Analysis of graded-index photonic bandgap structures

Abstract

Photonic bandgap (PBG) structures are periodic dielectric or metallic structures, which have no propagating light modes in certain frequency intervals. Because of the existence of forbidden frequency bands, PBG structures can manipulate and control the propagation of light, which is essential for lots of applications. In this thesis, one-dimensional PBG structures with graded-index profiles are analyzed based on three methods, transfer matrix method (TMM), the Wentzel–Kramers–Brillouin (WKB) method and the modified Airy function (MAF) method. With the help of these three methods, eigenvalue equations for band edges of PBG structures are derived, from which band structures are calculated, which is the main task in the analysis of PBG structure. Besides, electric-field patterns of the TE modes are studied. In order to demonstrate the application of the methods, several periodic symmetric graded-index profiles, sinusoidal, triangular and parabolic profiles, are considered. In addition, the performances of these methods are compared with each other, among which TMM is an exact analytical method, and whose results are treated as exact solutions.