sin ˚ i (5.3) Commonly,atransformedvariablesisthenintroduced[116]whichisperiodicinboth xandywithperiodicity x p and y p ,respectively. ~ E s ( x;y;z )= ~ P s ( x;y;z ) e j ( k i x x + k i y y ) (5.4) substitutingthisinto(5.1)yields 127 ~ P s ( x;y;z )= ~ P s ( x + x p ;y;z ) ; x-direction(5.5) ~ P s ( x;y;z )= ~ P s ( x;y + y p ;z ) ; x-direction(5.6) Thetransformedvariablecanthenbeexpandedasasummationofplanewavesasa Fourierseries. ~ P s ( x;y;z )= 1 X m = 1 X n = ~ A mn ( w ) e j [( 2 ˇm x p ) x +( 2 ˇn y p ) y ] (5.7) wherethemodalexpansioncotsaregivenbyequation8. ~ A mn ( ! )= 1 x p y p Z x p 0 Z y p 0 ~ P s ( x;y;z ) e j [( 2 ˇm x p ) x +( 2 ˇn y p ) y ] dxdy (5.8) Thefrequency, k zmn ,foragivenmodeisasthefrequencyatwhichmode begantopropagate,whereanyfrequencybelowtheisevanescent.Thefrequency canbefoundfromthewavenumbersinthex-andy-directions: k xm =( 2 ˇm x p ) k 0 sin i cos ˚ i (5.9) k yn =( 2 ˇn y p ) k 0 sin i sin ˚ i (5.10) thefrequencyisthengivenbythefollowingrelation. k zmn = 8 > > < > > : q k 2 0 k 2 xm k 2 yn ; propagatingwaves q k 2 xm + k 2 yn k 2 0 ; evanescentwaves (5.11) However,forthecaseofnormalincidence,itcaneasilybeshownthat 128 Table5.2Frequencies k zmn 01101102202112 Circle(GHz)346346490693693775775 DualCircle(GHz)346346490693693775775 Cross(THz)1.081.081.532.172.172.422.42 Minkowski(THz).846.8461.191.691.691.891.89 Table5.3ModalCots( 1%notshown) A mn 00011011 Circle104GHz96% 251GHz95% 297GHz73%12%6%2% DualCircle104GHz96% 251GHz95% 297GHz73%12%6%2% 325GHz86%5% Cross240GHz97% Minkowski225GHz82%7% ~ P s ( x;y;z )= ~ E s ( x;y;z )(5.12) and ~ A mn ( ! )= 1 x p y p Z x p 0 Z y p 0 ~ E s ( x;y;z ) e j [( 2 ˇm x p ) x +( 2 ˇn y p ) y ] dxdy (5.13) wherethewavenumbersalsosimplifytothefollowing. k xm =( 2 ˇm x p ) ;k yn =( 2 ˇn y p )(5.14) Itisinterestingtonotethatthefrequenciesproducedbyanormallyincidentplane waveonlydependontheperiodicityoftheunitcell,andnoneofthegeometricproperties ofthestructurecontainedwithin.Themodalcots,however,dependonthescattered electricwhichisprimarilyproducedbythegeometryofthestructureitself. 129 Thefrequenciesarecalculatedusingtheunitcelldimensionsandequation11, andaresummarizedinTable5.2.Thecircleresonatorshavethesamefrequencyfor thefundamentalmodeatapproximately346GHz.ThecrossandMinkowskifractalhave muchhigherfundamentalfrequencies,at1.08and.846THz,respectively.Anymodes contributingbelowthesefrequenciesoutsideofthefundamentalmodewillbeevanescent modes. Themodalcotsarefoundbysamplingthescatteredelectriconaplane approximatelyonewavelengthfromeachperiodicstructureusingequation13.As theyarefrequencydependent,themodalcotsareexaminedateachresonanceinthe frequencyspectraofeachstructure.ThesecotsareshowninTable5.3,intermsof thepercentageoftotalcontributiontotheplanewavecouplingintotheperiodicstructure. Thebehaviorofthecouplingatthefrequenciesofinterestforeachstructureareshownto primarilybecausedbyfundamentalquetmodeinteractions.Thefrequenciesofinterest inallofthestructuresaretlylowerthanthefrequenciesofanyofthehigher ordermodes,andthemodalcotsshowlittlecouplingintothehigherordermodes. Therefore,itisconcludedthatverylittleoftheenergyislostinhigherorderevanescent quetmodes.Thisleavesthetwoprimaryexplanationsforthisphenomenaasabsorption, orasurfacewavephenomena.Inthefollowingsections,itwillbeshownthatbasedonthe conductivepropertiesofthemetal,thesestructurescanbetailoredtoactaseitherabsorbers, orsurfacewaveinterconnects,eachwithmultipleapplicationsinTHzintegratedcircuits. 