  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 geometries that can be realized by nanofabrication techniques. Thus,
computational approaches are necessary to efficiently search for 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 implementing the adjoint method based on the complex-conjugate
pole-residue pair model within a parallel finite-difference time-domain solver,
suitable for high-performance computing systems. Our method is tested on the
canonical nanophotonic problem of field enhancement in a gap region. The
obtained free-form designs of metallic and dielectric materials satisfy the
fundamental curiosity of how optimized nanostructures look like in 3D.
Unconventional free-form designs revealed by our method, although may be
challenging or unfeasible with current technology, bring new insight into how
light interacts with nanostructures, and could provide new ideas to inspire
forward design.
