基于修正简化模式法的熔融石英光栅分束器设计

Fused-Silica Beam Splitter Grating Design Based on Modified Simplified Modal Method

对用于光栅优化设计初值估计的简化模式法（SMM）进行了修正。考虑介质光栅的反射对透射率的影响,从多层膜等效的角度结合模式理论,推导出介质光栅的透射效率公式,实现了对SMM的修正。计算结果表明,与SMM相比,修正后的方法与严格耦合波（RCWA）的计算偏差大大缩小,TE和TM波都小于2%。因此相对于只能提供设计参数优化初值的SMM,该方法可对光栅参数进行优化;与RCWA相比,该方法将透射光栅的衍射效率表达成模式的相位差偏移和光栅与空气导纳之差引起的反射,更直观地展示了光栅衍射的物理过程。基于此修正的简化模式法（MSMM）,优化设计了一个双端口光栅分束器,该光栅在1020~1100nm波段,TE波和TM波的0级和-1级透射效率都在50%左右,具有较好的分束效果。

The simplified modal method （SMM）, which is used to estimate the initial values of grating parameters, is modified. The reflection of dielectric grating is considered. Then grating is equivalent to multilayer thin films. Associating with the modal theory, transmission efficiency is calculated, and SMM is modified. The calculation results show that deviation between this modified method and RCWA is less than 2 % for TE and TM polarizations which is better than SMM, With respect to SMM, which only gives starting value of grating parameters, this method can be used to optimize the grating parameters. Contrast to RCWA, it gives a clear physical explanation of grating diffraction by considering the transmission efficiency as the result of phase shift of modes and difference of grating and aerial admittance. Then a grating beam splitter with two ports is designed and optimized by this modification of simplified modal method （MSMM）, which gets a good splitting result at the band of 1020 - 1100 nm. The transmission efficiency of 0th and --1st order for both TE and TM polarizations is near to 50 % at this band.