5.4 LinearWaveguideAnalysis Whilethepreviousanalysisconcernedonlyperiodicstructures,therealworld waveguidesanddevicesthatwillbeconstructedusingtheunitcellswillofcoursebe TheoveralldesignmethodologyfortheplasmonicTHzwaveguidesisshowninFigure5.4. First,asshownintheprevioussections,adesiredunitcellischosenananalyzedwith2D 130 periodicboundaryconditions.Nowthattheresonancesoftheindividualunitcellsareknown, theunitcellisexpandedintoaarray.Awaveguidecanthenbemadebyreducing theperiodicityinonedirection,allowingforpropagationalongtheother.Theanalysisand ofaarrayandthetransitiontoavarietyofwaveguidesispresentedinthe followingsections. 5.4.1 Array First,thecircleunitcellisexpandedinbothdirectionsasa5x5array.ATMpolarized planewaveisusedtoexcitethearrayinHFSSwithatransverseincidentangle(alongthe y-axis).ThepowerwineachdirectioniscalculatedusingEquation5.16overavertical planeinthedesireddirection. ~ P ( ! )= Z 5 x p 0 Z 5 y p 0 ~ E s ( x;y;z ) ~ H s ( x;y;z ) dxdy (5.15) Figure5.5showsthepowerwinboththex-andy-directions.Asexpected,thefre- quencyspectrumofthepowerwineachdirectionmatcheswellwiththeresonancesofthe individualunitcells.Inaddition,thepowerwinbothdirectionsisverysimilar.However, ifthearrayisreducedinonedirection,thenthepowerwcanbeincreasedintheother. Figure5.6comparesthepowerwinthey-directionforthe5x5array,andanarraywhere thex-directionisreducedtotwounitcells.Thefrequencyspectrumforbotharraysmatches verywell,whilethepowerwinthey-directionofthe5x2arrayisapproximatelydouble 131 Figure5.4Designprocessofplasmonicwaveguides,progressingthrough(a)periodicunit cell,(b)array,and(c)waveguide. 132 Figure5.5Powerwinboththex-andy-directionsalongthearray. 133 Figure5.6Comparisonofpowerwinthey-directionof2x5and5x5circlearrays. 134 thatofthe5x5array. 5.4.2 TerahertzWaveguides Whilethepreviousanalysisconcernedonlyperiodicstructures,thissectionintro- ducesstructuresbasedonhighlyconductivemetals.Thesestructuresexhibitasurface wavephenomenathatcanbeexploitedforanumberofTHzapplications.Inthiscase,the wavepropagationisonlydesiredinonedirectionofthearray.Therefore,inthe desireddirectionofwavepropagation,theunitcellsareexpandedtoadesiredlength,with theotherdirectionisminimizedtotwounitcellsinlength.Waveguidingstructuresaremade fromthefourunitcellsintroducedpreviously,includingthecircle,dualcircle,minkowski fractal,andcross. ThewaveguidingstructuresaremodeledwithHFSS,andexcitedusingaTMpolarized planewave,travelinginthelongitudinaldirection.Inthiscase,aplanewaveisusedasan excitationtoensurecomparableresultswiththequetexcitationsusedinthein periodicanalysis.However,withplanewaveexcitation,traditionalS-parametersareun- available.Therefore,todeterminethepropertiesofthewaveguidingstructures,2Dcutsin boththeXYandZYplanesareusedtosamplethepowerintensityalongthesurface,aswell asthepowerwthroughthewaveguide.Thepowerontheseplanesiscalculatedusingthe relationship ~ P ( ! )= Z 2 x p 0 Z Ny p 0 ~ E s ( x;y;z ) ~ H s ( x;y;z ) dxdy (5.16) where x p and y p arethelengthsofasingleunitcellineachdirection.Figure5.7showsthe geometryofasamplewaveguide,alongwiththesimulationsetup.Thenormalizedpower winthey-direction,aswellasthepoweronthesurfaceofeachstructures,isshownin Figures5.8and5.9forallfourunitcelltypes.Inthiscase,eacharecalculatedusingequation 15overeachsamplingplane. 