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An Adaptive Filter for Studying the Life Cycle of Optical Rogue Waves

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An Adaptive Filter for Studying the Life Cycle of Optical Rogue Waves An adaptive filter for studying the life cycle of optical rogue waves Chu Liu1, 2, 4, Eric J. Rees2, 4, Toni Laurila2, Shuisheng Jian1, and Clemens F. Kaminski 2, 3,* 1Institute of Lightwave Technology, Key Lab of All Optical Network and Advanced Telecommunication Network of EMC, Beijing Jiaotong University, Beijing 100044, China 2Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, CB2 3RA, UK 3SAOT School of Advanced Optical Technologies, Friedrich Alexander University, D-91058 Erlangen, Germany 4These authors contributed equally to this work *[email protected] Abstract: We present an adaptive numerical filter for analyzing fiber-length dependent properties of optical rogue waves, which are highly intense and extremely red-shifted solitons that arise during supercontinuum generation in photonic crystal fiber. We use this filter to study a data set of 1000 simulated supercontinuum pulses, produced from 5 ps pump pulses containing random noise. Optical rogue waves arise in different supercontinuum pulses at various positions along the fiber, and exhibit a lifecycle: their intensity peaks over a finite range of fiber length before declining slowly. 2010 Optical Society of America OCIS codes: (060.5530) Fiber optics and optical communications: Pulse propagation and temporal solitons; (190.4370) Nonlinear optics: Nonlinear optics, fibers. References and links 1. J. M. Dudley, and J. R. Taylor, Supercontinuum Generation in Optical Fibers, (Cambridge University Press, Cambridge, 2010) 2. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). 3. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000). 4. P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003). 5. T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). 6. J. Hult, R. S. Watt, and C. F. Kaminski, “Dispersion measurement in optical fibers using supercontinuum pulses,” J. Lightwave Technol. 25(3), 820–824 (2007). 7. M. Schnippering, P. R. Unwin, J. Hult, T. Laurila, C. F. Kaminski, J. M. Langridge, R. L. Jones, M. Mazurenka, and S. R. Mackenzie, “Evanescent wave broadband cavity enhanced absorption spectroscopy using supercontinuum radiation: A new probe of electrochemical processes,” Electrochem. Commun. 10(12), 1827– 1830 (2008). 8. L. van der Sneppen, G. Hancock, C. F. Kaminski, T. Laurila, S. R. Mackenzie, S. R. T. Neil, R. Peverall, G. A. D. Ritchie, M. Schnippering, and P. R. Unwin, “Following interfacial kinetics in real time using broadband evanescent wave cavity-enhanced absorption spectroscopy: a comparison of light-emitting diodes and supercontinuum sources,” Analyst (Lond.) 135(1), 133–139 (2009). 9. C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank and J. Hult, “Supercontinuum radiation for application in chemical sensing and microscopy,” Appl. Phys. B 92(3), 367–378 (2008). 10. J. Hult, R. S. Watt, and C. F. Kaminski, “High bandwidth absorption spectroscopy with a dispersed supercontinuum source,” Opt. Express 15(18), 11385–11395 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-18-11385. 11. J. M. Langridge, T. Laurila, R. S. Watt, R. L. Jones, C. F. Kaminski, and J. Hult, “Cavity enhanced absorption spectroscopy of multiple trace gas species using a supercontinuum radiation source,” Opt. Express 16(14), 10178–10188 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=OE-16-14-10178. 12. R. S. Watt, T. K. Laurila, C. F. Kaminski, and J. F. Hult, “Cavity enhanced spectroscopy of high-temperature H(2)o in the near-infrared using a supercontinuum light source,” Appl. Spectrosc. 63(12), 1389–1395 (2009). 13. S. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006). #136335 - $15.00 USD Received 8 Oct 2010; revised 19 Nov 2010; accepted 19 Nov 2010; published 30 Nov 2010 (C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 26113 14. S. Schlachter, S. Schwedler, A. Esposito, G. S. Kaminski Schierle, G. D. Moggridge, and C. F. Kaminski, “A method to unmix multiple fluorophores in microscopy images with minimal a priori information,” Opt. Express 17(25), 22747–22760 (2009), http://www.opticsinfobase.org/VJBO/abstract.cfm?URI=oe-17-25-22747. 15. J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, “A white light confocal microscope for spectrally resolved multidimensional imaging,” J. Microsc. 227(3), 203–215 (2007). 16. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007). 17. D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008). 18. J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16(6), 3644–3651 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=OE-16-6- 3644. 19. G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374(7), 989–996 (2010). 20. M. Erkintalo, G. Genty, and J. M. Dudley, “Rogue-wave-like characteristics in femtosecond supercontinuum generation,” Opt. Lett. 34(16), 2468–2470 (2009). 21. A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17(19), 17010–17015 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-19-17010. 22. C. Lafargue, J. Bolger, G. Genty, F. Dias, J. M. Dudley, and B. J. Eggleton, “Direct detection of optical rogue wave energy statistics in supercontinuum generation,” Electron. Lett. 45(4), 217–218 (2009). 23. K. Hammani, C. Finot, J. M. Dudley, and G. Millot, “Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers,” Opt. Express 16(21), 16467–16474 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-21-16467. 24. N. Akhmediev, J. Soto-Crespo, and A. Ankiewicz, “Extreme waves that appear from nowhere: On the nature of rogue waves,” Phys. Lett. A 373(25), 2137–2145 (2009). 25. A. Aalto, G. Genty, and J. Toivonen, “Extreme-value statistics in supercontinuum generation by cascaded stimulated Raman scattering,” Opt. Express 18(2), 1234–1239 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-2-1234. 26. M. Taki, A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, and M. Douay, “Third-order dispersion for generating optical rogue solitons,” Phys. Lett. 374(4), 691–695 (2010). 27. G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources (Invited),” J. Opt. Soc. Am. B 24(8), 1771– 1785 (2007). 28. J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-24-21497. 29. A. V. Gorbach, and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nat. Photonics 1(11), 653–657 (2007). 30. A. V. Gorbach, and D. V. Skryabin, “Theory of radiation trapping by the accelerating solitons in optical fibers,” Phys. Rev. A 76(5), 053803 (2007). 31. D. R. Solli, C. Ropers, and B. Jalali, “Rare frustration of optical supercontinuum generation,” Appl. Phys. Lett. 96(15), 151108 (2010). 32. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, San Diego, 2007). 33. J. Hult, “A fourth-order Runge-Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25(12), 3770–3775 (2007). 34. A. M. Heidt, “Efficient adaptive step size method for the simulation of supercontinuum generation in optical fibers,” J. Lightwave Technol. 27(18), 3984–3991 (2009). 35. S. M. Kobtsev, and S. V. Smirnov, “Modelling of high-power supercontinuum generation in highly nonlinear, dispersion shifted fibers at CW pump,” Opt. Express 13(18), 6912–6918 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-13-18-6912. 36. Q. Lin, and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31(21), 3086–3088 (2006). 37. F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, “Energy exchange between colliding solitons in photonic crystal fiber,” Opt. Express 14(21), 9844–9853 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe- 14-21-9844. 1. Introduction Supercontinuum (SC) light, generated by propagating intense laser pulses along photonic crystal fiber (PCF) [1–4], has attracted interest for many applications including frequency metrology [5,6], spectroscopy [7–12], telecommunications [13] and microscopy [14,15]. Such applications demand wide spectral coverage together with good stability and low noise. An interesting challenge to these aspects of SC generation is posed by optical rogue waves. Optical rogue waves (also called rogue solitons, RS) are packets of extremely intense and red- shifted light that can arise during the propagation of laser light along nonlinear optical fiber #136335 - $15.00 USD Received 8 Oct 2010; revised 19 Nov 2010; accepted 19 Nov 2010; published 30 Nov 2010 (C) 2010 OSA 6 December 2010 / Vol. 18, No. 25 / OPTICS EXPRESS 26114 [16–21]. They are rare, but striking because of their high intensity, extreme spectral shift and time-delay, with implications for light source stability and fiber damage. The properties of RS have been studied by experiment and numerical models [16–26]. When SC light is generated from long pump pulses, the initial phase of propagation involves modulation instability which can be interpreted as the growth of Akhmediev breather structures [27,28].
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