Voxelized topology optimization for fabrication-compatible inverse design of 3D photonic devices

Topology optimization for photonic device design, has been mostly used to optimize binary structures based on refractive index as the free parameter for each design cell. Typically, a constraint on the optimization variable to be z-invariant and a smoothing operation on small features are applied to make the structure fabricable by conventional lithography. To enable topology optimization to design fabricable 3D structures using emerging methods like grayscale lithography and focused ion beam milling, we propose here a framework that uses the refractive index step position as the free parameter for each 3D voxel. This choice of framework enables us to reuse the same mesh in each iteration and thereby reduce the time for optimization. We apply the framework to the fabricable design of both free-space and integrated photonic devices, at different wavelengths, demonstrating high-efficiency ultra-compact designs with wide wavelength tunability.