In the last decades, nanostructures have unlocked myriads
of functionalities
in nanophotonics by engineering light–matter interaction beyond
what is possible with conventional bulk optics. The space of parameters
available for design is practically unlimited due to the large variety
of optical materials and nanofabrication techniques. Thus, computational
approaches are necessary to efficiently search for the optimal solutions.
In this paper, we enable the free-form inverse design in 3D of linear
optical materials with arbitrary dispersion and anisotropy. This is
achieved by (1) deriving an analytical adjoint scheme based on the
complex-conjugate pole-residue pair model in the time domain and (2)
its implementation in a parallel finite-difference time-domain framework
with a topology optimization routine, efficiently running on high-performance
computing systems. Our method is tested on the design problem of field
confinement using dispersive nanostructures. The obtained designs
satisfy the fundamental curiosity of how free-form metallic and dielectric
nanostructures perform when optimized in 3D, also in comparison to
fabrication-constrained designs. Unconventional free-form designs
revealed by computational methods, although may be challenging or
unfeasible to realize with current technology, bring new insights
into how light can more efficiently interact with nanostructures and
provide new ideas for forward design.