This article deals with an approach to the design of planar antennas that use metamaterial-loaded substrates based on the effective medium approximations. Metamaterials are structured composite materials with unique electromagnetic properties due to the interaction of electromagnetic waves with the finer scale periodicity of conventional materials. They may be used to modify the effective electromagnetic parameters of planar antenna substrates and to design antennas with the improved coupling to the feed, increased impedance matching bandwidths, miniaturized dimensions, and narrower beamwidths compared to those that use conventional dielectric materials for the same purposes. The electromagnetic analysis and optimization based on the effective medium approximations of metamaterials is very convenient since it deals with only a few bulk medium parameters instead of a large number of parameters describing a discrete structure. At the same time, the most common way of obtaining these effective medium parameters is transmission/reflection simulations or measurements in free space or in a homogeneous background medium. For a host medium which is not homogeneous, as for a grounded substrate, the effective medium parameters are different from the free space ones. The scattering losses in a metamaterial medium need to be accurately taken into account and included as parameters in full-wave bulk medium models. For this reason, in the effective medium approach for antenna substrates, one needs to use the appropriate effective medium approximations that take the coupling between inclusions into account and also to evaluate the effects of the scattering losses. In practice, this is done by finding the effective medium parameters inside an arbitrary substrate medium, and not in a homogeneous host medium or in free space. This paper presents the methodology and the results of FDTD analysis of planar antennas that have substrates with various metamaterial inclusion densities. The effective bulk medium approach presented in the article is analyzed by comparing the antenna return losses and radiation patterns to the ones computed for a discrete structure. The Green's function of the host medium (antenna substrate) is used to calculate the approximate bulk effective medium parameters of the MTM-loaded substrate.
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