135 Figure5.7SimulationtopologyanddesignprocessofTHzwaveguides. 136 Figure5.8Powerwalongthesurfaceofthecrossandminkowskitypewaveguides. 137 Figure5.9Powerwalongthesurfaceofthecirclestructuretypewaveguides. 138 Forthecircleanddualcirclestructures,thefrequencyspectrumissimilartowhatwould beexpectedfromtheunitcellanalysis,multiplenarrowbandresonantpeaksofvarying intensity.ThecrossandMinkowskifractalbothdisplayasingle,wellresonancepeak, whichalsomatcheswellwiththeperiodicanalysis.However,itisalsoimportanttonote wherethepowertravelingthroughthewaveguideisprimarilyconcentrated.Asmentionedin theprevioussections,thecouplingoftheincidentwaveintotheseperiodicstructuresexcites aprimarypropagatingmode,whichcontributestoasurfacewaveplasmoniclikeifthe conductivityofthemetalishighenoughtolimittheabsorption. However,oneoftheprimarycharacteristicsoftheplasmonicphenomenonisthatthe occursatthedielectricandmetalinterface,whilethepropagationoccursatthesurface ofthisinterface.Toinvestigatethepropagationonthesurfaceofthesewaveguides,thepower issampledalongthesurfaceofthemetal.Thefrequencyspectrumonthesurfaceofeach waveguideisverysimilartothetransmittedpowerspectrumthroughtheXZplane.This showsthatnearlyallthepoweriscontainedatthesurfaceofthemetal,asthemaximum valuesofthepowersampledarenearlythesame. Whilethefrequencyspectrumsoftheindividualunitcellsandthewaveguidesmatch relativelywell,therearesomeinthelocationandmagnitudeofthetransmitted waveguideresonancesandtheresonancesfromtheperiodicstructures.The encebetweentheperiodicandperiodicarraychangesthespectrumslightly, butthechangeinincidentangleistheprimarycontributor.Figure5.10showstheangle dependanceofthecirclestructurefora2Ditelyperiodicunitcellandawave- guide.Theresonanceinboththeandpowertransmissionchangesbothinintensity andlocation,explainingsomeofthediscrepanciesintheresults.Inaddition,atthehigher incidenceanglesthetransmissionismaximized. Whiletheseinterconnectsdonotdisplaytypicalwaveguidecharacteristics,suchasphase velocity,groupvelocity,orfrequencies,theydodisplayhighlevelsofpowerc mentalongtheirsurface.Duetothehighlossestypicallyassociatedwithmetallicwaveguides 139 atTHzfrequencies,suchaphenomenaisverydesirableinmanyapplications,eventhough thetransmissionspectraisrelativelynarrowband.WhileothertypesofTHzwaveguides mayprovetobelower-lossinsimplewaveguideapplications,theproposedstructureshave potentialformanypassiveTHzcomponentsthatarenotrealizablewithotherTHzwaveg- uides. 