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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

Results obtained in a regime where phase retrieval allows experimental measurement of the spatial amplitude pattern.Fig. 5a shows the applied SLM phase, the measured intensity pattern and the corresponding spectrum at a propagation distance of 220 μm. Fig. 5b shows the retrieved amplitude pattern and computed statistics of (ii) elevation and (iii) wave height. The solid lines in these figures (ii) and (iii) plot Gaussian and Rayleigh distribution fits respectively. The bright peak A labelled in the figure is the highest peak observed in the distribution with amplitude ~2.23. The label HRW indicates the rogue wave height criterion.
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f5: Results obtained in a regime where phase retrieval allows experimental measurement of the spatial amplitude pattern.Fig. 5a shows the applied SLM phase, the measured intensity pattern and the corresponding spectrum at a propagation distance of 220 μm. Fig. 5b shows the retrieved amplitude pattern and computed statistics of (ii) elevation and (iii) wave height. The solid lines in these figures (ii) and (iii) plot Gaussian and Rayleigh distribution fits respectively. The bright peak A labelled in the figure is the highest peak observed in the distribution with amplitude ~2.23. The label HRW indicates the rogue wave height criterion.

Mentions: Figure 5a presents our experimental results in a way similar to Fig. 3 showing intensity patterns in Fig. 5a(i) and (ii), the applied phase in Fig. 5a(iii) and the spectrum in Fig. 5a(iv). The applied phase is clearly intermediate between that shown in Fig. 3a(iii) and Fig. 3b(iii), and we can indeed see how the intensity pattern shows characteristics of both the partial speckle and the caustic patterns described above. In particular, we see more strongly localised peaks than in the partially-developed speckle shown in Fig. 3a, but without the network structure of the caustic regime in Fig. 3b. Quantitatively, we can see how the peak intensity value of ~5 is also intermediate between that observed for the partially-developed speckle and the caustic network. The experimental results showing the measured pattern in the full measurement volume are displayed in an animation (rotating the observation viewpoint) in Supplementary Video S3.


Caustics and Rogue Waves in an Optical Sea.

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

Results obtained in a regime where phase retrieval allows experimental measurement of the spatial amplitude pattern.Fig. 5a shows the applied SLM phase, the measured intensity pattern and the corresponding spectrum at a propagation distance of 220 μm. Fig. 5b shows the retrieved amplitude pattern and computed statistics of (ii) elevation and (iii) wave height. The solid lines in these figures (ii) and (iii) plot Gaussian and Rayleigh distribution fits respectively. The bright peak A labelled in the figure is the highest peak observed in the distribution with amplitude ~2.23. The label HRW indicates the rogue wave height criterion.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: Results obtained in a regime where phase retrieval allows experimental measurement of the spatial amplitude pattern.Fig. 5a shows the applied SLM phase, the measured intensity pattern and the corresponding spectrum at a propagation distance of 220 μm. Fig. 5b shows the retrieved amplitude pattern and computed statistics of (ii) elevation and (iii) wave height. The solid lines in these figures (ii) and (iii) plot Gaussian and Rayleigh distribution fits respectively. The bright peak A labelled in the figure is the highest peak observed in the distribution with amplitude ~2.23. The label HRW indicates the rogue wave height criterion.
Mentions: Figure 5a presents our experimental results in a way similar to Fig. 3 showing intensity patterns in Fig. 5a(i) and (ii), the applied phase in Fig. 5a(iii) and the spectrum in Fig. 5a(iv). The applied phase is clearly intermediate between that shown in Fig. 3a(iii) and Fig. 3b(iii), and we can indeed see how the intensity pattern shows characteristics of both the partial speckle and the caustic patterns described above. In particular, we see more strongly localised peaks than in the partially-developed speckle shown in Fig. 3a, but without the network structure of the caustic regime in Fig. 3b. Quantitatively, we can see how the peak intensity value of ~5 is also intermediate between that observed for the partially-developed speckle and the caustic network. The experimental results showing the measured pattern in the full measurement volume are displayed in an animation (rotating the observation viewpoint) in Supplementary Video S3.

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