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Nonlinear Optics

Superluminal light pulses, subluminal information transmission

Daniel J. Gauthier, Michael D. Stenner, Mark Allen Neifeld

Published Jan 1, 2004• 0 citations
Publisher

Abstract

We describe optical pulse propagation through a medium where the group velocity exceeds the speed of light in vacuum. The information velocity is observed to be subluminal, consistent with the special theory of relativity.
DOI
10.1364/nlo.2004.fa4

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It is widely believed that the velocity of information ${\ensuremath{\upsilon}}_{i}$ encoded on an optical pulse is equal to the group velocity ${\ensuremath{\upsilon}}_{g}$, at least when ${\ensuremath{\upsilon}}_{g}$ is less than the speed of light in vacuum ccc. On the other hand, several authors suggest that ${\ensuremath{\upsilon}}_{i}=c$, although the size of the signal traveling at this velocity may be small, thereby making it difficult to measure. Here, we measure ${\ensuremath{\upsilon}}_{i}$ for pulses propagating through a resonant ``slow-light'' medium where ${\ensuremath{\upsilon}}_{g}\ensuremath{\approx}0.006c$. We find ${\ensuremath{\upsilon}}_{i}=1.03{c}_{\ensuremath{-}0.25c}^{+0.49c}$, or that ${\ensuremath{\upsilon}}_{i}\ensuremath{\approx}168{\ensuremath{\upsilon}}_{g}$, clearly demonstrating that the speed of information cannot be generally described by ${\ensuremath{\upsilon}}_{g}$, but is characterized by its own velocity.
Manipulating the group velocity of light has resulted in many advances, including slowing light to a car’s pace, stopping light and even forcing pulses to propagate faster than the speed of light in a vacuum. While the group velocity is equal to or less than the speed of light in a vacuum (c) when propagating through a medium exhibiting normal dispersion, anomalous dispersion allows the group velocity to be greater than c, or even negative. Strangely, the peak of a pulse propagating with a negative group velocity through a medium appears to exit the medium before entering it. This is a result of interference from spectral components of a pulse propagating with different phase velocities in the medium.
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.
The propagation of pulses through dispersive media was investigated by solving Maxwell's equations without any approximation. We show that the superluminal propagation of pulses through anomalous dispersive media is a result of the interference of different frequency components composed of the pulse. The coherence of the pulse plays an important role for the superluminal propagation. With the decrease of the coherence of the pulse, the propagation changes from superluminal to subluminal. We have shown that the anomalous dispersion (the real part of the susceptibility) not the amplification (the imaginary part of the susceptibility) plays the essential role in the superluminal propagation. Although the superluminality always exists as long as the spectrum of the coherent pulse is within the anomalously dispersive region, both the energy propagation velocity and the frontal velocity never exceed the light speed in the vacuum. The output pulse through the medium is not the original pulse; instead it carries the information of the original pulse and the information of the prepared medium.
Summary form only given. It is well known that the group velocity v/sub g/ of a light pulse can exceed c in an anomalously dispersive medium. As discussed many years ago by Sommerfeld and Brillouin, a group velocity greater than c does not violate causality because it is not the velocity of information transmission. They noted that the "frontal velocity," the velocity at which an infinitely sharp step-function-like disturbance of the light intensity propagates, can serve as a velocity of information transfer. We suggest here an operational definition of the signal velocity and apply it to the recently observed superluminal propagation of a light pulse in a gain medium.