Exact Finite-Difference Time-Domain Modelling of Broadband Huygens' Metasurfaces with Lorentz Dispersions

An explicit time-domain finite-difference technique for modelling zero-thickness Huygens' metasurfaces based on Generalized Sheet Transition Conditions (GSTCs), is proposed and demonstrated using full-wave simulations. The Huygens' metasurface is modelled using electric and magnetic surface susceptibilities, which are found to follow a double-Lorentz dispersion profile. To solve zero-thickness Huygens' metasurface problems for general broadband excitations, the double-Lorentz dispersion profile is combined with GSTCs, leading to a set of first-order differential fields equations in time-domain. Identifying the exact equivalence between Huygens' metasurfaces and coupled RLC oscillator circuits, the field equations are then subsequently solved using standard circuit modelling techniques based on a finite-difference formulation. Several examples including generalized refraction are shown to illustrate the temporal evolution of scattered fields from the Huygens' metasurface under plane-wave normal incidence, in both harmonic steady-state and broadband regimes. In particular, due to its inherent time-domain formulation, a significant strength of the methodology is its ability to model time-varying metasurfaces, which is demonstrated with a simple example of a pumped metasurface leading to new frequency generation and wave amplification.