Wave packet incident on negative-index media

This paper presents a study of the refraction and reflection of a wave packet in time and space at the plane boundary between free space and a negative index medium (NIM). We derive an analytic asymptotic expression that shows negative refraction at the angle predicted by the negative index evaluated at the center frequency with a speed of propagation in the NIM equal to the group velocity. Then we present numerical calculations of exact solutions that verify the asymptotic theory. Finally we present numerical calculations for cases with incidence beyond the critical angle. Here we find phenomena identified as backward lateral waves and a negative Goos-Hanchen shift.