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.

中文翻译：

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工作在-2阶的宽带高效光栅的简化模态法设计

众所周知，更高的衍射级表明具有相同周期的光栅具有更强的色散。在这里，一个宽带高效率三层全电介质矩形槽透射光栅在-2操作^第二命令根据第二布拉格发生率而设计的。通过使用简化模态法（SMM）快速获得光栅参数的初始解。此外，通过这种方法也对高效率和宽带宽背后的物理机制给出了清晰的解释。之后，基于严格的耦合波分析和模拟退火算法，进一步优化了光栅结构的更精确解。仿真结果表明，波长带宽从 $1.454~\mu \text{m}$ 至 $1.531~\mu\text{m}$ 并且可以实现从 37.32° 到 43.3° 的角度带宽，在第二布拉格入射波长下，效率超过 95% $1.5~\mu \text{m}$ 用于 TE 极化。这是首次使用 SMM 预测二次布拉格入射下多层光栅的宽带特性。