Topology optimization of photonics based on thermodynamically consistent variational principles

This work applies Hamilton’s principle to electrodynamics in stationary media and extends it within the framework of thermodynamically consistent topology optimization (TTO), a variational approach originally formulated for the mechanics of materials. This combination provides, to our knowledge, a novel approach to the topology optimization of photonics. Reducing the equations to two dimensions enables the description of light propagation through a single scalar variable. Assuming monochromatic radiation further reduces the wave equation to the Helmholtz equation. Based on this variational framework, the equations are embedded into an optimization problem, while taking into account Betti’s reciprocal theorem for electromagnetism. In total, two field equations and one for the density distribution are derived from a single action functional. The neighbored element method (NEM) is employed to solve the system of equations, and numerical examples are presented to demonstrate the optimized optical devices.