Group velocity media

P. L. Edwards, Ultrasonic Signal Distortion and its Effects on Velocity Measurements in Dispersive Constant-Group-Velocity Media , J. Acoust. Soc. Am. 1983, 73, 1608. 

We do not consider here the dependence of the group velocity on the beam divergence and the related spatiotemporal effeets in the nonlinear medium leading to additional changes in the pulse shape. In the region of the core, these effects are small, and the radiation field power for the levels of the input pulse power considered here is low. 

The propagation of EM waves in a dispersive medium has been investigated for a long time [25]. The group velocity of a wavepacket in such a medium is given by... 

Figure 4. The schematic illustrates a photon flux through a quantization volume. Each side of the chosen cube is assigned a length I. The photons traverse the box in a time l/vs where vs is the group velocity in the medium.

When an optical pulse with the spectral amplitude distribution E o)) propagates through a medium with refractive index n o)), its time profile will change because the group velocity... 

For a pulse of initial width r, which propagates with the group velocity Vg through a medium of length L, the solution of (11.19) yields the pulse width [11.58]... 

The fundamental modes of all waveguides considered in this text are cut off when F = 0. At cutoff the phase velocity of the mode is equal to that of a z-directed plane wave in an unbounded medium of refractive index n, but the modal fields are not TEM waves except in special cases. In general, a significant fraction of a mode s power can propagate within the core at cutoff, i.e. r]j of Eq. (11-24) is nonzero, and the group velocity differs from the phase velocity. Below cutoff, these modes propagate with loss and are the leaky modes of Chapter 24. 

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