Buddhi M. Rai

Doctoral Dissertation Announcement

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Candidate: Buddhi M. Rai

Degree of: Doctor of Philosophy

Department: Physics

Title: Modeling Transmission of Photonic Crystal Waveguide Modes Enhanced by Kerr Nonlinearity

Committee:
Dr. Arthur R. McGurn, Chair
Dr. Sung Chung
Dr. Thomas Gorczyca
Dr. Alvin Rosenthal
Dr. Dennis Pence

Date: Tuesday, May 15, 2012 10:00 a.m. to Noon
2202 Everett Tower

Abstract:
Nonlinear modes of electromagnetic fields propagating in photonic crystal systems are studied by implementing various computer simulation techniques using electromagnetic theory. The fundamentals of simulation of photonic crystals are analyzed using general purpose methodologies such as the FDTD or PWE. Information derived from the underlying physical insights into the systems could be utilized to describe the control mechanisms over the propagation of the modes around impurities in the photonic crystal lattice. The impurities trap the resonantly localized electromagnetic modes having a frequency in a stop band of the photonic crystal, suggesting novel optical controls in photonic crystal waveguides or microcavities. Our focus is on better understanding nonlinear modes existing with photonic crystal waveguides which interact with Kerr nonlinear optical media; this would enable us to reveal specific mechanisms of the nonlinear systems and their potential nonlinear functions. To gain full generality about nonlinear modes of increasing complexity, we propose a novel theoretical approach, the nonlinear difference equation, using Green's function theory of the inhomogeneous system. The recursively defined difference equations for guided modes of photonic crystal waveguides could be solved for the guided modes interacting with multiple bound modes localized on the impurity features. The interest is on the transmissivity of resonant scatterings of the nonlinear modes arising from in- or off- channel features formed of Kerr dielectrics in a 2D photonic crystal. The modes display the wide and interesting varieties of behavior present in the system, including among others, optical bistability and induced transparency. The scatterings are compared with results of the scatterings of the modes in the linear limit of the Kerr media. More interestingly, the transmissions are fully treated for the cases in which the field dependence of Kerr dielectric properties, enhancing nonlinear effects, allows two different frequency waveguide modes to interact with one another by a modulation of the Kerr properties. In this regard, we show the observation of one mode used to model numerically the transmission characteristics of the other, e.g. propagation of one frequency mode can turn on and off the resonant transmission of the other along the waveguide channel.