Electrostatic bulk waves propagation in a slab delay line of metallic nanowire-based hyperbolic metamaterials

As a new planar electrostatic (or, in a better word, quasi-electrostatic) waveguide, the characteristics of electrostatic bulk waves guided by a slab of metallic nanowire-based hyperbolic metamaterials are studied. The dispersion relation of the waves is obtained using the zig-zag ray approach based on the stationary-phase method which is the same as the result obtained from the field analysis. Also, we present a description for the investigation of the group velocity and associated group delay time of electrostatic bulk modes of the system. The analytical results based on the zig-zag ray approach show the group delay is produced partly at the boundaries of the slab and partly inside the slab. The former is not dependent on the order of the mode and can be neglected compared with the latter in the neighborhood of the frequency of resonance where electrostatic wave devices are usually operated.