  Inverse design has greatly expanded nanophotonic devices and brought
optimized performance. However, the use of inverse design for plasmonic
structures has been challenging due to local field concentrations that can lead
to errors in gradient calculation when the continuum adjoint method is used. On
the other hand, with the discrete adjoint method one can achieve the exact
gradient. Historically the discrete version is exclusively used with a Finite
Element model, and applying the Finite-Difference Time-Domain (FDTD) method in
inverse design of plasmonic structures is rarely attempted. Due to the
popularity of using FDTD in simulating plasmonic structures, we integrate the
discrete adjoint method with FDTD and present a framework to carry out inverse
design of plasmonic structures using density-based topology optimization. We
demonstrate the exactness of the gradient calculation for a plasmonic block
structure with varying permittivity. Another challenge that is unique with
plasmonic structures is that non-physical amplification caused by poorly chosen
material interpolation can destroy a stable convergence of the optimization. To
avoid this, we adopt a non-linear material interpolation scheme in the FDTD
solver. In addition, filtering-and-projection regularization is incorporated to
ensure manufacturability of the designed structures. As an example of this
framework, successful reconstruction of electric fields of a plasmonic bowtie
aperture is presented.
