Sailing the photon sea: rogue waves in a fiber

Ye auld mariners have long talked about rogue waves. However, the amount of rum partaken during the retelling of such stories tended to reduce their accuracy and believability, leading most people to conclude that such waves were a myth. This conclusion was largely supported by a simple analysis that told us that a simple linear combination of waves would be unlikely to reach the proportions as often as reported. Then a North Sea oil rig got hit by a rogue wave and the instruments on board hadn't been drinking and didn't tell their stories in a cute-but-strange accent. Closer examination of satellite imagery of the open sea showed that waves didn't follow the distribution expected by linear analysis and that rogue waves could be much more frequent than predicted.

The analysis had failed because it was a linear analysis, which is usually pretty good, but misses some important features, such as solitons. Solitons are solitary waves with the unusual property that they do not spread out. If you drop a stone in water, then a wave travels out from the stone. The wave has very sharp, high peaks that, as the wave travels, reduce in height and get wider. This is because that single peak is made up from a group of waves all of which have a different distance between their individual peaks.

These waves travel at slightly different speeds, which causes the single peak to disperse over time. If the stone were capable of producing a soliton, it would have a single high sharp peak that did not reduce in height and got no wider as it traveled away from the stone. This is because that single peak is large enough to modify the local properties of the water such that all the waves travel at the same speed and the soliton stays together. However, solitons are pretty special beasts and it is unclear that the open sea could provide the conditions required for a soliton to form for even a short period of time.

Luckily, light is also a wave and can also exhibit nonlinear behavior when it is sufficiently intense. This analogous behavior has led researchers to investigate the statistics of light pulses in a highly nonlinear optical fiber. The fiber is not an ordinary glass fiber, but has a honey comb shape that compresses the light into a very small area. This makes the light much more intense and generates highly nonlinear behavior. When strongly illuminated, these fibers turn laser light with a single color into white light, called a supercontinuum. In fact, the light often extends beyond the visible into the ultraviolet and the infrared as well. However, if the brightness of the laser is reduced, the supercontinuum vanishes and the output from the optical fiber is a series of spikes with a random brightness.

It turns out that the statistical properties of these pulses have the same distribution as those observed for ocean waves. Importantly, the researchers observe rogue optical waves with a reasonable statistical probability. These waves are not exactly solitons because they don't stay together, however, like solitons, the width of the wave doesn't increase as they travel. This indicates that there are some unknown mechanisms that cause these "soliton-like" waves to fall apart. I don't think knowledge of these mechanisms will result in ways of destroying rogue ocean waves, but they might allow us to figure out where rogue waves are more likely to form and warn sea-going vessels in the vicinity. More likely it will just turn out to be a cool, but not useful observation of the behavior of light in a fiber.