High-frequency uniform asymptotic solution for reflected and scattered fields over half-space metamaterial

Abstract

It is known that when the cylindrical wave propagates from a positive index material (PIM) to a negative index material (NIM), the backward lateral wave is excited along the interface between the PIM and the NIM over a half-space metamaterial. In this study, by using the saddle point technique, we shall derive a novel high-frequency uniform asymptotic solution for the reflected and scattered fields over a half-space metamaterial with the NIM. The validity and utility of the novel uniform asymptotic solution is confirmed by comparing with the reference solution calculated by the numerical integration of the integral representation for the reflected and scattered fields. We have also shown the physical interpretation of the uniform asymptotic solution.