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arXiv:physics/0503055 · Physical Review E

Optimal superluminal systems

B. Macke, Bernard Ségard, F. Wielonsky

Published Sep 6, 2005• 29 citations
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Abstract

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.

DOI
10.1103/physreve.72.035601

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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.
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.
The mechanisms leading to a seemingly superluminal propagation of light in dispersive media are examined. The anomalous dispersion near an absorption line, involved in the first experiments displaying negative group velocity propagation, is shown to be not only simpler but also more efficient than the so-called transparent dispersion used in the later experiments of Wang et al. (Nature (London) 406, 277 (2000)) and of Dogariu et al. (Phys.Rev.A 63, 053806 (2001)). The modest pulse advances observed by these authors can in particular be reproduced with a better overall transmittance of the medium and the significant advances attained with a single-line arrangement would probably be unattainable with their gain-doublet arrangement.
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.
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.
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.
In a dispersive medium, different monochromatic modes of light have different phase velocities. Under special circumstances, a superposition of these modes results in an interesting effect wherein the group velocity (the velocity at which the peak of the wavepacket propagates) could be greater than c or even negative although the phase velocities of the modes are all less than c . Can this superluminal group velocity be used for information transfer? We show here that the `superluminal' effect is due to a coherent optical wave superposition effect. Whatever the velocity of the `peak', the whole pulse cannot travel with a speed greater than the fastest phase velocity of its component modes. Thus the maximum speed for information transfer, which involves the sending of a finite pulse, cannot be greater than the maximum phase velocity in the medium.