Optimization of the parallelogrammic grating diffraction efficiency for normally incident waves

The diffraction directivity of parallelogrammic gratings with second-order pitch is examined for a plane wave normally incident upon a corrugated waveguide structure. The three diffracted components are assumed to be in the form of guided waves, which permits a self-consistent calculation. The efficiencies of diffraction into the horizontal components are obtained. Also, the dependence of efficiency on grating thickness, waveguide thickness, grating pitch, and angle of inclination is determined. The approach provides a useful simulation tool for optimizing the design parameters for waveguide couplers with an orthogonal source.