A uniform asymptotic solution for reflected and scattered fields over half-space metamaterials

We have derived the novel uniform asymptotic solution for the reflected and scattered fields over half-space metamaterial. The uniform asymptotic solution consists of the geometrically reflected ray, the backward lateral waves, and the transition wave which plays an important role only in the transition region near the critical angle. The validity of the uniform asymptotic solution is confirmed by comparing with the reference solution calculated numerically.