Time-domain topology optimization of power dissipation in dispersive dielectric and plasmonic nanostructures

TL;DR

This paper introduces a time-domain topology optimization method for enhancing power dissipation in dispersive nanostructures, leveraging the CCPR model and adjoint methods within FDTD simulations.

Contribution

It develops a novel gradient-based topology optimization framework incorporating the CCPR model for dispersive materials in the time domain.

Findings

Optimized nanostructures show increased absorption efficiency.

The method accurately models dispersive materials without limiting to specific classes.

Demonstrated on Gold and Silicon nanoparticles in visible-ultraviolet range.

Abstract

We present a density-based topology optimization scheme for locally optimizing the electric power dissipation in nanostructures made of lossy dispersive materials. By using the complex-conjugate pole-residue (CCPR) model, we can accurately model any linear materials' dispersion without limiting to specific material classes. We incorporate the CCPR model via auxiliary differential equations (ADE) into Maxwell's equations in the time domain, and formulate a gradient-based topology optimization problem to optimize the dissipation over a broad spectrum of frequencies. To estimate the objective function gradient, we use the adjoint field method, and explain the discretization and integration of the adjoint system into the finite-difference time-domain (FDTD) framework. Our method is demonstrated using the example of topology optimized spherical nanoparticles made of Gold and Silicon with an enhanced absorption efficiency in the visible-ultraviolet spectral range. In this context, a detailed analysis of the challenges of topology optimization of plasmonic materials associated with a density-based approach is given.