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Periodically textured planar waveguides Cowan, Allan R.

Abstract

A heuristic formalism is developed for efficiently determining the specular reflectivity spectrum of planar waveguides textured with an arbitrary number of two dimensionally (2D) periodic gratings. The formalism is based on a Green's function approach wherein the electric fields are assumed to vary little over the thickness of each textured region of the waveguide. Its accuracy, when the thickness of each textured region is much smaller than the wavelength of relevant radiation, is verified by comparison with a much less efficient, "exact" finite difference solution of Maxwell's equations. In addition to its numerical efficiency, the formalism provides an intuitive explanation of Fano-like features evident in the specular reflectivity spectrum when the incident radiation is phase matched to excite leaky electromagnetic modes "attached" to the waveguide. By associating various Fourier components of the scattered field with bare slab modes, the dispersion, polarization properties, and lifetimes of these Fano-like features are explained in terms of photonic eigenmodes that reveal the renormalization of the slab modes due to interaction with the 2D grating. The model has been used effectively to directly simulate experimental reflectivity data obtained by others.

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