Hyperbolic Metamaterials at Microwaves With Stacked Inductive Coiled-Wire Arrays

Metasurfaces made of arrayed wires are inductive only for propagating waves and become capacitive when illuminated by evanescent waves. We show how to extend the inductive behavior of such metasurfaces for the case of illumination by plane waves with large wavenumber, i.e., for evanescent waves. The proposed metasurface exhibits an effective surface inductance that is extended to evanescent waves with large transverse wavenumber using coiled wires. Metasurfaces with inductive response over a wide spatial spectrum can be used for the realization of hyperbolic metamaterials (HMs) at microwave frequencies. Stacking such inductive metasurfaces separated by thin dielectric spacers leads to a negative real part of the in-plane, effective dielectric permittivity, and thus, to hyperbolic wavevector dispersion at microwave frequencies. We establish the requirements for such hyperbolic dispersion condition using arrays of coiled wires, also accounting for losses. We show that the negative in-plane real part of dielectric permittivity stretches up to transverse wavenumbers that are several times larger than the free-space wavenumber, over a broad frequency bandwidth. The theory and important design analytic formulas are presented to demonstrate the inductive behavior, as well as the propagative nature of waves in the proposed HM, in agreement with full-wave simulations.