A novel method for wave focusing investigation in metamaterial half-space and slab lens structures

Summary Approximate image currents for the Sommerfeld half-space problem with vertical electric and magnetic current sources above double negative half-space is found using the discrete image theory and Laplace transform. This method would found its applications in investigation of dipole radiation above metamaterial half-space and in describing the focusing mechanism of metamaterial lenses. In order to efficiently consider the effects of metamaterial half-space, discrete image dipoles are defined by proposing an exponential series for reflection coefficient. Unknown constants (the loci of images) in the argument of the exponential function are determined by equating the coefficients of the Taylor series for exact reflection coefficient with those of the proposed approximate series. Thus, the calculation of integral with oscillating integrand reduces to the solution of polynomial equation for the zeros of polynomials. As an application for the proposed approach, the field focusing in double negative is investigated. Thanks to the fast and accurate methods for finding the zeros of polynomials, it is shown that in addition to its good accuracy, this method decreases the computational time for field calculations in comparison with the exact methods. It is seen that for the negative refractive index beside -1, the complex images approach to infinity and have negligible effect on the scattering field of dipole. For the other negative indexes the complex image blurs the real image.