Free-form inverse design of arbitrary dispersive materials in nanophotonics

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.