Dissertation/Thesis Abstract

Nonlinear Analysis of Silicon Microdisk Resonators
by Slawik, Alexander John, Ph.D., Northwestern University, 2015, 150; 3741327
Abstract (Summary)

This dissertation addresses the character, control, and application of self-sustained oscillations in two-photon absorption dominated optical cavities. The complex interactions of photons, electrons, and thermal effects are understood to drive these emergent oscillations, with the dynamics captured by a system of ordinary differential equations. First, I explore the dynamics of the model and characterize the emergent optical oscillations as relaxation oscillations of a fast-slow system under certain conditions. Within this framework, I establish the entrainment of the oscillations to periodic forcing, providing an easy mechanism for control. The model is further extended to an opto-mechanical system which can be used as a sensor for atomic force microscopy. Analysis of the system predicts that two-photon absorption based effects can excite the mechanical modes of the sensor and increase the signal to noise ratio of the optical readout.

Indexing (document details)
Advisor: Abrams, Daniel
Commitee: Kath, Willian, Silber, Mary
School: Northwestern University
Department: Applied Mathematics
School Location: United States -- Illinois
Source: DAI-B 77/05(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Optics
Keywords: Bifurcation, Entrainment, Limit cycle, Nonlinear, Relaxation oscillations, Whispering gallery modes
Publication Number: 3741327
ISBN: 978-1-339-33602-2
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