Skip to main content
SpringerLink
Log in
Book cover

Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics pp 405–434Cite as

Three-Wave Backward Optical Solitons

  • Chapter
  • First Online:

  • 1626 Accesses

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Three-wave solitons backward propagating with respect to a pump wave are generated in nonlinear optical media through stimulated Brillouin scattering (SBS) in optical fibers or through the non-degenerate three-wave interaction in quadratic (χ (2)) nonlinear media. In an optical fiber-ring cavity, nanosecond solitary wave morphogenesis takes place when it is pumped with a continuous wave (c.w.). A backward dissipative Stokes soliton is generated from the hypersound waves stimulated by electrostriction between the forward pump wave and the counterpropagating Stokes wave. Superluminous and subluminous dissipative solitons are controlled via a single parameter: the feedback or reinjection for a given pump intensity or the pump intensity for a given feedback. In a c.w. pumped optical parametric oscillator (OPO), backward picosecond soliton generation takes place for non-degenerate three-wave interaction in the quadratic medium. The resonant condition is automatically satisfied in stimulated Brillouin backscattering when the fiber-ring laser contains a large number of longitudinal modes beneath the Brillouin gain curve. However, in order to achieve quasi-phase matching between the three optical waves (the forward pump wave and the backward signal and idler waves) in the χ (2) medium, the nonlinear susceptibility should be periodically structurated by an inversion grating of sub-μm period in an optical parametric oscillator (OPO). The stability analysis of the inhomogeneous stationary solutions presents a Hopf bifurcation with a single control parameter which gives rise to temporal modulation and then to backward three-wave solitons. Above OPO threshold, the nonlinear dynamics yields self-structuration of a backward symbiotic solitary wave, which is stable for a finite temporal walk-off, i.e. different group velocities, between the backward propagating signal and idler waves. We also study the dynamics of singly backward mirrorless OPO (BMOPO) pumped by a broad bandwidth field and also with a highly incoherent pump, in line with the recent experimental demonstration of this BMOPO configuration in a KTP crystal. We show that this system is characterized, as a general rule, by the generation of a highly coherent backward field, despite the high degree of incoherence of the pump field. This remarkable property finds its origin in the convection-induced phase-locking mechanism that originates in the counter-streaming configuration: the incoherence of the pump is transferred to the co-moving field, which thus allows the backward field to evolve towards a highly coherent state. We propose other realistic experimental conditions that may be implemented with currently available technology and in which backward coherent wave generation from incoherent excitation may be observed and studied.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Armstrong, J.A., Jha, S.S., Shiren, N.S.: IEEE J. Quant. Elect. QE-6, 123–129 (1970)

    Article  ADS  Google Scholar 

  2. Nozaki, K., Taniuti, T.: J. Phys. Soc. Jpn. 34, 796–800 (1973)

    Article  ADS  Google Scholar 

  3. Kaup, D.J., Reiman, A., Bers, A.: Rev. Mod. Phys. 51, 275–309 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  4. Drühl, K., Wenzel, R.G., Carlsten, J.L.: Phys. Rev. Lett. 51, 1171 (1983)

    Article  ADS  Google Scholar 

  5. McCall, S.L., Hahn, E.L.: Phys. Rev. Lett. 18, 908 (1967)

    Article  ADS  Google Scholar 

  6. Chiu, S.C.: J. Math. Phys. 19 168–176 (1978)

    Article  ADS  Google Scholar 

  7. Montes, C., Mikhailov, A., Picozzi, A., Ginovart, F.: Phys. Rev. E 55, 1086–1091 (1997)

    Article  ADS  Google Scholar 

  8. Montes, C., Picozzi, A., Bahlouol, D.: Phys. Rev. E 55, 1092–1105 (1997)

    Article  ADS  Google Scholar 

  9. Picholle, E., Montes, C., Leycuras, C., Legrand, O., Botineau, J.: Phys. Rev. Lett. 66, 1454 (1991)

    Article  ADS  Google Scholar 

  10. Montes, C., Mamhoud, A., Picholle, E.: Phys. Rev. A 49, 1344 (1994)

    Article  ADS  Google Scholar 

  11. Montes, C., Bahloul, D., Bongrand, I., Botineau, J., Cheval, G., Mamhoud, A., Picholle, E., Picozzi, A.: J. Opt. Soc. Am. B 16, 932 (1999)

    Article  ADS  Google Scholar 

  12. Botineau, J., Cheval, G., Montes, C.: Opt. Comm. 257, 319–33 (2006)

    Article  ADS  Google Scholar 

  13. Montes, C.: In: Akhmediev, N., Ankiewicz, A. (eds.) Dissipative Solitons: From Optics to Biology and Medicine. Lecture Notes in Physics (LNP), vol. 751, pp. 221–260. Springer, Berlin (2008)

