Dual coherent light array model for reflective rectangular metallic grating

Abstract

To study the mechanism of periodic change of reflective rectangular metallic gratings’ diffraction efficiencies, a dual secondary coherent light source array model was established based on the theory of Fabry-Pérot resonator. It was assumed that when incident light falls on the grating surface, it transforms into two coherent sources on each grating period. One is on the upper surface of the grating, reflected by the metal surface; the other is at the entrance of the grating groove and propagates in the form of a fundamental mode (λf­­­). Based on the above mentioned hypothesis, formulae for the phase difference Δϕ of two sources and diffraction efficiency for the first and zero order with grating height h, were established. Δϕ and h are linear relationships, the phase difference Δϕ changed due to the change of grating height h is the essencial cause of periodic changes of the diffraction efficiencies. When Δϕ has a certain value, the energy is only distributed in the zero or the first order direction. The model does not only show the change regularity of each diffraction order’s diffraction efficiency of reflective rectangular metallic grating, but it also shows the correlation of each diffraction order. It can help to predict diffraction performance of rectangular metallic gratings and to design gratings.