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Exact theory of te-wave scattering from blazed dielectric gratings

We present an exact description of scattering of an incident plane wave with te-polarization at an interface between two dielectric media that is deformed by a grating with triangularly shaped teeth. The theory employs an expansion in plane waves outside of the grating region and describes the field in the grating region as a double Fourier series expansion. The results of this theory are represented graphically. That blazing provides substantial discrimination of the scattering process in favor of beams scattered into one or the other of the two media is shown. The exact theory is used to check an approximation for the effective reflection plane that is useful for future applications of the theory to scattering by gratings of guided waves in thin-film waveguides.