Boundary-element calculations of electromagnetic band-structure of photonic crystals

A boundary element method is developed for calculating the photon modes of periodic structures whose unit cells consist of piecewise homogeneous dielectric materials of arbitrary shapes. Green's function techniques are used to derive integral equations for these structures. These equations involve integrals over the boundaries between the regions, which are discretized and solved numerically. Thus the full set of Maxwell's equations with boundary conditions in d independent variables is changed into an integral equation in d - 1 variables. This allows for the calculation of mode frequencies and field patterns for wave vectors throughout the Brillouin zone, thus allowing the determination of photonic band gaps. An illustrative example is given here for a two-dimensional system. (C) 1998 Elsevier Science B.V. All rights reserved.