of complex refractive index, , one has

It can be shown that this generalization of group velocity continues to be related to the apparent speed of the peak of a wavepacket. The above definition is not universal, however: alternatively one may consider the time damping of standing waves (real , complex ), or, allow group velocity to be a complex-valued quantity. Different considerations yield distinct velocities, yet all definitions agree for the case of a lossless, gainless medium.

The

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