An explicit time-domain finite-difference technique for modeling zero-thickness Huygens' metasurfaces based on generalized sheet transition conditions (GSTCs) is proposed and demonstrated using full-wave simulations. The Huygens' metasurface is modeled 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 modeling 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.

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Keywords Electromagnetic (EM) metasurfaces, electromagnetic propagation, explicit finite difference, generalized sheet transition conditions (GSTCs), Lorentz dispersions
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Journal IEEE Transactions on Antennas and Propagation
Smy, T, & Gupta, S. (2017). Finite-difference modeling of broadband Huygens' metasurfaces based on generalized sheet transition conditions. IEEE Transactions on Antennas and Propagation, 65(5), 2566–2577. doi:10.1109/TAP.2017.2681323