Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics

Abstract: The propagation of guided and nonconfined optical waves at fixed frequency through dielectric structures with piecewise constant, rectangular permittivity is considered in two spatial dimensions. Bidirectional versions of eigenmodes, computed for sequences of multilayer slab waveguides, constitute the expansion basis for the optical electromagnetic field. Dirichlet boundary conditions are sufficient to discretize the mode sets. Superpositions of two such expansions (bidirectional eigenmode propagation (BEP) fields), oriented along the two perpendicular coordinate axes, establish rigorous semianalytical solutions of the relevant Helmholtz wave equation on an unbounded, cross-shaped computational domain. The overlap of the lateral windows of the two BEP sets can be viewed as a rectangular computational window with fully transparent boundaries. Simulation results for a series of model systems (Gaussian beams in free space, Bragg gratings, waveguide crossings, a square cavity with perpendicular ports, and a 90◦ bend in a photonic crystal waveguide) illustrate the performance of the approach.