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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.


Experimental results showing (a) partially-developed speckle and (b) a caustic network. For each case, (i) shows the computed intensity distribution; (ii) shows a zoom over a more limited region looking down on the pattern; (iii) shows a slice of the applied phase distribution to the SLM at y = 0; (iv) shows the calculated spatial spectrum corresponding to the intensity distribution in (i). Intensities in (b) are normalised relative to the maximum intensity for the partially-developed speckle in Fig. 3a. Note the different intensity scales used between (a,b).
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f3: Experimental results showing (a) partially-developed speckle and (b) a caustic network. For each case, (i) shows the computed intensity distribution; (ii) shows a zoom over a more limited region looking down on the pattern; (iii) shows a slice of the applied phase distribution to the SLM at y = 0; (iv) shows the calculated spatial spectrum corresponding to the intensity distribution in (i). Intensities in (b) are normalised relative to the maximum intensity for the partially-developed speckle in Fig. 3a. Note the different intensity scales used between (a,b).

Mentions: Our experiments were performed using identical random phase masks to those used in simulations, and intensity patterns were recorded for a range of propagation distances, allowing us to reconstruct the evolution of the field in the measurement volume shown in Fig. 1. For comparison with the simulation results shown in Fig. 2 we extracted transverse beam profiles at identical propagation distances as used in simulations (to within experimental error of ±1 μm). These measured intensity patterns are shown in Fig. 3, with these results to be compared directly with those shown in Fig. 2 (note that for completeness we reproduce the applied phase subfigures). The experimental patterns are both normalised in the same way as in simulations, relative to the maximum intensity observed in the partially-developed speckle pattern. Note that the experimental results showing the measured pattern in the full measurement volume are displayed in animations (rotating the observation viewpoint) in Supplementary Videos S1 and S2, corresponding to the partially-developed speckle in Fig. 3(a) and the caustic regime in Fig. 3(b) respectively.


Caustics and Rogue Waves in an Optical Sea.

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

Experimental results showing (a) partially-developed speckle and (b) a caustic network. For each case, (i) shows the computed intensity distribution; (ii) shows a zoom over a more limited region looking down on the pattern; (iii) shows a slice of the applied phase distribution to the SLM at y = 0; (iv) shows the calculated spatial spectrum corresponding to the intensity distribution in (i). Intensities in (b) are normalised relative to the maximum intensity for the partially-developed speckle in Fig. 3a. Note the different intensity scales used between (a,b).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Experimental results showing (a) partially-developed speckle and (b) a caustic network. For each case, (i) shows the computed intensity distribution; (ii) shows a zoom over a more limited region looking down on the pattern; (iii) shows a slice of the applied phase distribution to the SLM at y = 0; (iv) shows the calculated spatial spectrum corresponding to the intensity distribution in (i). Intensities in (b) are normalised relative to the maximum intensity for the partially-developed speckle in Fig. 3a. Note the different intensity scales used between (a,b).
Mentions: Our experiments were performed using identical random phase masks to those used in simulations, and intensity patterns were recorded for a range of propagation distances, allowing us to reconstruct the evolution of the field in the measurement volume shown in Fig. 1. For comparison with the simulation results shown in Fig. 2 we extracted transverse beam profiles at identical propagation distances as used in simulations (to within experimental error of ±1 μm). These measured intensity patterns are shown in Fig. 3, with these results to be compared directly with those shown in Fig. 2 (note that for completeness we reproduce the applied phase subfigures). The experimental patterns are both normalised in the same way as in simulations, relative to the maximum intensity observed in the partially-developed speckle pattern. Note that the experimental results showing the measured pattern in the full measurement volume are displayed in animations (rotating the observation viewpoint) in Supplementary Videos S1 and S2, corresponding to the partially-developed speckle in Fig. 3(a) and the caustic regime in Fig. 3(b) respectively.

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.