Gain through losses in nonlinear optics

Auro M. Perego; Sergei K. Turitsyn; Kestutis Staliunas

doi:10.1038/s41377-018-0042-9

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Gain through losses in nonlinear optics

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- Gain through losses in nonlinear optics
- Light: Science & Applications Vol. 7, Issue 5, Pages: 336-346(2018)
- Affiliations：
  
  1.Aston Institute of Photonic Technologies, Aston University, Birmingham, B4 7ET, UK
  2.Novosibirsk State University, Novosibirsk, 630090, Russia
  3.Institució Catalana de Recerca i Estudis Avançats, Pg. Lluis Companys 23, 08010, Barcelona, Spain
  4.Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Rambla Sant Nebridi 22, 08222, Terrassa, Barcelona, Spain
- Author bio：
  
  Auro M. Perego (peregoa@aston.ac.uk)
- Funds：
- DOI：10.1038/s41377-018-0042-9
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Perego, A. M., Turitsyn, S. K. & Staliunas, K. Gain through losses in nonlinear optics. Light: Science & Applications, 7, 336-346 (2018).
DOI：

Perego, A. M., Turitsyn, S. K. & Staliunas, K. Gain through losses in nonlinear optics. Light: Science & Applications, 7, 336-346 (2018). DOI： 10.1038/s41377-018-0042-9.

摘要

Abstract

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. These instabilities are at the heart of symmetry breaking, condensate dynamics, self-organisation, pattern formation, and noise amplification across diverse disciplines, including physics, chemistry, engineering, and biology. In nonlinear optics, modulation instabilities are generally linked to the so-called parametric amplification process, which occurs when certain phase-matching or quasi-phase-matching conditions are satisfied.,In the present review article, we summarise the principle results on modulation instabilities and parametric amplification in nonlinear optics, with special emphasis on optical fibres. We then review state-of-the-art research about a peculiar class of modulation instabilities (MIs) and signal amplification processes induced by dissipation in nonlinear optical systems. Losses applied to certain parts of the spectrum counterintuitively lead to the exponential growth of the damped mode themselves, causing ,gain through losses,. We discuss the concept of ,imaging of losses into gain, showing how to map a given spectral loss profile into a gain spectrum. We demonstrate with concrete examples that dissipation-induced MI, apart from being of fundamental theoretical interest, may pave the way towards the design of a new class of tuneable fibre-based optical amplifiers, optical parametric oscillators, frequency comb sources, and pulsed lasers.

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references

Zakharov, V. E., L'vov, V. S. & Falkovich, G. Kolmogorov Spectra of Turbulence I: Wave Turbulence. (Springer-Verlag, Berlin, 1992).

Staliunas, K. & Sánchez-Morcillo, V. J. Transverse Patterns in Nonlinear Optical Resonators. (Springer: Berlin, 2003).

Lugiato, L., Prati, F. & Brambilla, M. Nonlinear Optical Systems. (Cambridge University Press, Cambridge, 2015).

Cross, M. C. & Hohenberg, P. C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993).

Aranson, I. S. & Kramer, L. The world of the complex Ginzburg-Landau equation. Rev. Mod. Phys. 74, 99–143 (2002).

Agrawal, G. P. Nonlinear Fiber Optics. 4th edn, (Academic Press, San Diego, 2006).

Ablowitz, M. J. Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons.. (Cambridge University Press, Cambridge, 2011).

Zakharov, V. E. & Ostrovsky, L. A. Modulation instability: the beginning. Physica D 238, 540–548 (2009).

Benjamin, T. B. & Feir, J. E. The disintegration of wave trains on deep water part 1. Theory. J. Fluid. Mech. 27, 417–430 (1967).

Bespalov, V. I. & Talanov, V. I. Filamentary structure of light beams in nonlinear liquids. JETP Lett. 3, 307–311 (1966).

Tai, K., Hasegawa, A. & Tomita, A. Observation of modulational instability in optical fibers. Phys. Rev. Lett. 56, 135–138 (1986).

