The relationship between diffraction efficiency of multilayer diffractive optical elements (MLDOEs) and arbitrary incident angle was numerically analyzed with the effective area method. The method is based on the shield effect between two elements of MLDOEs; a generalized diffraction efficiency formulation was obtained in a wide range of tilt angles, which overcame the limitations of scalar diffraction theory when the period width of MLDOEs is taken into account. A detailed comparison of the proposed effective area method with the scalar diffraction theory is numerically presented for MLDOEs. The validity of the proposed method is verified by comparison with the rigorous electromagnetic analysis method, especially the finite-difference time-domain method. The analysis results show that the shield effect augments with the increase of the incident angles; the effect of incident angles on MLDOEs with finite period widths is more noticeable than that with large period widths. (C) 2016 Optical Society of America
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