    Google Scholar 

  14. Picozzi, A., Hælterman, M.: Opt. Lett. 23, 1808 (1998)

    Article  ADS  Google Scholar 

  15. Picozzi, A., Haelterman, M.: Phys. Rev. Lett. 84, 5760–5762 (2000)

    Article  ADS  Google Scholar 

  16. Montes, C., Picozzi, A., Hælterman, M.: In: Zakharov, V.E., Wabnitz, S. (eds.) Optical Solitons: Theoretical Challenges and Industrial Perspectives. Les Houches Workshop, Sept. 28-Oct. 2, 1998, pp. 283–292. EDP Springer, New York (1999)

    Google Scholar 

  17. Montes, C.: In: Porsezian, K., Kuriakos, V.C. (eds.) Optical Solitons: Theory and Experiments, Lectures Notes in Physics (LNP), vol. 613, pp. 353–371. Springer, Berlin (2003)

    Google Scholar 

  18. Durniak, C., Montes, C., Taki, M.: J.Opt. B Quant. Semiclass. Opt. 6, S241–S249 (2004)

    Article  ADS  Google Scholar 

  19. Montes, C., Picozzi, A., Durniak, C., Taki, M.: Eur. Phys. J. Spec. Top. 173, 167–191 (2009)

    Article  Google Scholar 

  20. Matsumoto, M., Tanaka, K.: IEEE J. Quant. Electron. 31, 700 (1995)

    Article  ADS  Google Scholar 

  21. Ding, Y.J., Khurgin, J.B.: IEEE J. Quant. Electron. 32, 1574–1582 (1996)

    Article  ADS  Google Scholar 

  22. Kang, J.U., Ding, Y.J., Burns, W.K., Melinger, J.S.: Opt. Lett. 22, 862 (1997)

    Article  ADS  Google Scholar 

  23. D’Alessandro, G., St. Russell, P., Wheeler, A.A.: Phys. Rev. A 55, 3211 (1997)

    Google Scholar 

  24. Canalias, C., Pasiskevicius, V.: Nat. Photonics 1, 459–462 (2007)

    Article  ADS  Google Scholar 

  25. Strömqvist, G., Pasiskevicius, V., Canalias, C., Montes, C.: Phys. Rev. A 84, 023845-1-4 (2011)

    Google Scholar 

  26. Strömqvist, G., Pasiskevicius, V., Canalias, C., Aschieri, P., Picozzi, A., Montes, C.: J. Opt. Soc. Am. 29, 1194–1202 (2012)

    Article  ADS  Google Scholar 

  27. Picozzi, A., Hælterman, M.: Phys. Rev. Lett. 86, 2010 (2001)

    Article  ADS  Google Scholar 

  28. Montes, C., Durniak, C., Taki, M., Picozzi, A.: Opt. Comm. 216, 419–426 (2003)

    Article  ADS  Google Scholar 

  29. Morozov, S.F., Piskunova, L.V., Sushchik, M.M., Freidman, G.I.: Sov. J. Quant. Electron. 8, 576 (1978)

    Article  ADS  Google Scholar 

  30. Craik, A.D.D., Nagata, M., Moroz, I.M.: Wave Motion 15, 173 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  31. Armstrong, J.A., Bloembergen, N., Ducuing, J., Pershan, N.: Phys. Rev. 127, 1918–1939 (1962)

    Article  ADS  Google Scholar 

  32. Busacca, A.C., Sones, C.L., Eason, R.W., Mailis, S.: Appl. Phys. Lett. 84, 4430–4432 (2004)

    Article  ADS  Google Scholar 

  33. Dmitriev, V.G., Gurzadyan, G.G., Nikogosyan, D.N.: Handbook of Nonlinear Optical Crystals. 74 for LiNbO3 and 103 for KTiOPO4. Springer, Berlin (1991)

    Google Scholar 

  34. Bava, G.P., Montrosset, I., Sohler, W., Suche, H.: IEEE J. Quant. Electron. QE-23, 42 (1987)

    Article  ADS  Google Scholar 

  35. Suche, H., Sohler, W.: Integrated optical parametric oscillators (invited). Optoelectron. Devices Technol. 4(1), 1–20 (1989)

    Google Scholar 

  36. Arbore, M.A., Fejer, M.M.: Opt. Lett. 22, 151–153 (1997)

    Article  ADS  Google Scholar 

  37. Hofmann, D., Herrmann, H., Schreiber, G., Grundkötter, W., Ricken, R., Sohler, W.: Continuous-wave mid-infrared optical parametric oscillators with periodically poled Ti:LiNbO3 waveguide. In: 9th European Conference on Integrated Optics and Technical Exhibition ECIO’99, p. 21 (EOS - European Optical Society) (1999)

