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Additional resources for Advances in Chemical Physics, Vol.119, Part 2. Modern Nonlinear Optics (Wiley 2001)
Such a concentrated local energy behavior is hard to reconcile with a plane wave, even when the distribution of photon impacts exhibits a probability character given by quantum theory. In the case of impinging individual photons, these marks seem to be consistent with a limited radial extension of the wavepacket as given by Eq. (173), at least when cos a ! 10À5 . Apart from the factor cos a, Eq. (173) agrees with a form by Hunter and Wadlinger  which appears to be consistent with microwave transmission experiments.
The field vectors E and C are parallel with the wave normal. Possibly this mode may form a basis for telecommunication without induced magnetic fields. 3. The Electromagnetic Space-Charge Mode When both k Á E 6¼ 0, and k Â E 6¼ 0, there is a nontransverse EMS wave with a magnetic field due to Eq. (49). This is the mode of most interest to this context. Here k Â C differs from zero, and Eqs. (48) and (49) combine to Á À 2 o À k2 c2 E þ ðk Á EÞF ¼ 0 ðB 6¼ 0Þ ð52Þ and F ¼ c2 k À oC ð53Þ which corresponds to Eq.
In most experimental situations there is a very large ratio 1=" d between the damping length and the wavelength of the incident wave, and this makes it difficult to decide which results on the homogeneous and inhomogeneous cases would be physically relevant. The results on inhomogeneous waves should first become applicable at large enough values of the damping factor "d, but this would require large initial amplitudes of the incident wave to give rise to a detectable reflected wave. VII. AXISYMMETRIC WAVE MODES As discussed for several decades by a number of authors, the nature of light and photon physics is related not only to the propagation of plane wavefronts but also to axisymmetric wavepackets, the concepts of a rest mass, a magnetic field in the direction of propagation, and an associated angular momentum (spin).