Date of Award

Summer 2003

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical/Computer Engineering

Committee Director

Sacharia Albin

Committee Member

John B. Cooper

Committee Member

Karl H. Schoenbach

Committee Member

Linda L. Vahala

Abstract

Photonic crystals are periodic electromagnetic media in optical wavelength scale. They possess photonic band gaps (PBGs) that inhibit the existence of light within the crystals in certain wavelength range. Such band gaps produce many interesting optical phenomena. In this dissertation, the frequency (plane wave method, PWM) and time domain (finite difference time domain method, FDTD) methods are developed for their modeling and simulation.

The theory and algorithm of plane wave method are studied in detail and implemented in a unique and efficient approach. PWM is used to obtain the gap and mode information of ideal and defective photonic crystals. Several material and structural parameters are shown to affect the band gap. Examples of devices studied include high-Q micro-cavities, linear waveguides, highly efficient sharp bend, and channel drop filters.

Effects of defects in photonic crystals are studied in detail. Results show that point defects can form resonator centers of very high quality factors, whereas line defects can form linear waveguides in low/high index material. Highly efficient energy transfer occurs between defect modes. A numerical analysis of the interaction mechanisms between them is carried out and the results serve as a theoretical guide for device designs.

Photonic crystal fiber (PCF) with periodic air holes in the cladding is analyzed using a modified PWM method. PCF is able to guide light in single mode in a very broad wavelength region, or it can guide light in air core, offering superior optical properties. By tailoring the microstructures of the cladding, mode shape and group velocity dispersion can be controlled.

Finally, a simulation tool using FDTD is developed to study and simulate the device design. The Order-N method using FDTD and periodic boundary conditions is also presented to reduce the heavy computation of PWM method. Light dynamics in PBG devices are simulated and analyzed using FDTD and Perfectly Matched Layer boundary conditions. Excitation sources, mode symmetry, and detection techniques are described to obtain complete and accurate information from the simulations. The combination of the time domain and frequency domain methods provides a powerful tool for analysis and design of PBG devices with high performance.

DOI

10.25777/kpwa-jt36

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