Diffraction into a corrugated waveguide from normally incident radiation

The diffraction of a plane wave normally incident upon a corrugated wavegui de with a second-order grating pitch is examined. Using a rectangular grati ng the efficiency of diffraction into the first-order components in the for m of guided waves is determined. Using simple approximations, closed-form e xpressions are found from which the dependence of efficiency upon grating t hickness, waveguide thickness, grating pitch, and indexes are predicted. Th e approach provides a useful simulation tool to predict the efficiency of c oupling into a waveguide from an external or internal orthogonal source.