Superextreme Waves Generation in the Linear Regime

Abstract: Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been considered a necessary ingredient to generate superextreme waves, i.e., an enhanced wave amplification, where the wave amplitudes exceed by far those of standard rogue waves. Here we show, experimentally and theoretically, that superextreme optical waves emerge in the simple case of linear one-dimensional light diffraction. The underlying physics is a long-range correlation on the random initial phases of the light waves. When subgroups of random phases appear recurrently along the spatial phase distribution, a more ordered phase structure greatly increases the probability of constructive interference to generate superextreme events, i.e., non-Gaussian statistics with super-long tails. Our results consist of a significant advance in the understanding of extreme waves formation by linear superposition of random waves, with applications in a large variety of wave systems.