Transient response of a signal through a dispersive invisibility cloak

The transient response of the invisibility cloak has long been an interesting research topic, since it is valuable to further understand the steady-state process and to design more effective cloaks. Here we investigate the transient response of a set of dispersive invisibility cloaks impinged on by a sinusoidal signal or a modulated Gaussian pulse using the finite difference time domain method. Cylindrical cloaks with linear, convex, and concave transformation functions are studied. We find that their time to reach a steady state is different and they grow significantly when the thickness of the cloak decreases. Moreover, a centrally depressed ladder-like spatial time delay distribution is observed with a modulated Gaussian pulse. We show that the central frequency of the Gaussian pulse suffers a blue-shift in the forward scattering direction in agreement with previous theoretical predictions.