Decomposition of a video pulse into traveling and evanescent waves

Using the general solution of the wave equation for the empty space (vacuum), it has been shown that spatially limited video pulses may exist in it. However, video pulses in the empty space necessarily consist of two components: traveling and evanescent waves. It has been demonstrated that such structures can be created immediately beyond the interface between an optically dense medium and the empty space, as in near-field optics. In this work, the traveling and evanescent components are illustrated for a video pulse with Gaussian temporal and spatial profiles. It has been shown that the traveling wave is a one-and-half cycle pulse and its duration is determined by the ratio of the transverse and longitudinal dimensions of the video pulse. The same ratio also determines the distance at which the evanescent wave decays, and the video pulse becomes a few-cycle traveling wave. Using Gauss’s theorem, it has been demonstrated that transversely limited video pulses are not unipolar. The transverse and longitudinal components of their field perpendicular and parallel to the wave propagation axis, respectively, can be comparable in magnitude and differ in the character of their time evolution.