Agrawal, G. P. Modulation instability induced by cross-phase modulation. Phys. Rev. Lett. 59, 880–883 (1987).

Berkhoer, A. L. & Zakharov, V. E. Self-excitation of waves with different polarizations in nonlinear media. Sov. Phys. JETP 31, 486–490 (1970).

Wabnitz, S. Modulational polarization instability of light in a nonlinear birefringent dispersive medium. Phys. Rev. A 38, 2018–2021 (1988).

Trillo, S., Wabnitz, S., Stolen, R. H., Assanto, G. & Seaton, C. T. et al. Experimental observation of polarization instability in a birefringent optical fiber. Appl. Phys. Lett. 49, 1224–1226 (1986).

Agrawal, G. P. Modulation instability in Erbium-doped fiber amplifiers. IEEE Photon. Technol. Lett. 4, 562–564 (1992).

Van Tartwijk, G. H. M. & Agrawal, G. P. Maxwell-Bloch dynamics and modulation instabilities in fiber lasers and amplifiers. J. Opt. Soc. Am. B 14, 2618–2627 (1997).

Turitsyn, S., Rubenchik, A. M. & Fedoruk, M. P. On the theory of the modulation instability in optical fiber amplifiers. Opt. Lett. 35, 2864–2866 (2010).

Dudley, J. M., Goënty, G. & Coen, S. Supercontinuum generation in photonic crystal fiber. Rev. Mod. Phys. 78, 1135–1184 (2006).

Kip, D., Soljacic, M., Segev, M., Eugenieva, E. & Christodoulides, D. N. Modulation instability and pattern formation in spatially incoherent light beams. Science 290, 495–498 (2000).

Zakharov, V. E. & Shabat, A. B. Exact theory of two-dimensional self-focussing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62–69 (1972).

Kuznetsov, E. Solitons in a parametrically unstable plasma. Sov. Phys. Dokl. 22, 507–508 (1977).

Akhmediev, N. & Korneev, V. I. Modulation instability and periodic solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 69, 1089–1093 (1986).

Peregrine, D. H. Water waves, nonlinear Schrödinger equations and their solutions.ANZIAM J. 25, 16–43 (1983).

Dudley, J. M., Dias, F., Erkintalo, M. & Genty, G. Instabilities, breathers and rogue waves in optics. Nat. Photon. 8, 755–764 (2014).

Faraday, M. On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philos. Trans. R. Soc. Lond. 121, 299–340 (1831).

Benjamin, T. B. & Ursell, F. The stability of the plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. A 225, 505–515 (1954).

Coullet, P., Frisch, T. & Sonnino, G. Dispersion-induced patterns. Phys. Rev. E 49, 2087–2090 (1994).

Petrov, V., Ouyang, Q. & Swinney, H. L. Resonant pattern formation in a chemical system. Nature 388, 655–657 (1997).

Melo, F., Umbanhowar, P. & Swinney, H. L. Transition to parametric wave patterns in a vertically oscillated granular layer. Phys. Rev. Lett. 72, 172–175 (1994).

Drake, J. F., Kaw, P. K., Lee, Y. C., Schmid, G. & Liu, C. S. et al. Parametric instabilities of electromagnetic waves in plasmas. Phys. Fluids 17, 778–785 (1974).

Staliunas, K., Longhi, S. & De Valcárcel, G. J. Faraday patterns in Bose-Einstein condensates. Phys. Rev. Lett. 89, 210406 (2002).

Engels, P., Atherton, C. & Hoefer, M. A. Observation of Faraday waves in a Bose-Einstein condensate. Phys. Rev. Lett. 98, 095301 (2007).

Centurion, M., Porter, M. A., Pu, Y., Kevrekidis, P. G. & Frantzeskakis, D. J. et al. Modulational instability in a layered Kerr medium: theory and experiment. Phys. Rev. Lett. 97, 234101 (2006).

