In-plane modal analysis of a metalayer formed by arrayed pairs of dogbone-shaped conductors

We present a comprehensive analysis of natural modes of a planar metamaterial layer (metalayer) formed by arrayed pairs of metallic dogbone-shaped conductors separated by a thin dielectric layer. The in-plane modes are classified based on the symmetric and anti-symmetric current distributions in the pairs. Of particular interest are the anti-symmetric modes, since the anti-symmetric current is associated with the magnetic resonance in metamaterial particles made of tightly coupled pairs. It is shown that the modal spectrum includes both TE and TM bound (proper real) and leaky (proper complex and improper complex) modes. An interesting observation is that a peculiar dominant TM improper leaky wave with a low attenuation constant, for the anti-symmetric current distribution, occurs at low frequencies, with a potential application in periodic leaky-wave antennas.