Comparison of two approaches to the waveguide scattering problem: TM polarization

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Abstract
Two theoretical formalisms, the most widely used version of coupled-mode theory and a first-order boundary-perturbation theory, are used to analyze the interaction between optical guided waves and surface roughness on an asymmetric planar waveguide. Each formalism is applied to two distinct problems for both TE and TM guided waves: (1) the determination of the far-field radiation patterns from randomly rough surfaces (with explicit results for the case of a sinusoidal roughness); and (2) the determination of guided-wave reflectivities from waveguide diffraction gratings. In all cases, the theoretical predictions agree for the TE polarization but disagree significantly for the TM polarization.