Topology design optimization of nanophotonic devices for energy concentration

Abstract

In this work, a novel topology optimization method for the synthesis of nanophotonic energy concentrators is proposed. The forward problem is governed by the Maxwell equations in the frequency domain. The basic idea consists in finding the best two phase material distribution that concentrates the energy in a given target domain. More precisely, a shape functional measuring the electrical energy of the system within a small region of the nanodevice is maximized with respect to silicon and glass spatial distribution by using the topological derivative method. Therefore, since the resulting optimization method is based on a scattering problem formulation, any issues that would come from eigenmode calculations are here avoided. In addition, the proposed shape functional can be properly defined both outside or overlapping the design (moving) domain itself, increasing the range of applications of the proposed approach. The associated topological gradient is rigorously derived and used to devise a simple and efficient black/white binary topology design algorithm, which naturally conforms to practical fabrication constraints for nanodevices. Finally, a set of numerical experiments are presented showing different features of the proposed approach, including its capability in selectively producing the required hot-spots within the nanodevices.