Broadband High-Efficiency Gratings Operating at the 2nd Order Designed by Simplified Modal Method

It is well known that higher diffraction order suggests a stronger dispersion for gratings with the same period. Here, a broadband high-efficiency three-layer all-dielectric rectangular-groove transmission grating operating at the −2 nd order is designed under second Bragg incidence. An initial solution of the grating parameters is obtained quickly by using the simplified modal method (SMM). Moreover, a clear explanation for the physical mechanism behind high efficiency and wide bandwidth is also given through this method. After that, a more accurate solution of the grating structure is optimized in further based on rigorous coupled wave analysis and simulated annealing algorithm. The simulation results indicated that a wavelength bandwidth from 1.454~\mu \text{m} to 1.531~\mu \text{m} and an angle bandwidth from 37.32° to 43.3° could be achieved for efficiency over 95% under second Bragg incidence at the wavelength of 1.5~\mu \text{m} for TE polarization. It is the first time using SMM to predict the broadband characteristic of multilayer-gratings under second Bragg incidence.