Analysis of photonic crystal structures

Photonic crystals are periodic structures with spatial variation of the dielectric, magnetic and metallic properties in one, two and three dimensions. For the present we confine this discussion to mixed dielectric structures. The propagation of electromagnetic waves through these crystals may result in pass and stop bands, depending on the structure. The wave propagation is governed by Maxwell's Eqs. and these calculations are usually performed for infinite structures and subsequently modified for finite structures. There are different approaches to solving the wave propagation problem and these range from the plane wave expansion method (PWEM) [1], the transfer matrix method [2], the finite difference time domain method (FDTD) [3] and the finite element method [4] which are among the most popular. In this chapter only the plane wave expansion and the finite difference methods are discussed.