Optical delay of a signal through a dispersive invisibility cloak

We present a full-wave analysis method on the transmission of a Gaussian light pulse through a spherical invisibility cloak with causal dispersions. The spatial energy distribution of the Gaussian light pulse is distorted after the transmission. A volcano-shaped spatial time-delay distribution of the transmitted light pulse is demonstrated as a concrete example in our physical model. Both the time-delay and the energy transport depend on the polarization of light waves. This study helps to provide a complete picture of energy propagation through an invisibility cloak.