An Efficient Method for Band Structure Calculations in 2D Photonic Crystals

. An e#cient method for band structure calculations in dielectric photonic crystals is presented. The method uses a finite element discretization coupled with a preconditioned subspace iteration algorithm. Numerical examples are presented which illustrate the behavior of the method. 1. Introduction. Photonic crystals are periodic structures composed of dielectric materials and designed to exhibit interesting properties, such as spectral band gaps, in the propagation of classical electromagnetic waves. Structures with band gaps have many potential applications, for example in optical communications, filters, lasers, and microwaves. See [2, 13] for an introduction to photonic crystals. Figotin and Kuchment have proved that periodic dielectric structures exist which exhibit band gaps [9, 10], and other band gap structures have been found through computational and physical experiments. Computation has become a primary tool for investigating the properties of these structures. Carrying out ..