Szwaj, C., Bielawski, S., Derozier, D. & Erneux, T. Faraday instability in a multimode laser. Phys. Rev. Lett. 80, 3968 (1998).

Matera, F., Mecozzi, A., Romagnoli, M. & Settembre, M. Sideband instability induced by periodic power variation in long-distance fiber links. Opt. Lett. 18, 1499–1501 (1993).

Abdullaev, F. K., Darmanyan, S. A., Bischoff, S. & Sørensen, M. P. Modulational instability of electromagnetic waves in media with varying nonlinearity. J. Opt. Soc. Am. B 14, 27–33 (1997).

Smith, N. J. & Doran, N. J. Modulational instabilities in fibers with periodic dispersion management. Opt. Lett. 21, 570–572 (1996).

Abdullaev, F. K., Darmanyan, S. A., Kobyakov, A. & Lederer, F. Modulational instability in optical fibers with variable dispersion. Phys. Lett. A 220, 213–218 (1996).

Bronski, J. C. & Kutz, J. N. Modulational stability of plane waves in nonreturn-to-zero communications systems with dispersion management. Opt. Lett. 21, 937–939 (1996).

Mussot, A., Conforti, M., Trillo, S., Copie, F. & Kudlinski, A. Modulation instability in dispersion oscillating fibers. Adv. Opt. Photon. 10, 1–42 (2018).

Staliunas, K., Hang, C. & Konotop, V. V. Parametric patterns in optical fiber ring nonlinear resonators. Phys. Rev. A 88, 023846 (2013).

Conforti, M., Mussot, A., Kudlinski, A. & Trillo, S. Modulational instability in dispersion oscillating fiber ring cavities. Opt. Lett. 39, 4200–4203 (2014).

Turing, A. M. The chemical basis of morphogenesis. Philos. Trans. R. Soc. B 237, 37–72 (1952).

Lugiato, L. A. & Lefever, R. Spatial dissipative structures in passive optical systems. Phys. Rev. Lett. 58, 2209–2211 (1987).

Copie, F., Conforti, M., Kudlinski, A., Mussot, A., & Trillo, S. Competing Turing and Faraday instabilities in longitudinally modulated passive resonators. Phys. Rev. Lett. 116, 143901 (2016).

Staliunas, K. & Sánchez-Morcillo, V. J. Turing patterns in nonlinear optics. Opt. Commun. 177, 389–395 (2000).

Haelterman, M., Trillo, S. & Wabnitz, S. Additive-modulation-instability ring laser in the normal dispersion regime of a fiber. Opt. Lett. 17, 745–747 (1992).

Coen, S. & Haelterman, M. Modulational instability induced by cavity boundary conditions in a normally dispersive optical fiber. Phys. Rev. Lett. 79, 4139–4142 (1997).

Perego, A. M., Smirnov, S. V., Staliunas, K., Churkin, D. V. & Wabnitz, S. Self-induced Faraday instability laser. Phys. Rev. Lett. 120, 213902 (2018).

Guasoni, M. Generalized modulational instability in multimode fibers: wideband multimode parametric amplification. Phys. Rev. A 92, 033849 (2015).

Longhi, S. Modulational instability and space–time dynamics in nonlinear parabolic-index optical fibers. Opt. Lett. 28, 2363–2365 (2003).

Krupa, K., Tonello, A., Barthélémy, A., Couderc, V. & Shalaby, B. M. et al. Observation of geometric parametric instability induced by the periodic spatial self-imaging of multimode waves. Phys. Rev. Lett. 116, 183901 (2016).

Wright, L. G., Liu, Z. W., Nolan, D. A., Li, M. J. & Christodoulides, D. N. et al. Self-organized instability in graded-index multimode fibres. Nat. Photon. 10, 771–776 (2016).

Haken, H. Analogy between higher instabilities in fluids and lasers. Phys. Lett. A 53, 77–78 (1975).

Arecchi, F. T., Giacomelli, G., Ramazza, P. L. & Residori, S. Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics. Phys. Rev. Lett. 65, 2531–2534 (1990).

