Every so often mariners report the sighting of a huge wave towering up to 30 m above the regular swells of the ocean surface. No one is sure why these rogue waves form, but now physicists in the US and Germany have managed to produce equivalent optical rogue waves by launching laser pulses into photonic-crystal fibres. Having performed computer simulations of the optical system, the researchers suggest that optical rogue waves, and therefore oceanic rogue waves, are seeded by noise.

A photonic-crystal fibre is a transparent strand containing hundreds of regularly-spaced air holes running throughout its length. The alternating refractive index produced by this structure has a non-linear effect on light waves, shifting their frequency depending on the wave intensity.

When a wave pulse — which comprises many waves with a bell-shaped distribution of frequencies — enters a photonic crystal fibre, its frequency spectrum is broadened. Rogue waves are examples of wave pulses, but their short, sharp nature requires too broad a frequency spectrum to be produced by this process alone.

Now, Daniel Solli and colleagues at the University of California at Los Angeles, together with Claus Ropers from the Max Born Institute for Non-linear Optics and Short Pulse Spectroscopy in Berlin, have discovered that noise on either side of a wave pulse’s frequency spectrum can occasionally strike just the right wavelength and intensity to make the broadening process in a photonic-crystal fibre much faster, leading to the production of a optical rogue wave (Nature 450 1054). “Understanding optical rogue waves can help us to understand the oceanic phenomenon,” Ropers told physicsworld.com. “It could, in the future, enable us to predict when and where oceanic waves form.”

The mathematics that describes optical wave production is extremely similar to that which describes water waves in the deep sea

Unusual distribution

The first hint of the underlying cause of optical rogue waves came when Solli, Ropers and colleagues used a laser to send trains of pulses into a photonic fibre without attempting to reduce noise. They found that more high-amplitude rogue waves were produced than would be expected from a usual Gaussian distribution.

To make sense of the findings, the researchers modelled the pulses’ propagation numerically using the non-linear Schrödinger equation. It appeared that, with the photonic-crystal fibre shifting all the frequencies differently, sometimes the noise by chance sums with the main pulse to make it very broad. As soon as this happens, part of the pulse detaches into a soliton — a special type of wave pulse that resists having its shape modified while it propagates because of a balancing act between dispersion and the fibre’s properties. Taking much of the main pulse’s energy and having a very broad frequency spectrum, this soliton stands out from the pulse train as a rogue wave.

Similar mathematics

How is this analogous to the ocean? Just like a photonic-crystal fibre, the ocean is a non-linear medium. It also has a lot of noise, produced, among other things, by the bombardment of wind. “The mathematics that describes optical wave production is extremely similar to that which describes water waves in the deep sea,” said Solli.

Still, to check if rogue waves really are produced by the same mechanism, scientists will have to find ways of accurately measuring the parameters of the non-linear Schrödinger equation — the degree of non-linearity and dispersion — for the open ocean.