Velocity and natural spreading of wave packets in mean fields

Thomas F. Jordan

Ajoy Kumar Ghatak, S. Lokanathan

Henry M. Bradford

The usual textbook discussions of the velocity and spreading of a wave packet are based on special cases and approximations which have a limited range of validity. In this paper more general relations are obtained by considering the time dependence of the moments of a wave packet. Both a packet of real sinusoidal plane waves (a real pulse, e.g., sound) and a packet of complex exponential plane waves (e.g., the quantum-mechanical wave function of a free particle) are considered. The results are similar if the real wave packet contains no standing wave components. It is shown that the centroid of a wave packet moves at a constant velocity which is a weighted average of the group velocity. The spreading of the wave packet depends on the product of the variance of the group velocity and the square of the time interval before or after the time of minimum packet width. The packet moves and spreads like a collection of particles in free flight, in which the velocities of the particles are the group velocities of the wave components of the packet.

Chandana Roy

Peeter Saari, Ioannis M. Besieris

Hall and Abouraddy [1] have reported first experimental observation of optical de Broglie-Mackinnon wave packets, which is a seminal achievement in the study of so-called non-diffracting optical pulses. These wave packets propagate in free space without spreading with subluminal relativistic velocities, i.e., with speeds slower but close to the velocity of light in vacuum. The experiments in [1] became possible thanks to the application of quite a witty method. Unfortunately, the explanation of the physical nature of the wave packets and their graphical and mathematical descriptions in the theoretical part of [1] suffer from some ambiguities that need to be clarified.

Marian Grabowski