Skip to main content
SpringerLink
Log in

Optical Self-Focusing: Stationary Beams and Femtosecond Pulses

  • Chapter
Self-focusing: Past and Present

Part of the book series: Topics in Applied Physics ((TAP,volume 114))

Abstract

This chapter provides a systematic account of the theory of self-focusing of waves. The parabolic equation method is applied to solve different self-focusing problems. Various self-focusing manifestations are described, specifically, the existence of homogeneous wave channels, the instability of plane waves, the formation of the regions with abnormally great field amplitudes (nonlinear foci) in cubic nonlinear media, suppression of self-focusing in periodic systems, and the spectral broadening of self-focusing pulses. Some questions of self-action of femtosecond pulses are discussed.

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

Access this chapter

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.A. Askarian: Effect of the gradient of a strong electromagnetic beam on electrons and atoms, Sov. Phys. JETP 15, 1088–1090 (1962). See also current book.

    Google Scholar 

  2. A.V. Gaponov, M.A. Miller: Potential wells for charged particles in high-frequency electromagnetic field, Sov. Phys. JETP 7, 168–169 (1958).

    Google Scholar 

  3. H.A.H. Boot, S.A. Self, R.B.R, Shersby-Harvie: Containment of a fully-ionized plasma by radio-frequiency fields, J. Electron. Controls 4, 434–453 (1958).

    Google Scholar 

  4. V.I. Talanov: On self-focusing of electromagnetic waves in nonlinear media, Izv. VUZ. Radiophysica 7, 564–565 (1964). See also current book.

    MATH  Google Scholar 

  5. R.Y. Chiao, E. Garmire, C.H. Townes: Self-trapping of optical beams, Phys. Rev. Lett. 13, 479–482 (1964).

    Article  ADS  Google Scholar 

  6. V.I. Talanov: On self-focusing of the wave beams in nonlinear media, JETP Lett. 2, 138–139 (1965).

    ADS  Google Scholar 

  7. P.L. Kelley: Self-focusing of optical beams, Phys. Rev. Lett. 15, 1005–1008 (1965).

    Article  ADS  Google Scholar 

  8. M. Hercher: Laser-induced damage in transparent media, J. Opt. Soc. Am. 54, 563 (1964). See also current book.

    Google Scholar 

  9. N.F. Pilipetsky, A.R. Rustamov: Observation of self-focusing of light in liquids, JETP Lett. 2, 55–56 (1965).

    Google Scholar 

  10. A.G. Litvak, V.I. Talanov: A parabolic equation for calculating the fields in dis-persive nonlinear media, Radiophys. Quant. Electron. 10, 296–302 (1967).

    Article  ADS  Google Scholar 

  11. V.I. Talanov, S.N. Vlasov: The parabolic equation in the theory of wave propa-gation (on the 50th anniversary of its publication), Radiophys. Quant. Electron. 38, 1–12 (1995).

    ADS  MathSciNet  Google Scholar 

  12. J.H. Marburger: Self-focusing theory, Prog. Quant. Electr. 4, 35–110 (1975).

    Article  ADS  Google Scholar 

  13. S.A. Akhmanov, A.P. Sukhorukov, R.V. Khokhlov: Self-focusing and diffraction of light in a nonlinear medium, Sov. Phys. Uspekhi. 10, 609–636 (1968).

    Article  ADS  Google Scholar 

  14. S.A. Akhmanov, R.V. Khokhlov, A.P. Sukhorukov: Self-focusing, self-defocusing, and self-modulation of laser beams. In: Laser Handbook, vol. 2, pp. 1151–1228, F.T. Arecchi, E.O. Schulz-Dubois (Eds.), North-Holland, Amsterdam (1972).

    Google Scholar 

  15. V.I. Talanov, S.N. Vlasov: Wave Self-Focusing. IAP RAS, N. Novgorod (1997).

    Google Scholar 

  16. R.W. Hellwarth: Third-order optical susceptibilities of liquids and solids, Prog. Quant. Electr. 5, 1–68 (1978).

    Article  ADS  Google Scholar 

  17. V.I. Bespalov, A.G. Litvak, V.I. Talanov: Self-action of electromagnetic waves in cubic isotropic media. In: Nonlinear Optics, R.V. Khokhlov, G.V. Krivoschekov (Eds.), Nauka, Novosidirsk, pp. 428–462 (1968).

