The quest for active media models : a self-consistent framework for simulating wave propagation in nonlinear systems
This work presents new approaches to simulations of active media at the level of individual particles. Active systems contain internal, nonlinear, processes beyond those of simple scattering systems; thus these new models afford high degrees of fidelity in exploring the underlying physics without recourse to continuum or spatially-averaged approximations.First, I examine the dynamics of microspheres set into motion by ambient acoustic radiation in a fluid described by potential flow in the long-wavelength limit. Variations in the local surface pressure caused by scattering from each microsphere set each microsphere into motion following Newton’s second law. By expanding this pressure in terms of spherical harmonics—natural eigenfunctions of the unretarded radiation kernel—I recover an analytic description of the force on individual microspheres due to an incident waveform. High-order numerical integrations then relate the surface potential on one microsphere to the surface pressure on the others, thereby coupling the microspheres’ trajectories. These simulations predict a dominant translational effect along the direction of propagation of the incident waveform, though they also reveal significant dipolar interactions between microspheres that produce secondary expansions and contractions of the collective microsphere system.Extending my approach from acoustic to electromagnetic systems, I apply it to a collection of quantum dots: “artificial” two-level atoms with a size-dependent energy structure. The optical Maxwell-Bloch equations give the evolution of quantum dots under the influence of electromagnetic fields; this evolution then produces secondary radiation that couples a collection of quantum dots together. In my computational model, I castmy secondary electromagnetic fields in terms of a point-to-point integral operator that accurately recovers both near- and far-field effects. These fields, then, drive a set of implicitly coupled Bloch equations (solved with an exponentially-fitted predictor/corrector scheme) to give the dynamics of the system as a whole. In ensembles of up to 10 000 quantum dots, my model predicts synchronized multiplets of particles that exchange energy, quantum dots that dynamically couple to screen the effect of incident external radiation, localization of the polarization due to randomness and interactions, as well as wavelength-scale regionsof enhanced and suppressed polarization.The remainder of the work uses the same physical quantum dot system while moving towards efficient computer-aided device design. I detail an improved propagation algorithm to reduce the time and space complexity of the simulation dramatically, thereby facilitating rapid analysis of promising device structures. The algorithm makes use of physical and numerical approximations to effect large-scale calculations in reasonable CPU time. A rotating-frame approximation removes high-frequency components in the evolution of the system while simultaneously preserving accurate interference phenomena in space,thereby affording far larger simulation timesteps. Additionally, projecting the source current distribution onto a regular spatial grid makes use of a low-rank approximation to the field propagator to communicate radiation information between distant groups of particles via fast Fourier transforms in a manner reminiscent of fast multipole methods.
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- In Collections
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Electronic Theses & Dissertations
- Copyright Status
- Attribution 4.0 International
- Material Type
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Theses
- Authors
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Glosser, Connor Adrian
- Thesis Advisors
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Piermarocchi, Carlo
Shanker, Balasubramaniam
- Committee Members
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Duxbury, Phillip
Tessmer, Stuart
Albrecht, John
Luginsland, John
- Date
- 2018
- Program of Study
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Physics - Doctor of Philosophy
- Degree Level
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Doctoral
- Language
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English
- Pages
- xvi, 88 pages
- ISBN
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9780355988284
0355988283
- Permalink
- https://doi.org/doi:10.25335/kcef-fq14