Resonant scattering and mode coupling in two-dimensional textured planar waveguides

A heuristic formalism ii: developed for efficiently determining the specula r reflectivity spectrum of two-dimensionally textured planar waveguides. Th e formalism is based on a Green's function approach. wherein the electric f ields are assumed to vary little over the thickness of the textured part of the waveguide. Its accuracy, when the thickness of the textured region is much smaller than the wavelength of relevant radiation, is verified by comp arison with a much less efficient, exact finite difference solution of Maxw ell's equations. In addition to its numerical efficiency, the formalism pro vides an intuitive explanation of Fano-like features evident in the specula r reflectivity spectrum when the incident radiation is phase matched to exc ite leaky electromagnetic modes attached to the waveguide. By associating v arious Fourier components of tile scattered field with bare slab modes, the dispersion, unique polarization properties, and lifetimes of these Fano-li ke features are explained in terms of photonic eigenmodes that reveal the r enormalization of the slab modes due to interaction with the two-dimensiona l grating. An application of the formalism, in tile analysis of polarizatio n-insensitive notch filters is also discussed. (C) 2001 Optical Society of America.