Relaxation mechanisms in three-dimensional metamaterial lens focusing

We study the transient behaviors in focusing a point source with a metamaterial lens (epsilon = mu = -1 + delta). We find the time evolutions of image formation are dictated by two relaxation mechanisms, namely, surface wave transport and absorption, determined, respectively, by Re(delta) and Im(delta). We show that image oscillations are inevitable in this three-dimensional configuration when Re(delta) double dagger 0 and establish relationships among the relaxation time, the resolution enhancement, and delta.