5.5 ApplicationsInPassiveElementDesign Asaresultofthehighpowertalongthesurfaceofthewaveguides,structures withsharperbendsareeasiertoimplementcomparedwithotherTHzinterconnects.Figure 5.11comparesatypicalcurvedstructureforadielectricwaveguide(a),traditionalplasmonic waveguide(b),andtheproposedplasmonicwaveguide(c).Inthecaseofthedielectricwave- guide,mostofthepowerislostinthecurvedportionofthewaveguide.However,inthe plasmonicwaveguide,highpowertcanbeshownalongthecurveandmaintained throughoutthestraightsectionthereafter.Thewaveguidemadeoftheperiodiccirclestruc- tureshowssimilarcontalongthecurvedportioncomparedwiththetraditionalTHz plasmonicwaveguide. AnotherimportantpassiveTHzstructureasidefromawaveguideisapowersplitter. Apowersplittercontainsawaveguidestructurewithtwobrancheswhichsplitthepower equallybetweeneachbranch.Thepowersplitterismadefromthecircleresonantstructure, withthesameperiodicityanddimensionsasthewaveguide.Figure5.11alsoshowsthe electricementforthepowersplitterat245GHz.Highdtcanbe seenalongthelengthofthestraightportion,aswellasinthetwobranchesofthepower splitter.Littlelossisdisplayedinthecurvesthatcomprisethepowersplitter,whichcan beacommonprobleminconventionalTHzwaveguides[35].Inaddition,Figure5.12shows thenormalizedpowerwthrougheachsectionofthepowersplitter.Thepowerdensity spectrumisverysimilarforsection(a)and(b),showingthatthepowerisevenly 140 Figure5.10Angledependanceinboththe(a)cotand(b)powerwofthe circletypestructure. 141 Figure5.11Bendingin(a)dielectricwaveguideat300GHz,(b)traditionalplasmonicwave- guideat300GHz,and(c)thinmetalbasedplasmonicwaveguideat297GHz.Fieldcon- tofapowersplitterisalsoshown. 142 Figure5.12Normalizedpowerwthrougheachsectionofthepowersplitter. 143 Figure5.13Proposedsetupofthin-sampledielectricsensor. 144 Figure5.14Simulatedchangeinphaseoftransmissionthoughacircletypewaveguidewith varyingsampledielectricconstant. 145 betweenbothsectionsofthesplitter. Duetothehightalongthesurfaceofthesestructures,theyalsocan beusedtodevelophighlyaccuratesensors.Figure5.13showstheproposedsetupofthe sensor.Inthiscase,athinsamplethatismuchlessthanawavelengthisplacedalongthe lengthofawaveguidingstructure.Astheareveryclosetothesurface,small samplesizescanbeeasilydetected.Figure5.14showsthesimulatedphaseofthetransmitted signalthroughthewaveguide,withadielectricsampleapproximately 0 = 30issizeplaced inthecenterofthestructure.Clearly,whenthedielectricconstantofthesampleisvaried, anoticeablechangeinthephasethroughthestructureisobserved. 5.6 FrequencyTailorableStructures WhilethepreviousanalysishasbeenprimarilyappliedtosimpleFSS-basedstructures,more complexgeometriescanalsobeexploitedtoenhancethepropertiesofthewaveguides.Figure 5.15showsasimplecirclebasedresonantstructurethatismobycuttingoutpieces ofthecircle.ThefrequencyresponseofeachstructureisshowninFigure5.16.Clearly, asthestructureisfurtherdivided,thenumberofresonancesinthefrequencyspectrumis increased. Theseresultsshowthatcertaindesiredcharacteristicsoftheunitcellsthatcanbeused tocreatethewaveguidesandotherdevices.Thisisparticularlyusefulinthecaseofthe abovedesignedwaveguides,astheirapplicationislimitediftheonlyoperationalbandis smallinbandwidth.Inaddition,onlythecopperstructureisneededtobemoasthe unitcellsizeandmaterialsareunchanged.Asimilartopologyoptimizationapproachthat waspresentedinthepreviouschaptercanthereforebeappliedtothesestructuresaswell. Figure5.17showsaproposedtopologyfortheoptimizationprocess.Inthiscase,5 concentriccirclesof50thicknessareseparatedinto20slices.Inthiscase,thestructuresare madeofthesamePETmaterialandfullybackedwithcopper.Theslicesofeachcircleare 