Modeling the Third-Order Electrodynamic Response of Graphene via an Efficient Finite-Difference Time-Domain Scheme

The third-order electrodynamic response of graphene and the subsequent non-linear effects are comprehensively investigated and numerically modeled in this article. Initially, the third-order conductivity of the medium is analyzed in order to transform it into a convenient expression for its efficient incorporation to explicit computational algorithms. Moreover, the simplified expression of the surface conductivity is imported into a suitably modified 3-D finite-difference time-domain scheme, where graphene is embodied as an equivalent surface current. Numerical examples, considering both an incident plane-wave toward graphene and surface-wave propagation, indicate the successful frequency upconversion, thus validating the proper third-order response modeling.