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

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.