Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures

We demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field. In nondispersive materials, opposite group and phase velocity corresponds to fields that are mostly oriented in the propagation direction. More generally, this relationship (including the case of dispersive and negative-index materials) offers a perspective on the phenomena of backward waves and left-handed media. As an application of this relationship, we demonstrate and explain an irrecoverable failure of perfectly matched layer absorbing boundaries in computer simulations for constant cross-section waveguides with backward-wave modes and suggest an alternative in the form of adiabatic isotropic absorbers.