Abstract
A Finite-Difference Time-Domain (FDTD) simulation of broadband electromagnetic metasurfaces based on direct incorporation of Generalized Sheet Transition Conditions (GSTCs) into a conventional Yee-cell region has been proposed for arbitrary wave excitations. This is achieved by inserting a zero thickness metasurface inside bulk nodes of the Yee-cell region, giving rise to three distinct cell configurations - Symmetric Cell (SC), Asymmetric Cell (AC) and Tight Asymmetric Cell (TAC). In addition, the metasurface is modelled using electric and magnetic surface susceptibilities exhibiting a broadband Lorentzian response. As a result, the proposed model guarantees a physical and causal response from the metasurface. Several full-wave results are shown and compared with analytical Fourier propagation methods showing excellent results for both 1D and 2D field simulations. It is found that the TAC provides the fastest convergence among the three methods with minimum error.
Highlights
Electromagnetic (EM) metasurfaces are two-dimensional equivalents of volumetric metamaterials and are composed of 2D arrays of sub-wavelength scatterers
We develop a rigorous Finite-Difference Time-Domain (FDTD) method, where the Generalized Sheet Transition Conditions (GSTCs) are directly integrated into the FDTD Yee-cell
An FDTD simulation of broadband electromagnetic metasurfaces has been proposed based on direct incorporation of GSTCs inside of Yee-cell region, for arbitrary wave excitations
Summary
Electromagnetic (EM) metasurfaces are two-dimensional equivalents of volumetric metamaterials and are composed of 2D arrays of sub-wavelength scatterers. The work in [28], [29] presented a GSTC-FDTD formulation of a dispersive metasurface for the first time, where the surface polarizabilities were described using physically motivated Lorentz-Drude models, typical of the physical sub-wavelength unit cell resonators used in constructing practical metasurfaces. Compared to the explicit FDTD model presented in [28], [29], [38], where the metasurface is treated as a boundary of a given simulation domain, the proposed method treats the metasurface as an EM scattering entity and is able to process arbitrary broadband excitations In this context, various strategies for integrating GSTCs in a conventional FDTD Yee-cell are proposed and compared here, assuming Lorentzian surface polarizabilities, which are naturally causal and rigorously captures the fundamentally dispersive nature of typical EM metasurfaces. The surface susceptibilities χee and χmm are treated a scalars for simplicity, as opposed to their most general tensorial forms that account for more general wave transformations
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