Metalens Topology Optimization

Abstract

Photonic metasurfaces are thin optical elements comprised of structures arranged strategically upon a surface to manipulate electromagnetic waves. To produce metasurfaces at a large scale, it is beneficial to obtain not just an optimal design, but also an understanding of which areas of the metasurface are most influential on the overall performance of the device and require greater manufacturing accuracy. My work consisted of implementing and testing a new physics-based method for identifying the relative importance of different regions of a proposed metasurface design. This method built on an existing topology optimization code, where the designable region of the metasurface was discretized, and the material density of each point in the design was optimized such that incoming light was maximally focussed to a target location. The existing optimization algorithm was then coupled to a molecular dynamics model called a Nosé-Hoover thermostat, by modelling the discrete locations on the design region as particles and their corresponding material densities as their positions. By numerically integrating the equations of motion of the thermostat model, I was able to generate metasurface designs at different thermostat temperatures, and observe how the designs changed with increasing temperature. To determine the most important areas of the metasurface design, I calculated the entropy of each of the "particles" for all temperature samples, and looked for design regions that had low entropy even at high temperatures, indicating strong convergence on an optimal material density value amidst high thermal noise. Once I implemented this design analysis framework, I tested it on both a metalens and a reflector design at multiple wavelengths of incoming light. My results demonstrated that this physics-based method provides easily interpretable information about the relative importance of different elements of a metasurface design.