Imaging properties of lossless double-negative metamaterial wedges: Analytical and numerical investigation

Abstract

The superlensing characteristics of a lossless double-negative metamaterial wedge are examined in this paper via an analytical technique. The algorithm incorporates the Kontorovich-Lebedev (KL) transform in a mathematically consistent manner whereas the role of the radiation condition on its correct application is quantitatively elucidated. Implementing a ray-approximation algorithm, the proper radiation conditions are resolved and the Helmholtz equation as well as the boundary conditions are accordingly transformed. To this end, the prior formulation introduces a linear operator which, given the KL transform of a specific kind, constructs the corresponding one of a different kind. Thus, the field can be described analytically in the entire domain, showing the ability of the wedge to, perfectly, focus a line source in two points, inside and outside the metamaterial, just like the planar double-negative slab. To validate the proposed analysis, the analytical results are compared to those acquired by means of the finite-difference time-domain method for various geometrical parameters and wedge configurations.