## Discrepancy between Group and Energy-Transport Velocities in Spherical Electromagnetic Cloaks

#### Arthur YaghjianHanscom Air Force Base

Maxwell's equations can be used to prove the general theorem that the group and energy-transport velocities are equal in linear, lossless, frequency dispersive, source-free, bianisotropic material. However, a cursory application of conventional formulas for local group and energy-transport velocities in spherical electromagnetic cloaks can lead to a discrepancy between the group and energy-transport velocities if the permittivity and permeability dyadics are not equal over a frequency range about the center frequency. This apparent paradox is explained by showing that the local fields of the spherical cloak uncouple into an E and H wave, each with its 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.

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