Rogue waves as high as a 10-story building have been offered as an explanation for the disappearance of ships as big as an ocean liner, despite the lack of survivors to tell the tale. Recently, remote sensors set up in the oceans of the world have confirmed that single rogue waves as tall as 100 feet occur more frequently than Gaussian statistics can explain. For the first time EEs have generated rogue waves in optical fibers and have confirmed the mechanism that generates them, which they say can occur in other media too, including the ocean.
"Rogue waves are an apparently random phenomenon that is seeded by noise," said lead investigator on the project Daniel Solli, a researcher at the University of California at Los Angeles (UCLA) Henry Samueli School of Engineering and Applied Science. "We have shown that noise with the correct properties can foster the generation of one of these rogue waves."
According to Solli and Bahram Jalali, a UCLA professor of electrical engineering and the research group leader, rogue waves are analogous to the butterfly effect, a phenomenon in which, under the right initial conditions, a butterfly flapping its wings can cause a hurricane. Of course, these initial conditions are exceedingly rare, but the bottom line for the butterfly effect, according to Solli and Jalali, is that weather is very sensitive to initial conditions, as is the generation of rogue waves.
"Like the weather, these rogue waves appear to be extremely sensitive to initial conditions," said Solli. "It is still a deterministic system, but one that is very difficult to predict, because a very, very minute change in initial conditions can have a dramatic impact on the result."
Researchers studying a microstructured optical fiber near the threshold of soliton-based supercontinuum generation observed the generation of rogue waves in the optical fiber, and they began modeling the mechanism. As a result, the researchers have now characterized the proper initial conditions for generating rogue waves in any medium.
"We show that a particular set of initial conditions are responsible for generating rogue waves," said Solli. "In our experiment we discovered that we were getting some rare events that were far larger than any of the neighboring pulses, and that led us to explore this connection between this phenomenon and the oceanic phenomenon which has a very similar kind of effect."
According to the researchers, rogue waves follow "L-shaped" statistics, as opposed to the more common Gaussian statistics. This accounts for the seemingly out-of-bounds size of rogue waves: in L-shaped distributions the heights of most waves are tightly clustered together, but large outliers also occur. Now Jalali's team is working on a more detailed model for the U.S. Department of Defense, which is aiming to harness the effect for military applications.
"The next step is learning how to engineer this phenomenon, because there must be some useful applications out there, if only we could predictably engineer the outcome of this event, which occurs very rarely now," said Jalali.
Other member of Jalali's team include UCLA engineering researchers Claus Ropers and Prakash Koonath. Funding is being provided by the U.S. Department of Defense and the Defense Advanced Research Projects Agency (DARPA).