Fast modeling of photonic bandgap structures by use of a diffraction-grating approach

Abstract

The rigorous coupled-wave method formulated by N. Chateau J. P. Hugonin [J. Opt. Soc. Am. A11, 1321 (1994)] and revisited by S. Peng G. M. Morris [J. Opt. Soc. Am. A12, 1087 (1995)] for one-dimensional (1D) diffraction gratings is used for the modeling of diffraction properties of photonic bandgap (PBG) structures. A two-dimensional (2D)-PBG structure is considered as a stack of 1D gratings. An original S-matrix algorithm is formulated for the modeling of any 1D grating, formed by rods that have a symmetry plane in the grating plane. Many examples—dealing with stacks of infinite rods of square (circular) sections, whose intersection with a perpendicular plane forms square, triangular, or hexagonal lattices—are studied. Particular attention is devoted to TM polarization in lossless (lossy) dielectric and metallic materials. For this polarization we take advantage of the convergence improvement formulated for 1D metallic gratings by P. Lalanne G. M. Morris [J. Opt. Soc. Am. A13, 779 (1996)] and G. Granet R. Guizal [J. Opt. Soc. Am. A13, 1019 (1996)]. The introduction of a periodic defect—made of dielectric material that has linear (nonlinear) optical properties—in a 2D-PBG structure and the feasibility of optical filters and switches in the 1.3–1.55 µm wavelength range are briefly studied. Limitations for the use of the modeling tool are illustrated through an example of a cubic three-dimensional (3D)-PBG structure of cubes.