A THz time-domain susceptibility for superconductors including strong-current effects

Finite-difference time-domain methods are increasingly being used to develop, model and analyze the response of materials, including engineered metamaterials that may contain superconductors. Though simple and useful expressions for the time-domain susceptibility exist for basic metals and dielectrics, the time-domain response for a superconductor has not been developed, mainly because the frequency-dependent expressions themselves are rather complex. In this paper we present a simple approximate expression for the time-domain susceptibility of a superconductor for the ħ/2Δ time scale (where Δ is the BCS energy gap) that fulfils causality requirements, and demonstrate its ability to model the transmission and reflection of a fully-gapped superconductor in the THz region. By allowing Δ to be a function of current, we also show how this model function can be used to describe nonlinear microwave response in superconductors.