Conventional definitions of velocities associated with the propagation of modulated waves cannot clearly describe the behavior of the wave packet in a multidimensional dispersive medium. The conventional definition of the phase velocity, which is perpendicular to the wave front, is a special case of the generalized phase velocity defined in this work, since there exist an infinite number of solutions to the equation describing the wave-front movement. Similarly, the generalized group-front velocity is defined for the movement of a wave packet in an arbitrary direction. The group-front velocity is the smallest speed at which the group-front travels in the direction normal to the group front. The group velocity, which is the velocity of energy flow in a nondissipative medium, also satisfies the group-front equation. Because the group-front velocity and the group velocity are not always the same, the direction in which the wave packet travels is not necessarily normal to the group front. In this work, two examples are used to demonstrate this behavior by considering the refraction of a wave packet from vacuum to either a positive-index material (PIM) or a negative-index material (NIM).
On the Group Front and Group Velocity in a Dispersive Medium Upon Refraction From a Nondispersive Medium
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division May 8, 2003; revision received December 23, 2003. Associate Editor: S. T. Thynell.
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Zhang , Z. M., and Park, K. (May 4, 2004). "On the Group Front and Group Velocity in a Dispersive Medium Upon Refraction From a Nondispersive Medium ." ASME. J. Heat Transfer. April 2004; 126(2): 244–249. https://doi.org/10.1115/1.1668035
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