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Optics Express

Recovering the propagation delay of an optical pulse

Federico Tommasi, Emilio Ignesti, Lorenzo Fini, Stefano Cavalieri

Published Nov 10, 2014• 3 citations
Publisher

Abstract

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.

DOI
10.1364/oe.22.028566

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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 present an experimental realization of slow and fast light schemes for a few ns long optical pulses that makes use of incoherent interactions in an atomic medium. The combination of such different schemes allows us to demonstrate that the propagation delay acquired in the slow light stage, can be completely recovered in a fast light one. The use of an incoherent interactions scheme makes the control of the propagation dynamics of light pulses easer to realize. Delays up to 13 ns, in slow light regime, and advances up to 500 ps, in fast light regime, are reported when the stages work individually for a 3 ns long pulse. When both stages are switched-on the fast light stage is able to recover a previously induced delay and even to produce an extra advance, with an overall advance up to 1 ns. Since every optical transmission line needs an amplification system to overcome the unavoidable losses, the results suggest the opportunity and perspective of a proper tailoring of the amplification stage for data timing purposes.
Anomalous dispersion cannot occur in a transparent passive medium where electromagnetic radiation is being absorbed at all frequencies, as pointed out by Landau and Lifshitz. Here we show, both theoretically and experimentally, that transparent linear anomalous dispersion can occur when a gain doublet is present. Therefore, a superluminal light-pulse propagation can be observed even at a negative 7group velocity through a transparent medium with almost no pulse distortion. Consequently, a negative transit time is experimentally observed resulting in the peak of the incident light pulse to exit the medium even before entering it. This counterintuitive effect is a direct result of the rephasing process owing to the wave nature of light and is not at odds with either causality or Einstein's theory of special relativity.
The existence of anomalous, i.e. superluminal or negative, group velocities [1] provides one of the most amazing phenomenon of wave propagation which is compatible with, and even a consequence of, causality [2]. Anomalous wave propagation generally relies on the resonant interaction of light with an atomic medium, i.e. it exploits the dispersive properties of absorptive [3] or inverted [4,5] atomic media near resonances. Evanescent wave propagation across photonic barriers [1] provides the other wide framework where anomalous group velocities have been observed, however in such cases the achievement of a negative group velocity seems unlikely. By exploiting the dispersive properties of a gain doublet, a narrow spectral region of transparent anomalous dispersion around the dip center of two Lorentzian gain lines, leading to negative transit times and no pulse attenuation, can be created [4]. A recent demonstration thereof has been indeed reported in an experiment by Wang and coworkers using Cs vapor [5].
Pulse propagation through 1-dimensional stratified media is studied. The general features of pulse propagation in relation to the delay or advancement of the pulse are discussed. It is shown that in a lossless system with spatial symmetry the reflected and the transmitted pulses have the same delay or advancement. The phase times and the explicit output pulse profiles for an input Gaussian pulse are calculated. While recalling recent results for a variety of systems (resonant absorbers or heterogeneous medium in a Fabry-Perot cavity, a slab of negative index medium, a left-handed/right-handed periodic structure, etc.), new results involving coupled waveguides and a high finesse cavity containing an electromagnetically induced transparency (EIT) medium are presented. Calculations clearly show that for pulses with a carrier tuned at the resonance of the stratified media, one generally has subluminal propagation. Alternatively, in stop gaps or away from the resonances one ends up with superluminal transit. In the case of the EIT cavity it is shown that the large dispersion offered by the intracavity medium can lead to substantial superluminality (ng≃−106) with peak transmission as high as 20%. This is in sharp contrast to large signal attenuation for usual superluminal transit. Note also that EIT, to the best of the authors knowledge, has so far been used to achieve only slow light.
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.