Caustics and Rogue Waves in an Optical Sea.

Amaury Mathis,John M Dudley,Luc Froehly,Goëry Genty,Frédéric Dias,Shanti Toenger

doi:10.1038/srep12822

Abstract

There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an “optical sea” with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.

Highlights

Formation of caustics in optics and the formation of rogue wave events in optical systems have not been the subject of detailed study
The use of a spatial light modulator to impose random phase on a coherent field has provided a flexible means of studying the rogue wave statistics of optical speckle, and to examine the particular conditions leading to extended tails in the associated probability distribution for the optical intensity
For the optical system under study, we identify the development of caustic structures in the random intensity pattern as the physical mechanism generating large amplitude events that satisfy commonly-applied criteria for rogue waves

Summary

Introduction

Formation of caustics in optics and the formation of rogue wave events in optical systems have not been the subject of detailed study. We report here a detailed study of rogue wave statistics in an optical system due to the caustic focussing of a random coherent spatial field. The simulations discretized the incident field profile to match the experimental SLM pixellation, upon which a smoothed random phase function was applied (see Methods). A coherent field with random phase will initially evolve into a regime of caustic focussing before developing progressively into a granular speckle pattern with propagation distance[33]. In our simulations and experiments, we choose applied phase distributions in order to highlight: (i) the differences (in form and statistics) between partially-developed speckle and caustic structures; and (ii) the correlation of high intensity caustics and rogue wave peaks with a broader intensity spectrum. Note that for the differing initial phase distributions, the distances where particular characteristics are observed were determined from our numerical modelling which was used to guide our experiments

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Conclusion