Formulation for electromagnetic scattering and propagation through gratingstacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method

We present a formulation for wave propagation and scattering through stacke d gratings comprising metallic and dielectric cylinders. By modeling a phot onic crystal as a grating stack of this type, we thus formulate an efficien t and accurate method for photonic crystal calculations that allows us to c alculate reflection and transmission matrices. The stack may contain an arb itrary number of gratings, provided that each has a common period. The form ulation uses a Green's function approach based on lattice sums to obtain th e scattering matrices of each layer, and it couples these layers through re currence relations. In a companion paper [J. Opt. Sec. Am. A 17, 2177 (2000 )] we discuss the numerical implementation of the method and give a compreh ensive treatment of its conservation properties. (C) 2000 Optical Society o f America [S0740-3232(00)02812-X] OCIS codes: 260.0260, 260.2110, 050.0050, 050.1960.