Design principles of apodized grating couplers

To optimize the coupling efficiency of grating couplers, we extend an analytical model for the design of apodized grating couplers, taking into account the constraints on the upper and lower bounds of the scattering strength as determined by fabrication technology. We prove that our model gives the global optimum distribution of the scattering strength with the presence of such constraints. We apply our model to the standard problem of coupling from a silicon chip to a single-mode fiber, as well as more complex problems including the coupling to a vortex beam, and the design of a focusing grating. In the problem of coupling to a vortex beam, we validate our model with full-wave numerical simulations. For this problem, our design obtains efficiency that is significantly higher compared with existing designs. Our theoretical study provides a solid foundation for apodized grating coupler design in different material platforms, and our deterministic algorithm can function as a near-optimum starting point for advanced optimizations.