Generalized scattering-matrix method for the analysis of two-dimensional photonic bandgap devices

Development of accurate numerical methods for the analysis of photonic-bandgap-based devices is a relevant issue in optimizing existing devices and/or developing new design solutions. Within this framework, we present an innovative and general approach for the evaluation of the electromagnetic behavior of two-dimensional finite-extent photonic crystals made of a finite set of parallel rods. The proposed approach is a generalization of the scattering-matrix method introduced by Maystre and co-workers and of its improved version proposed by the present authors, which exploits a suitable aggregation into "macrocells" to achieve a reduction of the number of unknowns. As a matter of fact, both of these approaches can be exploited only in those cases in which particular modal expansions for the fields hold true. In order to overcome this limitation, we propose a suitable exploitation of the method of auxiliary sources to provide a general and reliable method for the numerical computation of the scattering matrix of an object of arbitrary shape. By taking advantage of this, we can then generalize our improved scattering matrix method to further increase its computational effectiveness. A numerical analysis of some square-lattice configurations is reported to confirm the accuracy of the proposed method and the remarkable computational benefit.