Synthesis of Two-Dimensional Photonic Crystals for Large Band Gaps

Photonic crystals are periodic structures that possess some photonic band gaps (PBG’s), i.e., ranges of frequencies where the electromagnetic wave is forbidden to propagate in the crystal. For a photonic crystal, the larger the PBG, the greater the bandwidth for preventing the optical wave from propagation. Most important applications of photonic crystals are based on this property. Therefore, how to enlarge PBG’s would be an important research topic.
In this thesis, both Newton’s iteration method and simulated annealing (SA) approach are used to synthesize photonic crystals for large PBG’s. Based on the plane wave expansion method, Newton’s iteration method is an inversion approach to synthesize photonic crystals for large PBG’s. However, the synthesized dielectric constant is continuously distributed and is hard to realize. Unlike Newton’s iteration method, SA is a Monte Carlo approach for searching a global minimum. The synthesized dielectric constant can be in a discrete form which is easy to realize. In this thesis, numerical simulations are conducted to verify the feasibility of synthesizing photonic crystals for large PBG.