Hybrid FEM/BEM modeling of finite-sized photonic crystals for semiconductor laser beams

We propose a 2-D finite element/boundary element hybrid method for calculating the spatial distribution and frequency response of electromagnetic waves coming from a semiconductor laser when interacting with a finite-sized photonic crystal. We thus provide a flexible tool for the design of novel optical and microwave devices, among other applications. In opposition to current methodologies, we simultaneously take into account the laser modes, the finiteness of the crystal, and the unboundedness of the isotropic medium in which the crystal is embedded. At the laser output, instead of approximating reflected and transmitted beams by plane waves, we use the more realistic Hermite-Gauss functions. In the isotropic medium, we set an artificial boundary encircling the crystal and define exterior and interior domains. Radiating solutions for the scattered far field over the exterior are derived analytically through a series of Hankel polynomials. The interior domain is described by a finite element formulation coupled with Dirichlet-to-Neumann maps enforcing laser and far-field behaviors. Results and error analyses are provided in view of future improvements.