Rainbow and blueshift effect of a dispersive spherical invisibility cloak impinged on by a nonmonochromatic plane wave

We demonstrate some interesting phenomena associated with a nonmonochromatic plane wave passing through a spherical invisibility cloak whose radial permittivity and permeability are of Drude and Lorentz types. We observe that the frequency center of a quasimonochromatic incident wave will suffer a blueshift in the forward scattering direction. Different frequency components have different depths of penetration, causing a rainbowlike effect within the cloak. The concept of group velocity at the inner boundary of the cloak needs to be revisited. Extremely low scattering can still be achieved within a narrow band.