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Part of the book series: NATO Science Series ((ASHT,volume 61))

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Abstract

Nonlinear dispersion of coupled cw plane waves in quadratic media is considered. The parametric 2D- and 3D-soliton properties are discussed taking into account diffraction, dispersion and walk-off effect. Mutual self-focusing and defocusing are examined in the frame of ray optics theory. The formation of half-period parametric solitons due to femtosecond pulse interaction is also presented.

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References

  1. Karamzin, Ju.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 converters, JETP Lett. 20, 339–342.

    ADS  Google Scholar 

  2. Karamzin, Ju.N. and Sukhorukov, A.P. (1976) Mutual focusing of high-power light beams in media with quadratic nonlinearity, Sov. Phys. JETP 42, 414–420.

    Google Scholar 

  3. Karamzin, Ju.N., Sukhorukov, A.P., and Filipchuk, T.S. (1978) On a new class of coupled solitons in a dispersive medium with quadratic nonlinearity, Moscow Univ. Phys. Bull. 33(3), 73–79.

    Google Scholar 

  4. Sukhorukov, A.P. (1988) Nonlinear Wave Interactions in Optics and Radiophysics, Nauka Publishers, Moscow (in Russian).

    Google Scholar 

  5. Kanashov, A.A and Rubenchik, A.M. (1981) On diffraction and dispersion effects on three wave interaction Physica 4D, 123–134.

    ADS  Google Scholar 

  6. Torruellas, W.E., Wang, Z., Hagan, D.J., Van Stryland, E.W., Stegeman, G.I., Torner, L., and Menyuk, C.R. (1995) Observation of two-dimensional solitary waves in a quadratic medium, Phys. Rev. Lett. 74, 5036–5039.

    Article  ADS  Google Scholar 

  7. Schiek, R., Baek, Y., and Stegeman, G.I. (1996) One-dimensional spatial solitons due to cascaded second-order nonlinearities in planar waveguides, Phys. Rev. E 53, 1138–114.

    ADS  Google Scholar 

  8. Akhmanov, S.A, Sukhorukov, A.P., and Khokhlov, R.V. (1964) Self-focusing and diffraction of light in a nonlinear medium, Sov. Phys. Usp. 93, 609–636.

    Google Scholar 

  9. Khokhlov, R.V. (1961) On propagation of waves in nonlinear dispersive media, Radiotekh. Elektron. 6, 917–921 (in Russian).

    Google Scholar 

  10. Akhmanov, S.A. and Khokhlov, R.V. (1972) Problems of Nonlinear Optics, Gordon and Breach Publishers, New York (1964, Russian edition).

    Google Scholar 

  11. Bloembergen, N. (1965) Nonlinear Optics, Benjamin Publishers, New York.

    Google Scholar 

  12. Ostrovskii, L.A (1967) Self-action of light in crystals, JETP Lett. 5, 272–275.

    ADS  Google Scholar 

  13. Akhmanov, S.A., Sukhorukov, A.P., and Chirkin, A.S. (1969) Nonstationary phenomena and space-time analogy, Sov. Phys. JETP 28, 748–755.

    ADS  Google Scholar 

  14. Hayata, K. and Koshiba, M. (1993) Multidimensional solitons in quadratic nonlinear media, Phys Rev. Lett. 71, 3275–3278; (1994), 72, 178 (E).

    Article  ADS  Google Scholar 

  15. Werner, Y.J. and Drummond, P.D. (1993) Simulton solitons for the parametric amplifier, J. Opt. Soc. Am. B 10, 2390–2393.

    ADS  Google Scholar 

  16. Werner, Y.J. and Drummond, P.D. (1994) Strongly coupled nonlinear parametric solitary waves, Opt. Comm. 19, 613–615.

    Google Scholar 

  17. Kalocsai, A.G. and Haus, J.W. (1994) Nonlinear Schrodinger equation for optical media with quadratic nonlinearity, Phys Rev. A 49, 574–585.

    ADS  Google Scholar 

  18. Buryak, A.V. and Kivshar, Yu.S. (1994) Spatial optical solitons governed by quadratic nonlinearity, Opt. Lett. 19, 1612–1614.

    Article  ADS  Google Scholar 

  19. Steblina, V.V., Kivshar, Y.S., Lisak, M., and Malomed, B.A (1995) Self-guided beams in a diffractive χ(2) medium: variational approach, Opt. Comm. 118, 345–352.

    Article  ADS  Google Scholar 

  20. Agranovich, V.M., Darmanyan, S.A., Kamchatov, A.M., Leskova, T.A, and Boardman, A.D. (1997) Variational approach to solitons in systems with cascaded χ(2) nonlinearity, Phys. Rev. E 55 (in press).

    Google Scholar 

  21. Lu, X. and Sukhorukov, A.P. (1996) Three-dimensional spatial solitons in a quadratically nonlinear medium, Bull. RAS, phys. 60(12), 64–69.

    Google Scholar 

  22. Stegeman, G.L, Hagan, D.J., and Torner, L. χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons (1996) J. Opt. and Quantum Electron. 28, 1691.

