Modeling of Photonic Band Gap Structures for Optical Communication Systems

Abstract

In this work we study and model the light propagation in photonic crystal structures. The plane wave expansion method is developed with a more rigorous technique for the calculation of the photonic band gaps and the off­ plane propagation angles in a two dimensional photonic crystal.

The comparison with existing techniques shows that the new model enables to estimate the effective angles over the entire range of longitudinal propagation constant, and allows for an accurate determination of the off- .. ., , plane propagation angle of different bands. It thus enables to calculate more precisely the percentage of spontaneous emission, from an embedded point source, suppressed at a certain frequency.

Several methods of controlling the position of guided modes inside the photonic band gap have been presented and analyzed using the super cell approximation. The appearance of acceptor-type and donor-type modes is observed and explained. The importance of the relative position of holes versus the absolute amount of added high dielectric constant material is emphasized. Finally, the finite different time domain (FDTD) method is used to verify the results by simulating light propagation through a sharp bend photonic crystal wave-guide with varying air hole radii.