Transfer Matrix Model for Emission Profile Optimization of Radial Gratings

Radial Bragg gratings are commonly used to enhance light extraction from quantum emitters, but lack a well-suited, fast simulation method for optimization beyond periodic designs. To overcome this limitation, an algorithm based on the transfer matrix model (TMM) to calculate the free-space emission of such gratings is proposed and demonstrated. Using finite difference time domain (FDTD) simulations, free-space emission, and transfer matrices of single grating components are characterized. The TMM then combines any number of components to receive the total emission. Randomized benchmarks verify that results from this method agree within 98% with FDTD while reducing simulation time by one to two orders of magnitude. The speed advantage of this approach is shown by maximizing emission of a fifteen-trench circular grating into a Gaussian mode. It is expected that this novel algorithm will facilitate the optimization of radial gratings, enabling quantum light sources with unprecedented collection efficiencies.