Analytical strategy to achieve optimized grating couplers with high precision for both TE and TM polarizations on SOI platform

Diffraction elements are periodic structures that whose performance is based on the light diffraction principle. One application of this structure the are grating couplers which consist in coupling light on or off plane between two propagation means, in our case between a subwavelength waveguide and a single mode fiber optic. Optimized gratings are required to ensure a maximum coupling efficiency. Gratings on silicon on insulator (SOI) platform can be optimized in a few steps analyzing its behavior and linking some structure parameters. But advanced computational calculations and algorithms are used to optimize its design. Period and fill-factor are essential parameters in the optimization. In this paper, several analytical expressions based on the fundamental grating equation are proposed to accurately obtain the optimal period and fill-factor for a polarization transversal-electric and starting with the optimal values for this polarization get analytically the optimal parameters for polarization transversal-magnetic through a relation between both polarizations, avoiding simulation time.