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Physical Review A

Theory and simulations of superluminal optical pulses in gain media

Eric L. Bolda

Published Oct 1, 1996• 9 citations
Publisher

Abstract

I derive a simple model for the propagation of a smooth pulse detuned outside a gain line. The pulse moves superluminally and with little distortion provided the medium is not longer than the saturation length. If the medium is longer than this, two effects occur: amplified spontaneous emission interferes with the pulse (although this interference averages to zero over many experiments) and the magnitude of the group delay increases only logarithmically with the length. I argue that both of these effects are inherent to any optical system with gain. Numerical simulations of the superluminal pulse agree with the model presented. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.3514

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I derive a simple model for the propagation of a smooth pulse detuned outside a gain line. The pulse moves superluminally and with little distortion provided the medium is not longer than the saturation length. If the medium is longer than this, two effects occur: amplified spontaneous emission interferes with the pulse (although this interference averages to zero over many experiments) and the magnitude of the group delay increases only logarithmically with the length. I argue that both of these effects are inherent to any optical system with gain. Numerical simulations of the superluminal pulse agree with the model presented. \textcopyright{} 1996 The American Physical Society.
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.
We demonstrate that significant effects in the "superluminal propagation" of light pulses cannot be observed without involving systems whose gain explodes outside the pulse spectrum. We explicitly determine the minimum norm of the gain to attain given superluminal effects and the transfer function of the corresponding optimal system. The gain norms, which would be required with the most efficient systems considered up to now (dispersive media, photonic barriers) to attain the same effects, are shown to exceed the minimum by several orders of magnitude. We finally estimate the largest superluminal advances which could be attained in a realistic experiment.
Spectral reshaping and nonuniform phase delay associated with an electromagnetic pulse propagating in a temporally dispersive medium may lead to interesting observations in which the group velocity becomes superluminal or even negative. In such cases, the finite bandwidth of the superluminal region implies the inevitable existence of a cutoff distance beyond which a superluminal pulse becomes subluminal. In this paper, we derive a closed-form analytic expression to estimate this cutoff distance in abnormal dispersive media with gain. Moreover, the method of steepest descent is used to track the time-frequency dynamics associated with the evolution of the center of mass of a superluminal pulse to the subluminal regime. This evolution takes place at longer propagation depths as a result of the subluminal components affecting the behavior of the pulse. Finally, the analysis presents the fundamental limitations of superluminal propagation in light of factors such as the medium depth, pulse width, and the medium dispersion strength.
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.