Superluminal optical pulse propagation in nonlinear coherent media

Abstract

The propagation of light-pulse with negative group-velocity in a nonlinear medium is studied theoretically. We show that the necessary conditions for these effects to be observable are realized in a three-level Λ-system interacting with a linearly polarized laser beam in the presence of a static magnetic field. In low power regime, when all other nonlinear processes are negligible, the light-induced Zeeman coherence cancels the resonant absorption of the medium almost completely, but preserves the dispersion anomalous and very high. As a result, a superluminal light pulse propagation can be observed in the sense that the peak of the transmitted pulse exits the medium before the peak of the incident pulse enters. There is no violation of causality and energy conservation. Moreover, the superluminal effects are prominently manifested in the reshaping of pulse, which is caused by the intensity-dependent pulse velocity. Unlike the shock wave formation in a nonlinear medium with normal dispersion, here, the self-steepening of the pulse trailing edge takes place due to the fact that the more intense parts of the pulse travel slower. The predicted effect can be easily observed in the well known schemes employed for studying of nonlinear magneto-optical rotation. The upper bound of sample length is found from the criterion that the pulse self-steepening and group-advance time are observable without pulse distortion caused by the group-velocity dispersion.

Light Propagation in Optically Dressed Media

“…The pulse history is presented in the series of plots in Figure 10 (see also Ref. [29]). When an incoming pulse approaches the entrance of the sample a (a) 30 pair of pulses is created at its exit: one inside the sample and the other outside it.…”

Short pulse propagation in an inverted two-level medium

“…Authors of these works interpret the obtained results as propagation of pulses at the velocity exceeding speed of light in vacuum and even at negative group velocity. Theoretical consideration in linear media [11][12][13][14][15] is based on the Fourier formalism. This formalism gives in the first approximation with respect to dispersion the well known expression for the group velocity in a resonant medium, (1) where n(ω) is the index of refraction of the medium and ω 0 the pulse carrier frequency.…”

Absorption free superluminal light propagation in a three-level pump–probe system

“…The effect of superluminality is that the emerging pulse has essentially the same shape and width as that of the incident wave packet, but its peak travels with a velocity higher than c and even exits the medium before the incident pulse enters. This processes can be understood in terms of superposition and interference of traveling plane waves that have a distribution of frequencies and add up to form a narrow-band light pulse [7,8]. A rather simple mathematical proof shows that fast light behavior is completely consistent with Maxwell's equations describing pulse propagation through a dispersive material and hence does not violate Einstein's special theory of relativity (the special theory of relativity is based on Maxwell's equations) [9].…”