Toward nanophotonic optical isolation via inverse design of energy transfer in nonreciprocal media

In this paper we generalize the adjoint method of inverse design to nonreciprocal media. As a test case, we use three-dimensional topology optimization via the level-set method to optimize one-way energy transfer for pointlike source and observation points. To achieve this we introduce a suite of tools, chiefly what we term the "Faraday-adjoint" method which allows for efficient shape optimization in the presence of magneto-optical media. We carry out an optimization based on a very general equation that we derive for energy transfer in a nonreciprocal medium, and link finite-different time-domain numerics to analytics via a modified Born series generalized to a tensor permittivity. This paper represents a stepping stone towards practical nanophotonic optical isolation, often regarded as the "holy grail" of integrated photonics.