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Negative refraction and group velocity

Refraction distorts a wave packet that is incident on the interface between two media. The refracted wave packet, although distorted, travels in the direction given by Snell's law with the group velocity of the medium it has entered. This is true both for positive n (the usual case) and for the less familiar case of negative n, where n is the real part of the index of refraction.

Three PDF files (requiring Acrobat Reader 6.0) are attached to support these statements.

negativn.pdf gives formulas for a wave packet constructed using a distribution of wave vectors k. It discusses a gaussian wave packet and a two-waves beam, which is not a proper wave packet but can be instructive. It ends by stating (without proof) the general fomula for the group velocity.

negativnproof.pdf gives the proof of the general formula for the group velocity.

negativnpacket.pdf discusses the gaussian wave packet in full detail, using a distribution in frequency and angle, rather than in the components of the wavevector k. The algebra is messier, but the conclusions are the same.


V. Celli, Univ. of Virginia
Dec 13 16:27:59 EDT 2004