Modeling of Photonic Band Gap Crystals and Applications

Abstract

In this work, the authors have undertaken a theoretical approach to the complex problem of modeling the flow of electromagnetic waves in photonic crystals. The focus is to address the feasibility of using the exciting phenomena of photonic gaps (PBG) in actual applications. The authors start by providing analytical derivations of the computational electromagnetic methods used in their work. They also present a detailed explanation of the physics underlying each approach, as well as a comparative study of the strengths and weaknesses of each method. The Plane Wave expansion, Transfer Matrix, and Finite Difference time Domain Methods are addressed. They also introduce a new theoretical approach, the Modal Expansion Method. They then shift the attention to actual applications. They begin with a discussion of 2D photonic crystal wave guides. The structure addressed consists of a 2D hexagonal structure of air cylinders in a layered dielectric background. Comparison with the performance of a conventional guide is made, as well as suggestions for enhancing it. The studies provide an upper theoretical limit on the performance of such guides, as they assumed no crystal imperfections and non-absorbing media. Next, they study 3D metallic PBG materials at near infrared and optical wavelengths. The main objective is to study the importance of absorption in the metal and the suitability of observing photonic band gaps in such structures. They study simple cubic structures where the metallic scatters are either cubes or interconnected metallic rods. Several metals are studied (aluminum, gold, copper, and silver). The effect of topology is addressed and isolated metallic cubes are found to be less lossy than the connected rod structures. The results reveal that the best performance is obtained by choosing metals with a large negative real part of the dielectric function, together with a relatively small imaginary part. Finally, they point out a new direction in photonic crystal research that involves the interplay of metallic-PBG rejection and photonic band edge absorption. They propose that an absolute metallic-PBG may be used to suppress the infrared part of the blackbody emission and, emit its energy only through a sharp absorption band. Potential applications of this new PBG mechanism include highly efficient incandescent lamps and enhanced thermophotovoltaic energy conversion. The suggested lamp would be able to recycle the energy that would otherwise go into the unwanted heat associated with usual lamps, into light emitted in the visible spectrum. It is estimated this would increase the efficiency over conventional lamps by about 40%.