A Transmission Line Resonator Model for Fast Extraction of Electromagnetic Properties of Cavities in Two-Dimensional Photonic Crystals

In this paper, photonic cavities made of point defects in 2-D photonic crystals are modeled by finite-size transmission lines terminated at both ends by appropriate scalar impedances. The proposed model forms a simple transmission line resonator and is demonstrated to be quite beneficial in fast extraction of resonant frequency, quality factor, and mode profile of such photonic cavities. In this manner, an approximate yet quite accurate approach is introduced to characterize the electromagnetic properties of photonic crystal cavities. This method is successfully applied to different structures for both major polarizations and is shown to be as accurate as rigorous numerical methods, viz. the finite-element method.