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Caustics and Rogue Waves in an Optical Sea.

Mathis A, Froehly L, Toenger S, Dias F, Genty G, Dudley JM - Sci Rep (2015)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Institut FEMTO-ST, UMR 6174 CNRS-Université de Franche-Comté, Besançon, France.

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.

No MeSH data available.


Related in: MedlinePlus

Setup for studying statistics of partially-developed speckle and caustics.An SLM encodes random spatial phase on a coherent beam from a He-Ne laser. Free space propagation transforms this random phase to random intensity fluctuations. An imaging system is used to reduce the size of the beam so it can be recorded on a CCD camera which can be translated longitudinally over an extended measurement volume. All measurement distances given in the text are relative to the origin z = 0 of the axes shown. Here f1 = 500 mm, f2 = 250 mm, f3 = 100 mm, f4 = 9 mm.
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f1: Setup for studying statistics of partially-developed speckle and caustics.An SLM encodes random spatial phase on a coherent beam from a He-Ne laser. Free space propagation transforms this random phase to random intensity fluctuations. An imaging system is used to reduce the size of the beam so it can be recorded on a CCD camera which can be translated longitudinally over an extended measurement volume. All measurement distances given in the text are relative to the origin z = 0 of the axes shown. Here f1 = 500 mm, f2 = 250 mm, f3 = 100 mm, f4 = 9 mm.

Mentions: Our experimental setup is shown schematically in Fig. 1. A coherent beam from a continuous wave laser is expanded to fill the aperture of a spatial light modulator (SLM). The SLM then encodes a random two dimensional spatial phase pattern on the beam over a square 600 × 600 pixels array. The phase variations are smoothed over typically 10 pixels so that one can consider the SLM as physically equivalent to a random continuous refracting surface. The subsequent propagation of the beam results in the development of random intensity maxima and minima in the spatial beam profile, following the well-known physics of the development of optical speckle313233. An imaging system is used to reduce the size of the beam after the SLM to the measurement region indicated in Fig. 1 and to fill the aperture of the detector. The longitudinal extent over which we could perform measurements was 500 μm. Further details are given in the figure caption and Methods section. In our experiments, the measurements are not made in order to follow the field evolution to a fully-developed (granular) speckle, but we focus rather on the regime where smoothly-varying random intensity fluctuations are observed.


Caustics and Rogue Waves in an Optical Sea.

Mathis A, Froehly L, Toenger S, Dias F, Genty G, Dudley JM - Sci Rep (2015)

Setup for studying statistics of partially-developed speckle and caustics.An SLM encodes random spatial phase on a coherent beam from a He-Ne laser. Free space propagation transforms this random phase to random intensity fluctuations. An imaging system is used to reduce the size of the beam so it can be recorded on a CCD camera which can be translated longitudinally over an extended measurement volume. All measurement distances given in the text are relative to the origin z = 0 of the axes shown. Here f1 = 500 mm, f2 = 250 mm, f3 = 100 mm, f4 = 9 mm.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4526884&req=5

f1: Setup for studying statistics of partially-developed speckle and caustics.An SLM encodes random spatial phase on a coherent beam from a He-Ne laser. Free space propagation transforms this random phase to random intensity fluctuations. An imaging system is used to reduce the size of the beam so it can be recorded on a CCD camera which can be translated longitudinally over an extended measurement volume. All measurement distances given in the text are relative to the origin z = 0 of the axes shown. Here f1 = 500 mm, f2 = 250 mm, f3 = 100 mm, f4 = 9 mm.
Mentions: Our experimental setup is shown schematically in Fig. 1. A coherent beam from a continuous wave laser is expanded to fill the aperture of a spatial light modulator (SLM). The SLM then encodes a random two dimensional spatial phase pattern on the beam over a square 600 × 600 pixels array. The phase variations are smoothed over typically 10 pixels so that one can consider the SLM as physically equivalent to a random continuous refracting surface. The subsequent propagation of the beam results in the development of random intensity maxima and minima in the spatial beam profile, following the well-known physics of the development of optical speckle313233. An imaging system is used to reduce the size of the beam after the SLM to the measurement region indicated in Fig. 1 and to fill the aperture of the detector. The longitudinal extent over which we could perform measurements was 500 μm. Further details are given in the figure caption and Methods section. In our experiments, the measurements are not made in order to follow the field evolution to a fully-developed (granular) speckle, but we focus rather on the regime where smoothly-varying random intensity fluctuations are observed.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Institut FEMTO-ST, UMR 6174 CNRS-Université de Franche-Comté, Besançon, France.

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.

No MeSH data available.


Related in: MedlinePlus