Roughness-induced scattering and attenuation of guided modes in slab waveguides

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Abstract
After generalizing a given stationary coupled-mode concept toward both arbitrary field polarization and arbitrary direction of propagation, the roughness-induced scattering of slab-guided modes is considered in the framework of classical electromagnetic theory. The theory is illustrated by applying it to the case of a step-index slab waveguide. After developing formulas for the scattered power spectral density, we discuss in detail the relationship between the roughness correlation functions and the coupling-efficiency of guided modes among themselves as well as an appropriate principle for measuring these correlation functions. Finally, a simple formula emerges for the roughness-induced attenuation rate of the primary field.