Experimental observation of optical rogue waves. Single-shot time traces for three different pump power levels (increasing from top to bottom) and corresponding histograms. Each time trace contains ~15,000 events. Rogue events reach intensities of at least 30–40 times the average value.[1]
Optical rogue waves are rare pulses of light analogous to rogue or freak ocean waves.[1] The term optical rogue waves was coined to describe rare pulses of broadband light arising during the process of supercontinuum generation—a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input waveform—in nonlinear optical fiber. In this context, optical rogue waves are characterized by an anomalous surplus in energy at particular wavelengths (e.g., those shifted to the red of the input waveform) or an unexpected peak power. These anomalous events have been shown to follow heavy-tailed statistics, also known as L-shaped statistics, fat-tailed statistics, or extreme-value statistics.[1][2] These probability distributions are characterized by long tails: large outliers occur rarely, yet much more frequently than expected from Gaussian statistics and intuition. Such distributions also describe the probabilities of freak ocean waves[3][4][5] and various phenomena in both the man-made and natural worlds.[6][7][8][9][10][11] Despite their infrequency, rare events wield significant influence in many systems. Aside from the statistical similarities, light waves traveling in optical fibers are known to obey the similar mathematics as water waves traveling in the open ocean (the nonlinear Schrödinger equation), supporting the analogy between oceanic rogue waves and their optical counterparts.[1] More generally, research has exposed a number of different analogies between extreme events in optics and hydrodynamic systems. A key practical difference is that most optical experiments can be done with a table-top apparatus, offer a high degree of experimental control, and allow data to be acquired extremely rapidly.[1] Consequently, optical rogue waves are attractive for experimental and theoretical research and have become a highly studied phenomenon.[12][13] The particulars of the analogy between extreme waves in optics and hydrodynamics may vary depending on the context, but the existence of rare events and extreme statistics in wave-related phenomena are common ground.
^Dudley, John M.; Genty, Goëry; Eggleton, Benjamin J. (2008). "Harnessing and control of optical rogue waves in supercontinuum generation". Optics Express. 16 (6): 3644–51. arXiv:0801.2760. Bibcode:2008OExpr..16.3644D. doi:10.1364/OE.16.003644. ISSN 1094-4087. PMID 18542457. S2CID 19792730.
^Dean, R. G. (1990). "Freak Waves: A Possible Explanation". Water Wave Kinematics. pp. 609–612. doi:10.1007/978-94-009-0531-3_39. ISBN 978-94-010-6725-6.
^Kharif, Christian; Pelinovsky, Efim (2003). "Physical mechanisms of the rogue wave phenomenon". European Journal of Mechanics B. 22 (6): 603–634. Bibcode:2003EJMF...22..603K. CiteSeerX 10.1.1.538.58. doi:10.1016/j.euromechflu.2003.09.002. ISSN 0997-7546. S2CID 45789714.
^Gabaix, Xavier; Gopikrishnan, Parameswaran; Plerou, Vasiliki; Stanley, H. Eugene (2003). "A theory of power-law distributions in financial market fluctuations". Nature. 423 (6937): 267–270. Bibcode:2003Natur.423..267G. doi:10.1038/nature01624. ISSN 0028-0836. PMID 12748636. S2CID 1263236.
^Anderson, Chris. The Long Tail: Why the Future of Business Is Selling Less of More. Hyperion Books. ISBN 978-1401309664.
^Clauset, Aaron; Shalizi, Cosma Rohilla; Newman, M. E. J. (2009). "Power-Law Distributions in Empirical Data". SIAM Review. 51 (4): 661–703. arXiv:0706.1062. Bibcode:2009SIAMR..51..661C. doi:10.1137/070710111. ISSN 0036-1445. S2CID 9155618.
^Pisarenko, V; Rodkin, M. Heavy-Tailed Distributions in Disaster Analysis. Springer. ISBN 978-9048191703.
^Buzz Skyline (December 11, 2008). "Earthquakes and the Financial Crisis". physicsbuzz.physicscentral.com. Physics Central. Retrieved March 29, 2014.
^Taleb, Nassim Nicholas. The Black Swan: Second Edition. Random House Publishing. ISBN 978-0812973815.
^Dudley, John M.; Taylor, J. Roy (2009). "Ten years of nonlinear optics in photonic crystal fibre". Nature Photonics. 3 (2): 85–90. Bibcode:2009NaPho...3...85D. doi:10.1038/nphoton.2008.285. ISSN 1749-4885.
^Akhmediev, N; Dudley, J M; Solli, D R; Turitsyn, S K (2013). "Recent progress in investigating optical rogue waves". Journal of Optics. 15 (6): 060201. Bibcode:2013JOpt...15f0201A. doi:10.1088/2040-8978/15/6/060201. ISSN 2040-8978. S2CID 6824679.
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