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Part III - Spatially Dispersive Metasurfaces: Zero Thickness Modeling of Periodic and General Non-uniform Surfaces

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posted on 2022-08-11, 05:29 authored by jordan dugan, João Nizer RahmeierJoão Nizer Rahmeier, Tom J. Smy, Shulabh GuptaShulabh Gupta

A zero thickness model of non-uniform spatially dispersive (SD) metasurfaces is developed and demonstrated numerically for practical structures. This is an extension of [1], [2], which proposed a method of modeling uniform spatially dispersive metasurfaces by expressing their surface susceptibilities as rational polynomial functions in the spatial frequency domain. This led to the extended generalized sheet transition conditions (GSTCs) forming a set of differential equations relating the spatial derivatives of both difference and average fields around the surface that were then integrated into an integral equation (IE) solver. Here, the extended GSTCs are further developed to model non-uniform metasurfaces by approximating them as locally linear space invariant (LSI). Using this model, a semi-analytical Floquet method is derived to predict scattered fields from periodically varying metasurfaces. The extended GSTCs, Floquet method, and IE method are tested on several nonuniform surfaces consisting of short metal dipole cells of varying lengths exhibiting strong spatial dispersion. The physical surfaces are simulated in Ansys FEM-HFSS while their zero thickness equivalents, both dispersive and non-dispersive, are simulated using the Floquet and IE methods. Excellent agreement is shown between the Floquet-SD and IE-GSTC-SD methods and HFSS, demonstrating the importance of spatial dispersion to model their scattered fields.


Department of National Defence of Canada


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Carleton University

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  • Canada