Date of Award

Spring 2002

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Electrical Engineering - (Ph.D.)

Department

Electrical and Computer Engineering

First Advisor

Haim Grebel

Second Advisor

Gerald Martin Whitman

Third Advisor

Gregory A. Kriegsmann

Fourth Advisor

John Francis Federici

Fifth Advisor

Karl D. Moeller

Abstract

Photonic crystals were proposed fifteen years ago. Propagation is selectively prevented through these crystals resulting in a photonic band gap, that is, a frequency region where light cannot propagate. These frequency bands are analogous to electronic band gaps in solid-state crystals.

The optical properties of the photonic crystal in regions near the band gap remain relatively unexplored. Yet, there is significant evidence to suggest that this avenue of investigation can provide useful optical and microwave applications. Numerical studies have predicted that the effective permittivity near the photonic band gap approaches zero and becomes negative. Selfcollimation of the propagating beam and ultrarefraction, where radiation is redirected through large angles in the crystal, are predicted. Although not considered as the ideal structure, the face centered cubic (fcc) opaline photonic is crystal studied for reasons of practical realization.

The tools to examine the diffraction effects of photonic crystals, and in particular those for threedimensional structures, are somewhat lacking. To this end, commercial simulation software and a series of experimental studies were employed to gain insight of this unique wave propagation problem.

The emphasis of this study was upon frequency and polarization selectivity based on the azimuthal and incident angles with respect to the crystal morphology. Some of the results are consistent with calculations for two-dimensional crystals. However, they are demonstrated here in three-dimensional crystals for the first time.

Defect modes, where the photon density of states is modified to allow propagation in a certain direction was also explored. Although not optimized for low loss, significant evidence was found for the existence of defect modes in the fcc crystal.

Modification of the photonic crystal by adding periodic features with negative permittivity (metal) was examined as well. The addition of metal changed the refractive index contrast leading to frequency selective self-imaging beam splitting, as well as modification of the subwavelength selfimaging characteristic length.

It is expected that the experimental data will be useful toward in developing better theoretical approaches for photonic crystalline optics.

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