    Google Scholar 

  38. Hofmann, D., Herrmann, H., Schreiber, G., Haase, C., Grundkötter, W., Ricken, R., Sohler, W.: Nonlinear Guided Waves and Their Applications, FC2-1-3, p. 465. Optical Society of America, Washington, DC (1999)

    Google Scholar 

  39. Picozzi, A., Montes, C., Hælterman, M.: Phys. Rev E 66, 056605-1-14 (2002)

    Google Scholar 

  40. Montes, C., Picozzi, A., Gallo, K.: Opt. Comm. 237, 437–449 (2004)

    Article  ADS  Google Scholar 

  41. Picozzi, A., Aschieri, P.: Phys. Rev. E 72, 046606-1-12 (2005)

    Google Scholar 

  42. Montes, C., Grundkötter, W., Suche, H., Sohler, W.: J. Opt. Soc. Am. 24(11), 2796–2806 (2007)

    Article  ADS  Google Scholar 

  43. Harris, S.E.: Appl. Phys. Lett. 9, 114 (1966)

    Article  ADS  Google Scholar 

  44. Shi, W., Ding, Y.J.: Opt. Lett. 30, 1861–1863 (2005)

    Article  ADS  Google Scholar 

  45. Smith, S.P., Zarinetchi, F., Ezekiel, S.: Opt. Lett. 16, 393–395 (1991)

    Article  ADS  Google Scholar 

  46. Montes, C., Aschieri, P., Picozzi, A., SPIE Proc. 8011, 801136-1-10 (2011)

    Google Scholar 

  47. Kato, K., Takaoka, E.: Appl. Opt. 41, 5040 (2002)

    Article  ADS  Google Scholar 

  48. Piskarskas, A., Pyragaite, V., Stabinis, A.: Phys. Rev. A 82, 053817 (2010)

    Article  ADS  Google Scholar 

  49. Stabinis, A., Pyragaite, V., Tamošauskas, G., Piskarskas, A.: Phys. Rev. A 84, 043813 (2011)

    Article  ADS  Google Scholar 

  50. Özgören, K., Öktem, B., Yilmaz, S., Ilday, F.Ö., Eken, K.: Opt. Express 18, 17647–17652 (2011)

    Article  Google Scholar 

Download references

Acknowledgement

The authors thank G. Strömqvist, V. Pasiskevicius and C. Canalias for stimulating discussions. They also acknowledge the GDR PhoNoMi2 no. 3073 of the CNRS (Centre National de la Recherche Scientifique) devoted to Nonlinear Photonics in Microstructured Materials.

Author information

Authors and Affiliations

  1. CNRS, Laboratoire de Physique de la Matière Condensée, Université de Nice - Sophia Antipolis, 06108, Nice Cedex 2, France

    C. Montes & P. Aschieri

  2. CNRS, Institut Carnot de Bourgogne, 21078, Dijon Cedex, France

    A. Picozzi

  3. Laboratoire de Physique des Lasers, Atomes et Molecules, Université des Sciences et Technologies de Lille, 59655, Villeneuve d’Asq Cedex, France

    C. Durniak & M. Taki

Authors
  1. C. Montes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Aschieri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Picozzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. Durniak
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Taki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Montes .

Editor information

Editors and Affiliations

  1. , Dpt. Quimica-Fisica-I, UCM, Madrid, 28040, Spain

    Ramon G. Rubio

  2. Instituto Pluridisciplinar, UCM, Paseo Juan XXIII 1, Madrid, 28040, Spain

    Yuri S. Ryazantsev

  3. , Dpt. of Chemical Engineering, Loughborough University, Loughborough, LE11 3TU, United Kingdom

    Victor M Starov

  4. , Physics Dpt., East China Normal University, Zhongshan Northern Road 3663, Shanghai, 200062, China, People's Republic

    Guo-Xiang Huang

  5. , Faculty of Physics, Saratov State University, Astrakhanskaya Str. 83, Saratov, 410012, Russia

    Alexander P Chetverikov

  6. , Dpt. di Ingegneria Elettrica Elettronica, Università di Catania, V. le A. Doria 6, Catania, 95125, Italy

    Paolo Arena

  7. , Dept. of Mathematics, Technion, Haifa, 32000, Israel

    Alex A. Nepomnyashchy

  8. , Instituto Cajal, CSIC, Av. Dr. Arce 37, Madrid, 28002, Spain

    Alberto Ferrus

  9. Shirshov Institute of Oceanology, Nakhimovsky prospekt 36, Moscow, 117851, Russia

    Eugene G. Morozov

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Montes, C., Aschieri, P., Picozzi, A., Durniak, C., Taki, M. (2013). Three-Wave Backward Optical Solitons. In: Rubio, R., et al. Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34070-3_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34070-3_34

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34069-7

  • Online ISBN: 978-3-642-34070-3

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation