Diffraction pattern of triangular grating in the resonance domain

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We propose a combination of ray optics and Fraunhofer multiple-slit diffraction theory for calculating the twodimensional triangular periodic grating in the resonance domain. The peak of the envelope pattern of angular distribution of diffraction efficiency is calculated by ray optics while the peak width is calculated using Fraunhofer theory. It was clarified, using rigorous coupled-wave analysis and a nonstandard-finite-difference timedomain method, that the envelope pattern of the diffraction of the grating could be calculated easily and understood intuitively for the design of displays and lighting.