S-matrix absolute optimization method for a perfect vertical waveguide grating coupler

Vertical coupling using a diffraction grating is a convenient way to couple light into an optical waveguide. Several optimization approaches have been suggested in order to design such a coupler; however, most of them are implemented using algorithm-based modelling. In this paper, we suggest an intuitive method based on S-matrix formalism for analytically optimize 3-port vertical grating coupler devices. The suggested method is general and can be applied to any 3-port coupler device in order to achieve an optimal design based on user constrains. The simplicity of the model allows reduction of the optimization to two variables and the location of an absolute optimal operation point in a 2D contour map. Accordingly, in an ideal device near 100% coupling efficiency and insignificant return loss could be achieved. Our model results show good agreement with numerical finite difference time domain (FDTD) simulations and can predict the general tendencies and sensitivities of the device's behavior to changes in design parameters. We further apply our model to a previously reported high contrast uni-directional grating coupler device and show that additional improvement in the coupling efficiency is achievable for that layout.