Scalar Analysis of Conical Diffraction of Blazed Grating

Based on the extended scalar diffraction theory, the relative diffraction efficiency of any diffraction order is deduced considering the azimuth of incident light (conical diffraction) for transmission and reflection. It is proved that the relative diffraction efficiency formulas are different when using the extended scalar theory for a blazed grating bounded by the plane and medium interface, respectively. However, the optimized depth and blaze wavelength are the same, with corresponding explicit expressions provided. The two relative diffraction efficiency formulas are applied to a blazed grating with specific parameters to compare with rigorous coupled-wave analysis. The results show that the difference between the two formulas is minimal, and both are consistent with the rigorous coupled-wave analysis.