Skip to main content

Experiments on Quadratic Solitons

  • Chapter

Part of the book series: NATO Science Series ((NAII,volume 31))

Abstract

Spatial solitons are beams that do not diffract by virtue of a strong nonlinear interaction with the medium in which they propagate.[1] Quadratic solitons are a rather special member of the spatial soliton family because their existence is not linked to a self- induced refractive index change and subsequent guiding of the beam by the induced waveguide. Instead they exist by virtue of the strong coupling via the second order nonlinearity χ(2) between beams of different frequencies.[2] For example, for Type I second harmonic generation (SHG) in which there is a single fundamental and harmonic beam, the beams exchange photons with propagation distance leading to mutual self- trapping. Although such solitons were predicted back in the 1970s, they were not observed experimentally until the mid 1990s. [24] Over the last five years there has been a great deal of experimental progress in this field and the purpose of this chapter is to review some aspects of this work. (A separate chapter by Sukhorukov in this book deals with the details of the theory of quadratic solitons and related effects.)

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Segev, M. and Stegeman, G.I. (1998) Self-Trapping of Optical Beams: Spatial Solitons, Physics Today 51 42–48.

    Article  Google Scholar 

  2. Karamzin, Y.N. and Sukhorukov, A.P. (1974) Nonlinear Interaction of Diffracted Light Beams in a Medium with Quadratic Nonlinearity: Mutual Focusing of Beams and Limitation on the Efficiency of Optical Frequency Convertors, JETP Lett. 20, 339–342; Karamzin, Y.N. and Sukhorukov, A.P. (1976) Mutual Focusing of High-Power Light Beams in Media with Quadratic Nonlinearity Zh. Eksp. Tear. Phys 68, 834-40 (Sov. Phys.-JETP 41, 1420).

    ADS  Google Scholar 

  3. Torruellas, W.E., Wang, Z., Hagan, D.J., VanStryland, E.W., Stegeman, G.I., Tomer, L. and Menyuk, C.R. (1995) Observation of Two-Dimensional Spatial Solitary Waves in a Quadratic Medium Phys. Rev. Lett., 74, 5036–5039.

    Article  ADS  Google Scholar 

  4. Schiek, R., Baek, Y. and G.I. Stegeman, G.I. (1996) One-Dimensional Spatial Solitons Due to Cascaded Second-Order Nonlinearities in Planar Waveguides Phys. Rev. E, 53, 1138–1141.

    Article  ADS  Google Scholar 

  5. Stegeman, G.I., Hagan, D.J. and Tomer, L. (1996) χ(2) Cascading Phenomena and Their Applications to All-Optical Signal Processing, Mode-Locking, Pulse Compression and Solitons J. Optical and Quant. Electron. 28 1691–1740.

    Article  Google Scholar 

  6. Canva, M.T.G., Fuerst, R.A., Baboiu, D., Stegeman, G.I. and Assanto, G. (1997) Quadratic Spatial Soliton Generation By Seeded Down Conversion of a Strong Pump Beam Opt. Lett. 22 1683–1685.

    Article  ADS  Google Scholar 

  7. Di Trapani, P., Valiulis, G., Chianglia, W. and Adreoni, A. (1998) Two-Dimensional Spatial Solitary Waves from Traveling Wave Parametric Amplification of the Quantum Noise Phys. Rev. Lett. 80 265–269.

    Article  ADS  Google Scholar 

  8. Bourliaguet, B., Couderc, V., Barthelemy, A., Ross, G.W., Smith, P.G.R., Hanna, D.C. and De Angelis, C. (1999) Observation of Quadratic Spatial Solitons in Periodically Poled Lithium Niobate Opt. Lett. 24, 1410–1412.

    Article  ADS  Google Scholar 

  9. Liu, X., Qian, L.J. and Wise, F.W. (1999) Generation of Optical Spatiotemporal Solitons Phys. Rev. Lett. 82 4631–4634.

    Article  ADS  Google Scholar 

  10. Di Trapani, P., Caironi, D., Valiulis, G., Dubietis, A., Danielius, R. and Piskarkis, A. (1998) Observation of Temporal Solitons in Second Harmonic Generation with Tilted Pulses Phys. Rev. Lett., 81 570–573.

