Planar optical waveguides coupled by means of Bragg scattering

A new analytic approach to the analysis of grating-assisted couplers is proposed and used for description of the noncollinear coupling of two slab waveguides with arbitrary mode polarizations (TE and TM), propagation directions, and phase velocities. This approach is based on the boundary-perturbation theory, the method of successive approximations, and the energy-conservation law, and does not use any overlap integrals. The specific case in which the converted mode propagates parallel to a periodic array boundary (extremely asymmetric coupling) is considered by means of an original simple analytic approach that allows for the diffractional divergence of the converted wave. Applicability conditions of the results obtained are derived in both the cases of conventional and extremely asymmetrical coupling. Comparison with the previous methods is carried out for the collinear coupling.