volume | PIER Journals

Abstract

A study is presented of several types of nondiffracting and slowly diffracting spatiotemporally localized waves supported by a simple dielectric medium moving uniformly with speed smaller or larger than the phase speed of light in the rest frame of the medium. The Minkowski material relations are not independent in the case that the speed of motion equals the phase speed of the medium; hence, the electric displacement and magnetic induction vectors cannot be uniquely determined from them. Following, however, a waveguide-theoretic approach, separate equations can be written for the longitudinal and transverse (with respect to the direction of motion) electromagnetic field intensities. The fundamental solutions associated with these equations provide a uniform transition between the cases of ordinary and Čerenkov-Vavilov radiation. The equation satisfied by the longitudinal field components in the absence of sources is examined in detail. In the temporal frequency domain one has an exact parabolic equation which supports accelerating beam solutions. The space-time equation supports several types of nondiffracting and slowly diffracting spatiotemporally localized waves. Comparisons are also made with the acoustic pressure equation in the presence of a uniform flow.

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Professor Ioannis Besieris