A Closed-Form Representation of Isofrequency Dispersion Curve and Group Velocity for Surface Waves Supported by Anisotropic and Spatially Dispersive Metasurfaces

A general closed-form representation is introduced for representing the isofrequency dispersion curve (IDC) of an anisotropic, spatially, and frequency dispersive metasurface (MTS) constituted by a dense periodic texture of metallic elements printed on a grounded substrate. The formulation is restricted to printed elements isolated from each other (namely, patches and not slots) whose geometry exhibits at least two axes of symmetry. The expression is valid for the dominant TM surface wave (SW) until the limit of the Floquet-Bloch (FB) region and generalizes our previous formulation to arbitrary direction of propagation. This generalization permits a closed-form representation of the IDCs and of the group velocity as a function of two parameters only; these are the equivalent quasi-static capacitances along the symmetry directions of the geometry. The limit of validity of the closed-form representation has been defined and the formulation has been tested by full-wave analysis. The present formulation simplifies the design of MTS antennas and flat transformation optics devices.