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Optical Memory and Neural Networks

Short pulse propagation in an inverted two-level medium

G. G. Grigoryan, V. O. Chaltykyan, Vanush Paturyan

Published Dec 1, 2011• 0 citations
Publisher

Abstract

We consider propagation of a pulse carrying optical information in a resonant medium of two-level atoms and revisit the concept of the group velocity. We obtain conditions when this concept may be used and show that in a population inverted medium the possible superluminal propagation may result in advance times much shorter than the pulse duration because of lethargic amplification following from the complete exact solution of the problem.

DOI
10.3103/s1060992x11040035

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We consider propagation of a pulse carrying optical information in a resonant medium of two-level atoms and revisit the concept of the group velocity. We obtain conditions when this concept may be used and show that in a population inverted medium the possible superluminal propagation may result in advance times much shorter than the pulse duration because of lethargic amplification following from the complete exact solution of the problem.
We investigate a light-pulse propagation with negative group velocity in a nonlinear coherent medium. We show that the necessary conditions for nonlinear superluminal effects to be observable are realized in a three-level $\ensuremath{\Lambda}$ system interacting with a linearly polarized laser field in the presence of a static magnetic field. The initially prepared Zeeman coherence cancels the resonant absorption of the medium almost completely, but preserves its dispersion anomalous and very high. In this medium the light pulse propagates superluminally in the sense that the peak of the transmitted pulse exits the medium before the peak of the incident pulse enters. At the same time the pulse group velocity is intensity dependent, which leads to the self-steepening of the pulse trailing edge due to the fact that the more intense parts of the pulse travel slower. This is in contrast with the shock wave generation in a nonlinear medium with normal dispersion. The predicted effect can be easily observed in the well-known schemes employed in the studies 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.
In the region between two lines of a doublet of an inverted medium, there exists a point of zero group-velocity dispersion, where highly superluminal effects may be observable without significant gain, loss, distortion, or broadening. The results of this group-velocity analysis hold for sufficiently narrow-band, analytic pulses, and do not constitute a violation of causality, although the group, ``signal,'' and energy velocities as defined by Sommerfeld and Brillouin may all exceed c or even become negative. No sharp disturbance in the pulse (a real signal) could propagate faster than light, but the scheme offers an unusual noiseless amplification scheme for the leading edge of a pulse, both at the classical and at the single-photon level.
Causality and special relativity pose an upper limit to the amount of advance that an optical pulse can acquire during a superluminal propagation. Such a limit can be circumvented if the pulse, before entering the superluminal medium, is retarded by letting it propagate under normal dispersion. We present an experimental evidence of this fact by showing that a laser pulse propagating in an atomic vapor, quasi resonant with an inverted transition and in conditions of anomalous dispersion, moves faster if it is previously retarded in a cell containing the same medium with no population inversion. Optical transmission lines often need an amplification stage to overcome the signal attenuation and the unavoidable delay respect to propagation at c; in this paper we tailor such stage to provide also an optical controlled recover of such delay. We believe that our results can open exciting prospects for real-life optical data processing and communication.
We consider the propagation of a light pulse in a medium with a single resonance. If the frequency of the pulse is tuned far from resonance and the pulse duration is much shorter than the lifetime of the excited state of the resonant particles in the medium (atoms in a gas, impurity ions in a solid, etc.), the group velocity of the pulse is appreciably reduced. It is shown that the slowing down of the group velocity of the pulse is accompanied with a pulse chirp, which produces a pulse broadening in time. It is proposed to use two samples in sequence with opposite chirps (up chirp and down chirp or vice versa) compensating the pulse broadening. Then the pulse can be delayed with almost no losses, distortion, and broadening. However, there is a maximum distance, beyond which the pulse experiences corruption. Pumping with an auxiliary laser beam can control the delay time of the light pulse in the medium. Conditions to eliminate the contribution of the dephasing processes in the pulse propagation are considered.