  Topology optimization techniques have been applied in integrated optics and
nanophotonics for the inverse design of devices with shapes that cannot be
conceived by human intuition. At optical frequencies, these techniques have
only been utilized to optimize nondispersive materials using frequency-domain
methods. However, a time-domain formulation is more efficient to optimize
materials with dispersion. We introduce such a formulation for the Drude model,
which is widely used to simulate the dispersive properties of metals,
conductive oxides, and conductive polymers. Our topology optimization algorithm
is based on the finite-difference time-domain (FDTD) method, and we introduce a
time-domain sensitivity analysis that enables the evaluation of the gradient
information by using one additional FDTD simulation. The existence of
dielectric and metallic structures in the design space produces plasmonic field
enhancement that causes convergence issues. We employ an artificial damping
approach during the optimization iterations that, by reducing the plasmonic
effects, solves the convergence problem. We present several design examples of
2D and 3D plasmonic nanoantennas with optimized field localization and
enhancement in frequency bands of choice. Our method has the potential to speed
up the design of wideband optical nanostructures made of dispersive materials
for applications in nanoplasmonics, integrated optics, ultrafast photonics, and
nonlinear optics.
