Robust shape and topology optimization of nanophotonic devices using the level set method

Abstract

This article deals with the optimal design of the individual nanophotonic components of photonic integrated circuits. In the mathematical setting of the three-dimensional, time-harmonic Maxwell equations, we propose a shape and topology optimization algorithm combining Hadamard's boundary variation method with a level set representation of shapes and their evolution. A particular attention is devoted to the robustness of the optimized devices with respect to small uncertainties over the physical or geometrical data of the problem. In this respect, we rely on a simple multi-objective formulation to deal with the two main sources of uncertainties plaguing nanophotonic devices, namely uncertainties over the incoming wavelength, and geometric uncertainties entailed by the lithography and etching fabrication process. Several numerical examples are presented and discussed to assess the efficiency of our methodology.