Input Impedance of Horizontal Dipole Located Above Lossy Metamaterial Half-Space

In this letter, accurate analytical expressions for the impedance of horizontal electric and magnetic dipoles located above half-space materials of arbitrary permittivity and permeability are derived. In this regard, the Fresnel reflection coefficients are approximated by series of exponential functions, and the impedance integrals are analytically solved. The results are compared to the case of natural materials (positive permittivity and permeability), and the key differences are explained. It is shown that for horizontal dipoles above materials of high and/or low conductivities, both results are coincident. For dipoles in the vicinity of low-loss materials, the results are somewhat identical. However, a better agreement could be obtained using higher-order approximations for the integrand.