The Fast-Light Debate

The concern about fast light began in the early part of the 20th century after Einstein developed his theory of special relativity. According to relativity, if information can travel faster than c, the speed of light in vacuum, then for some observers, it will arrive at its destination before it leaves its source. This would be a violation of causality because an effect could occur before its own cause! It was therefore accepted that (if relativity is correct, as it appears to be) information cannot travel faster than c.

The problem was that until that time, it was believed that information encoded on optical pulses moved at the group velocity (described in the Fast Light Tutorial), which was known to exceed c, at least theoretically.

Sommerfeld and Brillouin

 Arnold Johannes Wilhelm Sommerfeld. You can view a biography of Sommerfeld hosted by the University of St. Andrews.

In response to this concern, Sommerfeld and Brillouin performed a very thorough analysis of pulse propagation. By performing a theoretical analysis of the propagation of square pulses, they arrived at a number of interesting conclusions. They found that the front of an optical pulse always travels at c. The front is simply the very leading edge of the pulse.

 Léon Brillouin. You can view a biography of Brillouin provided by Wolfram.

They also found that when the group velocity exceeded c, their pulses no longer traveled at the group velocity! They found their pulses to be strongly distorted, with the bulk of the pulse moving slower than c. They defined yet another velocity, which they called the signal velocity, as the velocity of the main part of the pulse1.

For decades, the work of Brillouin and Sommerfeld was accepted as a demonstration that information does not propagate faster than c in a medium with a fast group velocity. In fact, it was well accepted that the group velocity was meaningless when faster than c. In that case, it was believed that the signal velocity vs was the proper descriptor of pulse propagation and that vs was always less than c [2].

Then, in 1970, Garrett and McCumber demonstrated theoretically that smooth pulses (recall that Sommerfeld and Brillouin used square pulses) could propagate largely undistorted at group velocities faster than c. Very soon after, Faxvog, Chow, Bieber and Carruthers studied pulses propagating back and forth in a mode-locked laser containing a fast-light medium (a neon absorption cell) and found that the pulse repetition frequency was modified by the presence of the cell. By analyzing this data, they inferred that the pulses were traveling thorugh the neon gas cell with a group velocity exceeding the speed of light in vacuum, but they could not directly measure the pulse waveform to determine if it was distorted. In 1982, Chu and Wong measured the speed of pulses propagating through a fast-light medium using an auto-correlation technique. This measurement allowed them to directly verify group velocities greater than c, but they could not assess the extent of any pulse distortion. In 1985, Ségard and Macke measured terahertz pulses propagating through a fast-light medium, where direct detection allowed them to measure the pulse envelope. They also verified pulse group velociies faster than c, observed small pulse distortion, and demonstrated that small noise flucutations on the input pulse envelope were accentuated by the fast-light medium. These experiments paved the way for further debate.

Recent work

Since then, there have been many different and often conflicting experimental and theoretical results. While most (but not all) of these results argue that relativistic causality is not threatened, the explanations vary wildly.

For example, Nimtz and Haibel claim that all information-bearing waveforms have non-zero temporal extent and, while these waveforms can be superluminally advanced, causality is preserved because the advancement must be less than the extent of the entire waveform. However, this claim seems to rest on the assumption that no information is available until the entire waveform has been received.

In contrast, Chiao and coworkers suggest that information is encoded in points of non-analyticity, which cannot be superluminally advanced. In fact, they claim that these non-analytic points move at precisely c in any medium because they necessarily have infinite bandwidth, and that the refractive index n(ω) → ∞ as ω → ∞ for any medium. Nimtz and Haibel object to the suggestion of infinite bandwidth, and therefore to the concept of a true physical discontinuity. There is also the question of how a point on a waveform can be detected; it contains no energy itself so there is nothing to detect!

In another interesting paper, Kuzmich et al. demonstrate that points on a waveform with a constant signal to noise ratio move no faster than c, although they present no strong link between these points and information.

Footnotes and References

1. They defined the signal velocity to be the velocity of the first point where the pulse reached half its peak height.
2. It has since been shown that vs as defined by Sommerfeld and Brillouin can indeed be faster than c.