146 controlledwithasimplebinaryGA,with100states,and2 100 totalcombinations. TheentiregeometryofoneunitcellisshowninFigure5.18,withasampletopologyfound throughtheGAshownaswell. Foraninitialtestofconcept,theGAisusedtosimplyoptimizethelocationofresonances inthecotofthestructures.Twosamplelocationsareselected,oneat120 GHz,andanotherat275.TwoseparateGAoptimizationsimulationsarethenperformedto theoptimallylowestcotatthedesiredfrequencies. Figure5.19showstwopossibletopologiesfoundwiththeGAforoptimalresonancein therecotat120and275GHz.Inthiscase,cotsof-17.9dB and-15.8dBarefoundfor120and275GHzfromeachstructure,lefttoright.Thefrequency responseofthecocientforbothstructuresisalsoshowninFigure5.20. 147 Figure5.15Geometryof(a)basiccirclestructure,(b)circlestructurewithholes(c)circle structurewithmoreholes. 148 Figure5.16tioncotsofthestructuresintroducedin5.15. 149 Figure5.17Proposedstructureforoptimization. 150 Figure5.18Simulatedstructurewith(a)allpixelsonand(b)aselectedexampleofone topologyafteroptimization 151 Figure5.19Twooptimizedstructureswithresonancesat(a)120GHz,and(b)275GHz. 152 Figure5.20ncotofstructurespresentedin5.19. 153 5.7 FabricationandMeasurementResults 5.7.1 FabricationMethod Twocircuitswerefabricated,astraightguided-wavestructureandapowersplitter,both fromthecircletyperesonantstructures.Thesesampleswerefabricatedona50 mthick pieceofRogers3850LCPbothsidesbackedwithcopper.Thesubstratepropertiesin thedesiredfrequencyrangeareasfollows: r =3.5,dielectriclosstangent =0.01,and Cuthicknessof17 m[117].Thecopperisretainedonthebackside,whilethetopsideis patternedusingconventionalmicro-fabricationprocesses.Asimplephoto-lithographyand wetetchingprocessisusedtopatternthetop-layermetal. 5.7.2 MeasuredResults ThefabricatedstructuresaremeasuredwithtwoseparateTHzmeasurementsystemsto ensurerepeatableresults.First,thewaveguideandpowersplitteraremeasuredusinga PicometrixT-Ray2000time-domainTHztestsetup.Withthissystem,THzwavesaregen- eratedusingaphotoconductiveswitchandafemtosecondlaser.Thesystemiscoupledwith THzopticstoproducealinearlypolarizedandcollimatedbeam,andhasbothatransmitter (Tx)andreceiver(Rx)thatcanbeeasilyadjusted.However,oncethetime-domainsignal istransformedintothefrequencydomain,themaximumstepresolutionisapproximately12 GHz,makingittomeasurenarrowbanddevices.Theothermeasurementsystem usedisaEmcorePB-7200frequencydomainsetup.Thefrequencydomainsystemiscapable ofmeasuringverynarrowbandstructures,withafrequencyresolutionaslowas10MHz. Thissystemalsohasbothatransmitter(Tx)andreceiver(Rx)coupledwitheroptics. DielectricfocusingprobesareusedtocoupletheTHzradiationfromtheTxandRxheads tothestructures,asproposedinchapter2.Theprobesaswellasthefabricatedcircuitsare showninFigure5.21.Themeasurementsetupofthewaveguidewiththeprobesisshownin 154 Figure5.21Fabricatedwaveguide,powersplitter,andHDPEprobes. 155 Figure5.22Waveguidemeasurementsetup. 156 Figure5.23Measuredtransmissionspectraforcircletypewaveguidewith(a)frequency domainsystem,(b)timedomainsystem. 157 Figure5.24Measuredtransmissionspectraforcircletypewaveguidecomparedwithdielectric ofsamedimensions. 