The diffraction of a plane wave normally incident upon a corrugated waveguide with a second-order grating pitch is examined. Using a rectangular grating the efficiency of diffraction into the first-order components in the form of guided waves is determined. Using simple approximations, closed-form expressions are found from which the dependence of efficiency upon grating thickness, waveguide thickness, grating pitch, and indexes are predicted. The approach provides a useful simulation tool to predict the efficiency of coupling into a waveguide from an external or internal orthogonal source.
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