Design of double-layer metal-dielectric reflecting polarizing beam splitter grating based on simplified mode method

In this paper, the simplified mode method (SMM) is applied to guide the design of a reflecting polarizing beam splitter (RPBS) grating based on multilayer metal-dielectric structure for the first time. The process of analyzing grating diffraction can be simplified by using two main propagation modes with the grating period comparable to the incident wavelength. The expressions for the diffraction efficiency and phase difference of propagation modes are obtained by analyzing the propagation and coupling of the modes characterized by the effective index. With the modified SMM, a broadband double-layer RPBS grating with a high extinction ratio is designed. The grating parameters are optimized based on the expressions of the diffraction efficiency obtained from the SMM, combined with the rigorous coupled-wave analysis (RCWA) and simulated annealing (SA) algorithms. Moreover, the fabrication tolerances and incidence angle tolerances of the designed grating are analyzed. The outstanding performance demonstrate not only the potential of the RPBS grating for practical applications, but also the potential of the proposed SMM to guide the design of multilayer metal-dielectric gratings. Therefore, this work provides an effective tool for the design of various multilayer metal-dielectric gratings consisting of multilayer dielectric rectangular grooves and a highly reflective mirror.