Inverse design in photonics by topology optimization: tutorial

Topology optimization methods for inverse design of nano-photonic systems have recently become extremely popular and are presented in various forms and under various names. Approaches comprise gradient and non-gradient based algorithms combined with more or less systematic ways to improve convergence, discreteness of solutions and satisfaction of manufacturing constraints. We here provide a tutorial for the systematic and efficient design of nano-photonic structures by Topology Optimization (TopOpt). The implementation is based on the advanced and systematic approaches developed in TopOpt for structural optimization during the last three decades. The tutorial presents a step-by-step guide for deriving the continuous constrained optimization problem forming the foundation of the Topology Optimization method, using a cylindrical metalens design problem as an example. It demonstrates the effect and necessity of applying a number of auxiliary tools in the design process in order to ensure good numerical modelling practice and to achieve physically realisable designs. Application examples also include an optical demultiplexer.