Discrepancy between group and energy transport velocities in spherical electromagnetic cloaks

Maxwell's equations can be used to prove the general theorem that the group and energy transport velocities are equal in linear, homogeneous, lossless, frequency dispersive, source-free, bianisotropic material. However, for the material of a spherical cloak, it would appear that if the permittivity and permeability dyadics are not equal for ω ≠ ω0 (even though they are equal for ω = ω0), or, more generally, do not satisfy equation (26) in the main text, then the group and energy transport velocities are not equal (for a homogeneous material having the local values of the permittivity and permeability dyadics of the cloak). This apparent paradox is explained by showing that the local fields of the spherical cloak uncouple into E and H waves, each with their own group and energy transport velocities, and that the group and energy transport velocities of either the E wave or the H wave are equal and thus satisfy the general theorem. © 2009 IEEE.