    Google Scholar 

  18. A.G. Litvak: Finite-amplitude wave beams in magnetoactive plasma, Sov. Phys. JETP, 30, 344 (1970).

    ADS  Google Scholar 

  19. A.G. Litvak, G.M. Fraiman: Interaction of opposite electromagnetic wave beams in a transparent nonlinear medium, Radiophy. Quant. Electron. 15, 1024–1029 (1972).

    Article  ADS  Google Scholar 

  20. Z.K. Yankauskas: Radial field distributions in a self-focusing light beam, Radiophys. Quant. Electron. 9, 261–263 (1966).

    ADS  Google Scholar 

  21. H.A. Haus: High-order trapped light beam solutions, Appl. Phys. Lett. 8, 128–129 (1966).

    Article  ADS  Google Scholar 

  22. N.G. Bondarenko, I.V. Eremina, A.I. Makarov: Measurement of coefficient of nonlinearity of an optical and laser glass, Sov. J. Quant. Electron 8, 482–484 (1978).

    Article  ADS  Google Scholar 

  23. V.S. Averbach, A.A. Betin, V.A. Gaponov et al.: Effects of the stimulated scattering and self-action in gases and effect them on propagation of optical radiation, Radiophys. Quant. Electron. 21, 755–775 (1978).

    Article  ADS  Google Scholar 

  24. S.N. Vlasov, V.A. Gaponov, I.V. Eremina et al.: Self-focusing of beams with elliptic polarization, Radiophys. Quant. Electron. 21, 358–362 (1978).

    Article  ADS  Google Scholar 

  25. A.G. Litvak, G.M. Fraiman, A.D. Junakovskii: Thermal self-action of wave beams in plasma with not local nonlinearity, Phys. Plasma, 1, 60–71 (1975).

    Google Scholar 

  26. G.A. Markov, V.A. Mironov, A.M. Sergeev et al.: Multi-beam self-channeling of plasma waves, Sov. Phys. JETP 53, 1183 (1981).

    Google Scholar 

  27. V.I. Bespalov, V.I. Talanov: About filamentation of beams of light in a nonlin-ear liquid. JETP Lett. 3, 307–310 (1966).

    ADS  Google Scholar 

  28. V.I. Talanov, S.N. Vlasov: About some features of scattering of signal wave on opposite pumping beams at degenerate four-photon interaction. In: The Conjugate Wave Front Generation of Optical Radiation in Nonlinear Media. V.I. Bespalov (Ed.), IAP RAS, Gorky, pp. 85–91 (1979).

    Google Scholar 

  29. H. Pu, N.P. Bigelow: Collective excitations, metastability, and nonlinear response of a trapped two-species Bose–Einstein condensate, Phys. Rev. Lett. 80, 1134–1137 (1998).

    Article  ADS  Google Scholar 

  30. V.I. Talanov: Self-similar wave beams in nonlinear dielectric, Radiophys. Quant. Electron. 9, 260–261 (1966).

    ADS  Google Scholar 

  31. V.I. Talanov: About self-focusing of light in cubic media, JETP Lett. 11, 199–201 (1970).

    ADS  Google Scholar 

  32. S.N. Vlasov, S.N. Gurbatov: The self-action theory of intense light beams in smoothly imhomogeneouse media, Radiophys. Quant. Electron. 19, 811–816 (1976).

    Article  ADS  Google Scholar 

  33. S.N. Vlasov, V.A. Petrischev, V.I. Talanov: Average description of wave beams in linear and nonlinear media, Radiophys. Quant. Electron. 14, 1062–1070 (1971).

    Article  ADS  Google Scholar 

  34. V.N. Goldberg, V.I. Talanov, R.E. Erm: Self-focusing of axiall-symmetrical wave beams, Radiophys. Quant. Electron. 10, 368–375 (1967).

