Constraining continuous topology optimizations to discrete solutions for photonic applications
Photonic topology optimization is a technique used to find the electric permittivity distribution of a device that optimizes an electromagnetic figure-of-merit. Two common techniques are used: continuous density-based optimizations that optimize a grey-scale permittivity defined over a grid, and discrete level-set optimizations that optimize the shape of the material boundary of a device. More recently, continuous optimizations have been used to find an initial seed for a concluding level-set optimization since level-set techniques tend to benefit from a well-performing initial structure. However, continuous optimizations are not guaranteed to yield sufficient initial seeds for subsequent level-set optimizations, particularly for high-contrast structures, since they are not guaranteed to converge to solutions that resemble only two discrete materials. In this work, we present a method for constraining a continuous optimization such that it converges to a discrete solution. This is done by inserting a constrained sub-optimization at each iteration of an overall gradient-based optimization. This technique can be used purely on its own to optimize a device, or it can be used to provide a nearly discrete starting point for a level-set optimization.
Attribution 4.0 International (CC BY 4.0) This work was supported by the Defense Advanced Research Projects Agency EXTREME program (HR00111720035), the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, under a contract with the National Aeronautics and Space Administration (APRA 399131.02.06.04.75 and PDRDF 107614-19AW0079), the National Institutes of Health (NIH) brain initiative program grant NIH 1R21EY029460-01, and Caltech Rothenberg Innovation Initiative. The authors thank Oscar P. Bruno for helpful discussion during the course of this work.
Submitted - 2107.09468.pdf