Fused-silica beam splitter grating design based on modified simplified modal method

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.