Modal analysis of one-dimensional Electromagnetic Metamaterial grounded slab

Electromagnetic Metamaterials (MTMs) are artificial materials with novel electromagnetic properties not available in nature. MTMs have the potential to facilitate significant improvement on performance of low-profile (i.e. microstrip) and conformal antennas, including reduction of antenna size and antenna coupling. In this paper, we develop analytic expressions and corresponding tractable approximations for impedance and dispersion relations for one-dimensional MTMs applicable to a wide frequency range. Our technique obtains properties relevant for the application of MTMs to antennas without the need to derive the effective medium parameters first. We apply this technique to investigate surface wave modes supported by a single-layer and double-layer one-dimensional electromagnetic crystal on a ground plane. We use modal analysis for one-dimensional stratified periodic MTM media. The modal formalism is directly applicable to the surface wave problem and bypasses difficulties associated with defining average constitutive parameters that are valid only in the quasi-static region. We use transmission-line theory to solve the propagation problem in one direction, while modal functions are determined for the transverse plane. The stratified material is decomposed into unit cells. We apply Floquet's theorem and the chain matrix method to determine the characteristic impedance and the dispersion relation. We develop algebraic approximations to trigonometric functions in order to obtain approximate expressions in various frequency regimes. These approximations can be used to determine reactive impedance (stopgap) regions, surface-wave modes Greens functions (Antenna patterns), and resonance conditions for microstrip and conformal antennas. We apply this technique to the open slab configuration using transverse resonance. This work is an initial stage in CERDEC's effort to develop an approach to tailor MTM properties to meet military application-driven antenna requirements.