Risken, H. & Nummedal, K. Instability of off resonance modes in lasers. Phys. Lett. A 26, 275–276 (1968).

Graham, R. & Haken, H. Quantum theory of light propagation in a fluctuating laser-active medium. Z. Phys. A 213, 420–450 (1968).

Pessina, E. M., Bonfrate, G., Fontana, F. & Lugiato, L. A. Experimental observation of the Risken-Nummedal-Graham-Haken multimode laser instability. Phys. Rev. A 56, 4086–4093 (1997).

Nakazawa, M., Suzuki, K. & Haus, H. A. The modulational instability laser. I. Experiment. IEEE J. Quant. Electron. 25, 2036–2044 (1989).

Boyd, R. W. Nonlinear Optics. (Academic Press, San Diego, 1991).

Armstrong, J. A., Bloembergen, N., Ducuing, J. & Pershan, P. S. Interactions between light waves in a nonlinear dielectric. Phys. Rev. 127, 1918–1939 (1962).

Cappellini, G. & Trillo, S. Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects. J. Opt. Soc. Am. B 8, 824–838 (1991).

Ott, J. R., Steffensen, H., Rottwitt, K. & McKinstrie, C. J. Geometric interpretation of four-wave mixing. Phys. Rev. A 88, 043805 (2013).

Stolen, R. H. Phase-matched-stimulated four-photon mixing in silica-fiber waveguides. IEEE J. Quant. Electron. 11, 100–103 (1975).

Marhic, M. Fiber Optical Parametric Amplifiers, Oscillators and Related Devices. (Cambridge University Press, Cambridge, 2007).

Torounidis, T., Andrekson, P. A. & Olsson, B. E. Fiber-optical parametric amplifier with 70-dB gain. IEEE Photon. Technol. Lett. 18, 1194–1196 (2006).

Stephens, M. F. C., Phillips, I. D., Rosa, P., Harper, P. & Doran, N. J. Improved WDM performance of a fibre optical parametric amplifier using Raman-assisted pumping. Opt. Exp. 23, 902–911 (2015).

Hansryd, J., Andrekson, P. A., Westlund, M., Li, J. & Hedekvist, P. O. Fiber-based optical parametric amplifiers and their applications. IEEE J. Sel. Top. Quant. Electron. 8, 506–520 (2002).

Radic, S. & McKinstrie, C. J. Two-pump fiber parametric amplifiers. Opt. Fiber Technol. 9, 7–23 (2003).

McKinstrie, C. J. & Radic, S. Phase-sensitive amplification in a fiber. Opt. Exp. 12, 4973–4979 (2004).

Marhic, M. E., Andrekson, P. A., Petropoulos, P., Radic, S. & Peucheret, C. et al. Fiber optical parametric amplifiers in optical communication systems. Laser Photon. Rev. 9, 50–74 (2015).

Barthelemy, A. & De La Fuente, R. Unusual modulation instability in fibers with normal and anomalous dispersions. Opt. Commun. 73, 409–412 (1989).

Turitsyn, S. K., Bednyakova, A. E., Fedoruk, M. P., Papernyi, S. B. & Clements, W. R. L. Inverse four-wave mixing and self-parametric amplification in optical fibre. Nat. Photon. 9, 608–614 (2015).

Picozzi, A., Garnier, J., Hansson, T., Suret, P. & Randoux, S. et al. Optical wave turbulence: towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics. Phys. Rep. 542, 1–132 (2014).

Hall, B., Lisak, M., Anderson, D., Fedele, R. & Semenov, V. E. Statistical theory for incoherent light propagation in nonlinear media. Phys. Rev. E 65, 035602 (2002).

Churkin, D. V., Kolokolov, I. V., Podivilov, E. V., Vatnik, I. D., & Nikulin, M. A. et al. Wave kinetics of random fibre lasers. Nat. Commun. 2, 6214 (2015).

