Advanced microwave effective medium theory for two-component nonmagnetic metamaterials: fundamentals and antenna substrate application

A modification of effective medium theory for two-component nonmagnetic metal---dielectric metamaterials is developed for use in the microwave frequency range. The metamaterial is represented as an unbounded isotropic dielectric host material with periodically embedded nonmagnetic metallic inclusions of cylindrical or spherical shape. The effective electromagnetic response of the metamaterial is represented by the tensor of the effective relative permittivity and tensor of the effective relative permeability. The losses of the metamaterial are also evaluated in this study. A physical interpretation for the nature of the effective properties of such metamaterials is given. Analytical models of the proposed effective medium theory are benchmarked against numerical simulations using commercial electromagnetic software. Two compact microwave rectangular dual-band patch antennas on such metamaterial substrates are designed in this study.