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Physical Review E

Superluminal propagation of solitary kinklike waves in amplifying media

Maciej Janowicz, Jan Mostowski

Published Apr 27, 2006• 7 citations
Publisher

Abstract

It is shown that solitary-wave, kinklike structures can propagate superluminally in two- and four-level amplifying media with strongly damped oscillations of coherences. This is done by solving analytically the Maxwell-Bloch equations in the kinetic limit. It is also shown that the true wave fronts--unlike the pseudo wave fronts of the kinks--must propagate with velocity c, so that no violation of special relativity is possible. The conditions of experimental verification are discussed.

DOI
10.1103/physreve.73.046613

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It is shown that solitary-wave, kinklike structures can propagate superluminally in two- and four-level amplifying media with strongly damped oscillations of coherences. This is done by solving analytically the Maxwell-Bloch equations in the kinetic limit. It is also shown that the true wave fronts--unlike the pseudo wave fronts of the kinks--must propagate with velocity c, so that no violation of special relativity is possible. The conditions of experimental verification are discussed.
Running-wave solutions to three systems of partial differential equations describing wave propagation in atomic media in the kinetic limit have been obtained. Those systems include approximations to (i) standard two-level Maxwell–Bloch equations; (ii) equations describing processes with saturated absorption in three-level systems and (iii) equations describing processes with reversed saturation in four-level systems. It has been shown that in all three cases kink-like solitary waves can emerge if the dynamical equation for the intensity includes a linear contribution to the Lambert–Beer law. Those solitary waves can propagate with either sub- or superluminal velocity of the edge of the kink, and in a direction which can be either the same as or opposite to that of the carrier wave. In addition, simple qualitative information about the behaviour of waves near the wavefronts has been obtained.
Analytic, limited-bandwidth signals, e.g. Gaussian wavepackets, whose frequencies lie in a transparent spectral window far below the resonance of an amplifying atomic medium, can propagate with phase, group, energy and 'signal' velocities (as defined by Sommerfeld and Brillouin) all exceeding the vacuum speed of light c. This 'superluminal' propagation may occur without significant distortion or gain. The front velocity, however, is not superluminal, and therefore Einstein causality is not violated. Applications will be discussed, including the possibility of using superluminal atomic coherence in condensed matter (e.g. macroscopic mass currents in superfluid helium which arise from vortex motions) for efficient gravitational antennae.
The propagation of pulses through dispersive media was investigated by solving Maxwell's equations without any approximation. We show that the superluminal propagation of pulses through anomalous dispersive media is a result of the interference of different frequency components composed of the pulse. The coherence of the pulse plays an important role for the superluminal propagation. With the decrease of the coherence of the pulse, the propagation changes from superluminal to subluminal. We have shown that the anomalous dispersion (the real part of the susceptibility) not the amplification (the imaginary part of the susceptibility) plays the essential role in the superluminal propagation. Although the superluminality always exists as long as the spectrum of the coherent pulse is within the anomalously dispersive region, both the energy propagation velocity and the frontal velocity never exceed the light speed in the vacuum. The output pulse through the medium is not the original pulse; instead it carries the information of the original pulse and the information of the prepared medium.
An optical kink is a shock-wave-like field structure which can appear in a resonant two-level medium as a result of the nonlinear process of self-steepening. We numerically simulate this process using an adiabatically switching wave form as an input and confirm the self-similarity of resulting kinks. The analysis is also applicable to a more general wave form with a decaying trailing edge which we call a kinklike pulse. We study in detail collisions of kinks with other kinks and ultrashort pulses and demonstrate the possibility to control kink speed by changing the parameters of counterpropagating fields. The effects considered can be treated as belonging to a wide class of unexplored phenomena in the regime of incoherent light-matter interaction.
The propagation of pulses through dispersive media was investigated by solving Maxwell's equations without any approximation. It was demonstrated that the superluminal or subluminal pulse propagation originates essentially from the interference of the different frequency components of the pulse. The coherence of the different frequency components plays an important role in superluminal propagation. When the pulse becomes partially coherent, the propagation changes from superluminal to subluminal. Since superluminality always exists as long as the spectrum of the coherent pulse is within the anomalously dispersive region whatever the shape of the pulse is, such a coherent pulse must be transmitted superluminally.