Babin, S. A., Churkin, D. V., Ismagulov, A. E., Kablukov, S. I. & Podivilov, E. V. Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser. J. Opt. Soc. Am. B 24, 1729–1738 (2007).

Deng, L., Hagley, E. W., Wen, J., Trippenbach, M. & Band, Y. et al. Four-wave mixing with matter waves. Nature 398, 218–220 (1999).

Trippenbach, M., Band, Y. B. & Julienne, P. S. Theory of four-wave mixing of matter waves from a Bose-Einstein condensate. Phys. Rev. A 62, 023608 (2000).

Vogels, J. M., Xu, K. & Ketterle, W. Generation of macroscopic pair-correlated atomic beams by four-wave mixing in Bose-Einstein condensates.Phys. Rev. Lett. 89, 020401 (2002).

Karlsson, M. Modulational instability in lossy optical fibers. J. Opt. Soc. Am. B 12, 2071–2077 (1995).

Krechetnikov, R. & Marsden, J. E. Dissipation-induced instabilities in finite dimensions. Rev. Mod. Phys. 79, 519–553 (2007).

Tanemura, T., Ozeki, Y. & Kikuchi, K. Modulational instability and parametric amplification induced by loss dispersion in optical fibers. Phys. Rev. Lett. 93, 163902 (2004).

Trillo, S. & Wabnitz, S. Dynamics of the nonlinear modulational instability in optical fibers. Opt. Lett. 16, 986–988 (1991).

Xu, K., Liu, H. Y., Dai, Y. T., Wu, J. & Lin, J. T. Synthesis of broadband and flat parametric gain by idler loss in optical fiber. Opt. Commun. 285, 790–794 (2012).

Coen, S., Wardle, D. A. & Harvey, J. D. Observation of non-phase-matched parametric amplification in resonant nonlinear optics. Phys. Rev. Lett. 89, 273901 (2002).

Sylvestre, T., Maillotte, H., Lantz, E. & Tchofo Dinda, P. Raman-assisted parametric frequency conversion in a normally dispersive single-mode fiber. Opt. Lett. 15, 1561–1563 (1999).

Castelli, F., Brambilla, M., Gatti, A., Prati, F. & Lugiato, L. A. The LLE, pattern formation and a novel coherent source. Eur. Phys. J. D. 71, 84 (2017).

Myers, L. E., Eckardt, R. C., Fejer, M. M., Byer, R. L. & Bosenberg, W. R. et al. Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO 3. J. Opt. Soc. Am. B 12, 2102–2116 (1995).

Lowenthal, D. D. CW periodically poled LiNbO3 optical parametric oscillator model with strong idler absorption. IEEE J. Quant. Electron. 34, 1356–1366 (1998).

Rustad, G., Arisholm, G. & Farsund, Ø. Effect of idler absorption in pulsed optical parametric oscillators. Opt. Exp. 19, 2815–2830 (2011).

Jauregui, C., Steinmetz, A., Limpert, J. & Tünnermann, A. High-power efficient generation of visible and mid-infrared radiation exploiting four-wave-mixing in optical fibers. Opt. Exp. 20, 24957-24965 (2012).

Ma, J. G., et al. Quasi-parametric amplification of chirped pulses based on a Sm3+-doped yttrium calcium oxyborate crystal. Optica 20, 1006–1009 (2015).

Perego, A. M., Tarasov, N., Churkin, D. V., Turitsyn, S. K. & Staliunas, K. Pattern generation by dissipative parametric instability. Phys. Rev. Lett. 116, 028701 (2016).

Tarasov, N., Perego, A. M., Churkin, D. V., Staliunas, K. & Turitsyn, S. K. Mode-locking via dissipative Faraday instability. Nat. Commun. 7, 12441 (2016).

Perego, A. M. High-repetition-rate, multi-pulse all-normal-dispersion fiber laser. Opt. Lett. 42, 3574–3577 (2017).

Staliunas, K. Removal of excitations of Bose-Einstein condensates by space- and time-modulated potentials. Phys. Rev. A. 84, 013626 (2011).

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