    Article  ADS  Google Scholar 

  35. S.N. Vlasov: Instability of an intensive plane wave in periodically nonlinear media, Sov. J. Quant. Electron. 6, 245–246 (1976).

    Article  ADS  Google Scholar 

  36. S.N. Vlasov: Stabilization of instability of a plane wave in a periodic system, Technical Physics Letters (Pis’ma v Zhurnal Tekhnicheskoi Fisiki) 4, 795–800 (1978).

    ADS  Google Scholar 

  37. S.N. Vlasov, V.E. Yashin: Self-focusing suppression in neodymium–glass laser systems by means of relay, Sov. J. Quant. Electron. 11, 313–318 (1981).

    Article  ADS  Google Scholar 

  38. S.N. Vlasov, V.A. Petrischev, V.I. Talanov: Nonlinear quasi-optical system, Radiophys. Quant. Electron. 15, 886–894 (1972).

    Article  ADS  Google Scholar 

  39. L.V. Piskunova, V.I. Talanov, S.N. Vlasov: Field structure near a singularity produced on self-focusing in a cubic medium, Sov. Phys. JETP 48, 808–812 (1978).

    ADS  Google Scholar 

  40. D. Wood: The self-focusing singularity in nonlinear Schrodinger equation, Stud-ies in Appl. Math. 71, 103–115 (1984).

    MATH  Google Scholar 

  41. G.M. Fraiman: Asymptotic stability of manifold of self-similar solutions on self-focusing, Sov. Phys. JETP 61, 228 (1985).

    MathSciNet  Google Scholar 

  42. M.J. Landman, G.C. Papanicolaou, C. Sulem et al.: Rate of blowup for solution of the nonlinear Schrodinger equation at critical dimension, Phys. Rev. A 38, 3837–3843 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  43. B.J. Mesurier, G.C. Papanicolaou, C. Sulem et al.: Local structure on the self-focusing singularity of the cubic Schrodinger equation, Physica D Nonlinear Phenomena 32, 210–226 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  44. S.N. Vlasov: The structure of the circularly polarized wave beam field in the vicinity of a nonlinear focus in a cubically nonlinear medium, Sov. J. Quant. Electron. 17, 1191–1193 (1987).

    Article  ADS  Google Scholar 

  45. M.D. Feit, J.A. Fleck, Jr.: Beam nonparaxiality, filament formation, and beam break-up in self-focusing of optical beams, J. Opt. Soc. Am. B 5, 633–640 (1988)

    Article  ADS  Google Scholar 

  46. V.N. Lugovoi, A.M. Prokhorov: Theory of the propagation of high-power laser radiation in a nonlinear medium, Sov. Phys. Uspekhi. 16, 658–679 (1974)

    Article  ADS  Google Scholar 

  47. A.L. Dyshko, V.N. Lugovoi, A.M. Prokhorov: Self-focusing of intense light beams, JETP Lett. 6, 146–148 (1968)

    ADS  Google Scholar 

  48. A.L. Dyshko, V.N. Lugovoi, A.M. Prokhorov: Multifocus structure of a light beam in a nonlinear medium, Sov. Phys. JETP 34, 1235–1241 (1972)

    ADS  Google Scholar 

  49. V.N. Lugovoi, A.M. Prokhorov: A possible explanation of the small-scale self-focusing filaments, JETP Lett. 7, 117–119 (1968)

    ADS  Google Scholar 

  50. L.V. Piskunova, V.I. Talanov, S.N. Vlasov: Three-dimensional wave collapse in a nonlinear Schrodinger equation model, Sov. Phys. JETP 68, 1125–1128 (1989).

    Google Scholar 

  51. E.A. Kuznetsov, V.E. Zakharov: Quasi-classical theory of three-dimensional wave collapse, Sov. Phys. JETP 64, 773 (1986).

    Google Scholar 

  52. A.G. Litvak, T.A. Petrova, A.M. Sergeev et al.: About multiple splitting of wave structures in nonlinear media, JETP Lett. 44, 12–15 (1986).

