  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.