158 Figure5.25Transmissionversuschangeinprobeplacementforthecircletypepowersplitter at100GHz. 159 Figure5.22. Figure5.23showsthemeasuredtransmittancethroughthewaveguideforboththetime domainandfrequencydomainmeasurement.Thetransmissionspectrumfromthetimedo- mainmeasurementshowstransmissionpeaksnear0.1,0.22,and0.38THz.Theseresonance peaksarenearthepeaksexpectedforthecirclestructure.However,duetotheresolution ofthesystemanddataaveraging,someofthepeaksarenotpresentorshifted.Inthecase ofthefrequencydomainmeasurement,fourtransmissionpeaksoccuratapproximately.1, .16,.26,and.35THz.Onlyonehalfofthe.1THzpeakisshown,asthatistheminimum measurablefrequencyforthesystem.Whiletheresonancesdonotmatchexactlyasthepre- dictedresonances,thisdiscrepancyisbelievedtobecausedbyafewfactors.Theprimary contributionsaremostlikelyduetomisalignmentbetweentheprobesandthewaveguide,as wellastheprobeanglenotbeingexactlytransversetothewaveguide,similartothechange inresonanceshowninFigure5.10.Also,theinitialresonancesweresimulatedas periodicinbothdimensions,whileinrealitythisperiodicityisHowever,nearly60%of thepoweristransmittedthroughthewaveguideatoneofthepossibleresonancefrequencies. Figure5.24showsthemeasuredtransmittedpowerovertwofrequencyrangescorresponding tothestrongesttransmissionpeaksofthefrequencydomainmeasurement,comparedwith adielectricstripmadeofthesamedimensionsasthewaveguide.Clearly,amuch largertransmissionisdetectedoverthefrequencyrangewheretheresonantfrequencyofthe toplayermetaloccurs. Thetransmissionpropertiesofthepowersplitteraremeasuredbytheprobepo- sitionattheinputtothepowersplitter,whilevaryingthepositionofthesecondprobe alongbothoutputbranches.Here,thetimedomainsystemisusedtomeasurethepower splitter.Theintensityismeasuredatapproximately100GHz,nearthehighestpoint ofthetransmissionspectra.Figure5.25showsthemeasuredintensityasafunction ofposition.Here,thezeropositionrepresentsthemiddlepointbetweenthetwobranches. Fromthemeasureddata,itisclearlyshownthatthewavepropagatesalongthepatterned 160 metalandisnotconcentratedinthedielectric. 5.8 ErrorAnalysisandDiscussion Inthischapter,theerrorsassociatedwiththewaveguidemeasurementsaresimilartothat ofchapter3.Again,themosterroroccurswhentheprobesarenotalignedwellwiththe waveguide,butisagaintoquantify.Inthecaseofthesewaveguides,theincident anglealsochangesthefrequencyspectrumofthewaveguidesasshowninFigure5.10,which compoundstheerrorevenfurther. InthecaseoftheTHzsystemsusedtomeasurethewaveguides,thefrequency-domain systemfromthesameissuesdiscussedinChapter2.However,thetimedomainsystem alsohasitsownerrorsassociatedwithit.Primarily,thisiscausedbythesmallfrequency resolutionofapproximately12GHzwhentheFouriertransformisusedtoconvertthetime- domainresultsintothefrequency-domain.However,incomparisonwithotherwaveguide measurementtechniquespresentedintheliterature,themeasuredresultspresentedhereare wellwithinatolerableerror. 