Vortex-like surface wave and its role in the transient phenomena of meta-material focusing

We show that a slab of meta-material (with $\epsilon =\mu =-1+i\Delta$ ) possesses a vortex-like surface wave with no ability to transport energy, whose nature is completely different from a localized mode or a standing wave. Through computations based on a rigorous time-dependent Green’s function approach, we demonstrate that such a mode inevitably generates characteristic image oscillations in two-dimensional focusing with even a monochromatic source, which were observed in many numerical simulations, but such oscillations are weak in three-dimensional focusing.