    Article  ADS  Google Scholar 

  11. Dubietis A., Valiulis, G., Danielius, R., and Piskarskas, A. (1996) Fundamental-Frequency Pulse Compression Through Cascaded Second-Order Processes in a Type II Phase-Matched Second Harmonic Generator Opt. Lett. 21, 1262–1264; Valiulis, G., Dubietis, A., Danelius, R., Caironi, D., Visconti, A. and Di Trapani, P. (1999) Temporal Solitons in χ(2) Materials with Tilted Pulses J. Opt. Soc. Am. B, 16 722-31

    Article  ADS  Google Scholar 

  12. Stegeman, G.I. and Segev, M. (1999) Optical Spatial Soliton and Their Interactions: Universality and Diversity Science 286 1518–1523.

    Article  Google Scholar 

  13. Y. Baek, Y., Schiek, R., Stegeman, G.I., Baumann, I. and Sohler, W. (1997) Interactions Between One-Dimensional Quadratic Solitons Opt.Lett. 22 1550–1552; Schiek, R., Baek, Y., Stegeman, G.I., Baumann, I. and Sohler, W. (1998) Interactions Between One-Dimensional Quadratic Soliton-like Beams Opt. Quant. Electron. 30 861-879.

    Google Scholar 

  14. Costantini, B., De Angelis, C., Barthelemy, A., Bourliaguet, B., and Kermene, V. (1998) Collisions Between Type II Two-Dimensional Quadratic Solitons Opt. Lett. 23 424–426.

    Article  ADS  Google Scholar 

  15. Enfield, E. and Rowlands, G. (1990) Nonlinear Waves, Solitons and Chaos Cambridge University Press, Cambridge.; Nayfeh, A.H. and Mook, D.T. (1979) Nonlinear Oscillations, Wiley, New York.

    Google Scholar 

  16. for an early review see Akhmanov, S.A., Khokhlov, R.V. and A. P. Sukhorukov, A.P. (1972) chapter in Laser Handbook, ed. Arecchi, F.T. and Schulz-DuBois, E.O., North Holland, Amsterdam, ppl 151–1228.

    Google Scholar 

  17. K. Tai, K., Hasegawa, A. and Tomita A (1986) Observation of Modulational Instability in Optical Fibers Phys. Rev. Lett. 56 135–138.

    Article  ADS  Google Scholar 

  18. Mamaev, A.V., Saffman, M., Anderson, D.Z., and Zozulya, A.A. (1996) Propagation of Light Beams in Anisotropic Nonlinear Media: From Symmetry Breaking to Spatial Turbulence, Physical Review A 54, 870–879.

    Article  ADS  Google Scholar 

  19. Fuerst, R.A., Baboiu, D.-M., Lawrence, B., Torruellas, W.E., Stegeman, G.I. and Trillo, S. (1997) Spatial Modulational Instability and Multisoliton-Like Generation in a Quadratically Nonlinear Optical Medium, Phys. Rev. Lett. 78, 2760–2763.

    Article  ADS  Google Scholar 

  20. Fang, H., Malendevich, R., Schiek, R. and G. I. Stegeman, G.I. (2001) Spatial Modulational Instability in One-Dimensional LiNbO3 Slab Waveguides, Opt. Lett. in press.

    Google Scholar 

  21. Kip, D., Soljacic, M., Segev, M., Eugenieva, E. and Christodoulides, D.N. (2000) Modulation Instability and Pattern Formation in Spatially Incoherent Light Beams Science 290, 495–498.

    Article  ADS  Google Scholar 

  22. A. E. Kaplan, A.E. (1993) Etgenmodes of χ(2) Wave Mixings: Cross-induced Second Order Nonlinear Refraction Opt. Lett., 18, 1223.

    Article  ADS  Google Scholar 

  23. Trillo, S. and Ferro, P. (1995) Modulational instability in second-harmonic generation, Opt. Lett. 20, 438–440.

    Article  ADS  Google Scholar 

  24. Minardi, S., Sapone, S., Chinaglia, W., Di Trapani, P., and Berzabskis, A. (2000) Pixellike Parametric Generator Based on Controlled Spatial-soliton Formation Opt. Lett. 25, 326–328.

    Article  ADS  Google Scholar 

  25. Petrov, D.V., Tomer, L., Martorell, J., Vilaseca, R., Torres, J.P., and Cojocaru, C. (1998) Observation of Azimuthal Modulational and Formation of Patternsa of Optical Solitons in a Quadratic Nonlinear Crystal Opt. Lett. 23, 1444–1446.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Stegeman, G.I. (2001). Experiments on Quadratic Solitons. In: Boardman, A.D., Sukhorukov, A.P. (eds) Soliton-driven Photonics. NATO Science Series, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0682-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-0682-8_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-7131-1

  • Online ISBN: 978-94-010-0682-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics