Constraining Continuous Topology Optimizations to Discrete Solutions for Photonic Applications.

Photonic topology optimization is a technique used to find the permittivity distribution of a device that optimizes an electromagnetic figure-of-merit. Two common versions are used: continuous density-based optimizations that optimize a gray scale permittivity defined over a grid, and discrete level-set optimizations that optimize the shape of the material boundary of a device. In this work we present a method for constraining a continuous optimization such that it is guaranteed to converge to a discrete solution. This is done by inserting a constrained suboptimization with low computational overhead cost at each iteration of an overall gradient-based optimization. The technique adds only one hyperparameter with straightforward behavior to control the aggressiveness of binarization. Computational examples are provided to analyze the hyperparameter behavior, show this technique can be used in conjunction with projection filters, show the benefits of using this technique to provide a nearly discrete starting point for subsequent level-set optimization, and show that an additional hyperparameter can be introduced to control the overall material/void fraction. This method excels for problems where the electromagnetic figure-of-merit is majorly affected by the binarization requirement and situations where identifying suitable hyperparameter values becomes challenging with existing methods.