Modification And Research On Simplified Modal Method For Dielectric Subwavelength Gratings Design

Dielectric subwavelength grating is a new type grating developing with evolutionof nano technology. Because of high efficiency, it is used frequently in opticalcommunication, computation, metrology, holography, laser pulse compression andso on. Many researchers focused on this issue. For the purpose of increasing thespeed of calculation in designing dielectric subwavelength gratings and giving agood prediction of grating structure, the simplified method will be researched in thispaper.In this paper, the factors of computational accuracy are analyzed when therigorous coupled wave analysis (RCWA) method is used to design a grating. Thisanalysis shows the result that RCWA could be used to be a reference as a theoreticalvalue for other algorithm in grating design.The simplified modal method (SMM) is analyzed and the deviation betweenSMM and RCWA is calculated to find the reason of its big error. Take a triangulargrating as an example, which is seen as multilayer films and the each layer owns anew effective index. The reflection and transmission of grating could becharacterized by optical admittance of the films. Then formulas of gratingtransmission in SMM are modified by reflection. The calculation by this modifiedsimplified modal method (MSMM) is a better approximation to RCWA than othermethods. Based on MSMM, for a rectangular grating, although the admittance changeswith duty cycle, its variation range is very near the admittance of air. This means thereflection of rectangular grating will not change a lot when duty cycle is changed.And a rectangular grating cann’t get transmission efficiency near100%. Then themode indices and admittance versus the period of triangular gratings and the dutycycle of rectangular grating are analyzed. A grating with transmission efficiencymore than99.9%for both TE and TM-polarized light is designed.The relations between grating structure and transmission efficiency areanalyzed by MSMM. The splitting result of rectangular and triangular grating areanalyzed for both TE and TM polarization.Based on these calculations,1×2beamsplitters are designed and optimized by MSMM. A polarization-independent splittergrating will get a good splitting result at the band1020nm-1100nm. Thetransmission efficiency of0th and-1st order for both TE and TM polarization is nearto50%at this band. The extinction ratio of a polarization-dependent splitter is biggerthan10at this band.Contrast to RCWA, MSMM gives a clear physical explanation of gratingdiffraction by considering the transmission efficiency as the result of phase shift ofmodes and difference of grating admittance and aerial admittance. This method canbe applicable to triangular, sinusoidal and rectangular gratings. Because it can beused to optimize the grating parameters directly, MSMM is better than SMM whichonly gives starting value of grating parameters. Thus MSMM gives a goodunderstanding on dielectric subwavelength gratings and is useful in designing andoptimizing them.