5.9 ConclusionsandDiscussion Inthischapter,anotherapproachtodevelopTHzwaveguidelikedevicesisinvestigated.The design,fabricate,andmeasureTHzplanarplasmoniccircuitsbasedonthinmetalresonant structuresispresented.Theresonancefrequencyatwhichtheplasmonic-likemodecan belaunchedcanbepredictedbysimulatinganarrayofperiodicstructures.Each structurewasthentodisplayplasmoniclikewaveguidingbysimulatingboth straightwaveguidesandapowersplitter.Thesestructureswerecreatedwithsimpleclean roomfabricationprocessesonalow-costLCPsubstrate.Anewapproachtocouplingthe signalontoplasmonicstructureswithadielectricfocusingprobeisalsointroduced.Measured resultsshowthatlongrangewaveguidingcanbeachievedusingplanarplasmonicstructures 161 atTHzfrequencies.Measurementsofastraightwaveguideandpowersplittershowstrong entalongthelengthofthewaveguideandalongeachbranchofthepower splitter,presentingthepossibilityforuseinthedesignofnovelTHzplanarcircuits. 162 CHAPTER6 ConclusionsandDiscussion Inthisdissertation,t,integrationcompatibleTHzpassivedevicesaredeveloped. Threeprimarytypesofpassivedevicesareconsidered:Thzwaveguides,andcouplers. ThecouplingofTHzradiationbetweencommercialTHzsystemsandTHzdevicesis realizedwithHDPEdielectricfocusingprobes.Theseprobesaredesignedsuchthatthey canbeexcitedviaTxandRxheadsavailableincommercialTHzsystems.Theprobes arestudiedwithFEMmodelingtodeterminethefocalpointandtalong asmallsectionoftheprobetip.Thecouplingcharacteristicsoftheprobeswhenusedin conjunctionwithasimpledielectricwaveguideisstudied,andthelossoftheprobesand couplingispresented. basedarealsointroduced,whichareintegrationcompatiblealthough stillmeasuredinaquasi-opticalmanner.Thecharacteristicsareoptimizedusinga multi-objectivegeneticalgorithmthatisinterfacedwiththecommercialFEMsolverHFSS. Primarily,band-stopareinvestigated,andthebandwidth,rejection,andmulti-band characteristicsareoptimized. Twowaveguidetypesarealsointroduced.First,asiliconbaseddielectricridgewave- guidewhichcanbeeasilyfabricateddirectlyon-waferisinvestigated.Thetransmission characteristicsofthewaveguidearestudiedrstthroughaapproximate2-Dtheoreticalso- 163 lution,andthenthrough3-DFEMmodeling.Theridgewaveguidesshowlowattenuation especiallywhentheridgewidthandheightissmall,butabetweencurvatureand tpropertieswiththeheightandwidthoftheridgeisfound.Secondly,ahybrid waveguidewithbuiltinpropertiesisintroduced.Thewaveguidesareinspiredby traditionalplasmonicwaveguides,butcreatedfromtyperesonators.Atheoretical quetanalysisisperformedtoensurenohigherorderevanescentmodesarecoupledinto. FEManalysisofthewaveguidepowertandintensityisalsoperformedto ensureadesiredfrequencyresponse. Bothwaveguidesarethenmeasuredusingcommercialtimeandfrequency-domainTHz systems.Inconjunctionwiththefocusingprobesintroducedpreviously,thefrequencyre- sponseofbothwaveguidetypesisattained.Complexpower-splittermeasurementsarealso performedwhichshowthepotentialforthesewaveguidestocreateotherTHzpassivedevices. Overall,thisdissertationintroducest,integrationcompatibleTHzpassivedevices. Therealizationofnotonlypassivedevicessuchaswaveguidesandbutalsothe introductionofacouplingmethodcapableofbridgingbetweenthecurrentquasi-optical systemswithwafer-levelintegratedcircuitsprovidesacompletesimulationtomeasurement correlationfortheproposedTHzdevices.Theseresultsshowpromiseforthefutureof integratedTHzsystems,andtheimprovementofcurrentquasi-opticaltestsystems. 164 BIBLIOGRAPHY 165 BIBLIOGRAPHY [1] Siegel,PeterH.Terahertztechnology.MicrowaveTheoryandTech-niques,IEEETrans- actionson50.3(2002):910-928. 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