    Google Scholar 

  53. A.G. Litvak, V.A. Mironov, N.A. Zharova: The structural features of wave collapse in medium with normal group velocity dispersion, Sov. Phys. JETP 96, 643–652 (2003).

    Article  ADS  Google Scholar 

  54. V.A. Petrischev, V.I. Talanov: About nonstationary self-focusing of light, Sov. J. Quant. Electron. 1, 587–592, (1972).

    Article  Google Scholar 

  55. V.I. Talanov: Some questions of self-focusing theory, Sov.t Phys. Uspekhi 15, 521–522 (1972).

    Article  MathSciNet  ADS  Google Scholar 

  56. R.R. Alphano, S.L. Shapiro: Observation of self-phase modulation and small-scale filaments in crystal and glasses, Phys. Rev. Lett. 24, 592–594 (1970).

    Article  ADS  Google Scholar 

  57. N.G. Bondarenko, I.V. Eremina, V.I. Talanov: Broadening of spectrum in self-focusing of light beams in crystals, JETP Lett. 12, 85–87 (1970); Errata 12, 267.

    Google Scholar 

  58. V.I. Talanov, S.N. Vlasov: Modulational instability at sum and difference frequencies in media with a high-order nonlinearity, JETP Lett. 60, 639–642 (1994).

    ADS  Google Scholar 

  59. A.G. Litvak, V.A. Mironov, S. A. Skobelev: Dynamics of self-action of super-short electromagnetic pulses, JETP Lett. 82, 119–123 (2005).

    Article  Google Scholar 

  60. D.J. Kaup, A.C. Newell: An exact solution for a derivative nonlinear Schrödinger equation, J. Math. Phys. 19, 798 (1978).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  61. H. Stendel: The hierarchy of multi-solitons of the derivative nonlinear Schrödinger equation, J. Phys. A Math. Gen. 36, 1931 (2003).

    Article  ADS  Google Scholar 

  62. A.G. Litvak, V.A. Mironov, N.A. Zharova: Selfaction of shock wave envelopes in nonlinear dispersive medium, Sov. Phys. JETP 103, 15–22 (2006).

    Article  ADS  Google Scholar 

  63. S.A. Kozlov, Yu.A. Shpolyanskiy, A.O. Oukrainski et al: Spectral evolution of propagation extremely short pulses, Phys. Vibration 7, 19–27 (1999).

    Google Scholar 

  64. Th. Brabec, F. Krausz: Nonlinear optical pulse propagation in the single-cycle regime. Phys. Rev. Lett. 78, 3282–3285 (1997).

    Article  ADS  Google Scholar 

  65. M. Kolesic, J.V. Moloney: Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations, Phys. Rev. E-70, 036604 (2004).

    ADS  Google Scholar 

  66. A. Ferrando, M. Zacares, P.F. Cordoba et al.: Forward–backward equations for nonlinear propagation in axially invariant optical systems, Phys. Rev. E-71, 016601 (2005).

    ADS  Google Scholar 

  67. S.N. Vlasov, E.V. Koposova, V.I. Talanov: Use of decomposition of the wave equations and pseudo-differential operators for the description of nonparaxial beams and broadband wave packets. Radiophys. Quant. Electron., 49, 258–301 (2006).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Physics of RAS, Nizhniy Novgorod, Russia

    G. M. Fraiman

Authors
  1. G. M. Fraiman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A.G. Litvak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V.I. Talanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S.N. Vlasov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Rochester, Rochester, NY, UK

    Robert W. Boyd  & Svetlana G. Lukishova  & 

  2. University of California, Berkeley, CA

    Y.R. Shen

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Fraiman, G.M., Litvak, A., Talanov, V., Vlasov, S. (2009). Optical Self-Focusing: Stationary Beams and Femtosecond Pulses. In: Boyd, R.W., Lukishova, S.G., Shen, Y. (eds) Self-focusing: Past and Present. Topics in Applied Physics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-0-387-34727-1_3

Download citation

Publish with us

Policies and ethics

Search

Navigation