    Google Scholar 

  23. Torner, L., Menyuk, C.R., Torruellas, W.E., and Stegeman, G.I (1995) Two-dimensional solitons with second-order nonlinearities, Opt. Lett. 20, 13–15.

    Article  ADS  Google Scholar 

  24. Torner, L., Menyuk, C.R., and Stegeman, G.I (1995) Bright solitons with second-order nonlinearities, J. Opt. Soc. Am. B 12, 889–897.

    ADS  Google Scholar 

  25. Malomed, B.A, Andersen, D., and Lisak, M. (1996) Three-wave interaction solitons in a dispersive medium with quadratic nonlinearity, Opt. Comm. 126, 251–254.

    Article  ADS  Google Scholar 

  26. Buryak, A.V. and Kivshar, Yu.S. (1997) Multistability of three-wave parametric self-trapping. Phys. Rev. Lett. 78, 3286–3289.

    Article  ADS  Google Scholar 

  27. Boardman, A.D. and Xie K. (1997) Vector spatial solitons influenced by magneto-optic effects in cascadable nonlinear media, Phys Rev. E 55, 1–11.

    Google Scholar 

  28. Akhmanov, S.A., Chirkin, A.S., Drabovich, K.N., Khokhlov, R.V., and Sukhorukov A. P. (1968) Nonstationary nonlinear optical effects and ultra-short light pulses formation, IEEE. Quant. Electron. QE-4, 598–605.

    Article  ADS  Google Scholar 

  29. Zakharov, V.E. and Shabat, A.B. (1971) Sov. Phys. JETP 34, 62.

    MathSciNet  ADS  Google Scholar 

  30. Kobyakov, A. and Lederer, F. (1996) Cascading of quadratic nonlinearities: An analytical study, Phys. Rev. A 54, 3455–3471.

    ADS  Google Scholar 

  31. Danielus, R., Piskarskas, A., Sirutkaitis, V., Stabinis, A., and Jasevichute, J. (1983) Optical parametric oscillators and picosecond spectroscopy, Mokslas Publishers, Vilnius (in Russian).

    Google Scholar 

  32. Danielus, R., Dubietis, A., Valiulis, G., and Piskarskas, A. (1995) Femtosecond high-contrast pulses from a parametric generator by the self compressed second harmonic of a Nd laser, Opt. Lett. 20, 2225–2227.

    Article  ADS  Google Scholar 

  33. Khaydarov, J. D. V., Andrews, J. H., and Singer, K. D. (1994) Pulse compression in a synchronously pumpud optical parametric oscillator from group-velocity mismatch, Opt. Lett. 19, 831–834.

    Article  ADS  Google Scholar 

  34. Azimov, B.S., Karamzin, Ju.N., Sukhorukov, A.P., and Sukhorukova, A.K (1980) Interaction of weak pulses with a low-frequency high-intensity wave in a dispersive medium, Sov. Phys. JETP. 51, 40–46.

    ADS  Google Scholar 

  35. Lu, X. and Sukhorukov, A.P. (1997) Mutual focusing in media with quadratic nonlinearity, Bull. RAS. phys 61 (in press).

    Google Scholar 

  36. Balashenkov, N.R., Gagarskii, S.V., and Inochkin, M.V. (1989) Nonlinear refraction of light on second harmonic generation, Opt. Spectrosc. 66, 806–808.

    ADS  Google Scholar 

  37. DeSalvo, R., Hagan, D.J., Shiek-Bahae, M., Stegeman, G.I., and Vanherzeale, H. (1992) Self-focusing and self-defocusing by cascaded second-order effects in KTP, Opt. Lett. 17, 28–30.

    Article  ADS  Google Scholar 

  38. Komissarova, M.V. and Sukhorukov, A.P. (1981) On parametric processes in the interference of several channels of wave interaction, Laser Physics 6, 1036–1041.

    Google Scholar 

  39. Akhmanov, S.A, Vysloukh, V.A., and Chirkin, A.S. (1988) Optics of femtosecond laser pulses, Nauka Publishers, Moscow (in Russian).

    Google Scholar 

  40. Sukhorukov, A.A. On the theory of parametrically coupled solitons with high-order dispersion, Bull. RAS, phys. 61(12) (in press).

    Google Scholar 

  41. Dubrovskaya, O.B. and Sukhorukov, A.P. (1992) Interaction of optical pulses with a number of ocsillations in media with quadratic nonlinearity, Bull. RAS, phys. 56(12), 184–188.

    Google Scholar 

  42. Karamzin, Ju.N., Potashnikov, A.S., and Sukhorukov, A.P. (1996) Interaction extremely short electromagnetic pulses in media with quadratic nonlinearity, Bull. RAS, phys. 60(12), 29–38.

    Google Scholar 

  43. Gottwald, G., Grimshaw, R., Malomed, B. (1997) Parametric envelope solitons in coupled Korteweg-de Vries equations, Phys. Lett. A 227, 47–54.

    Article  MathSciNet  MATH  ADS  Google Scholar 

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© 1999 Springer Science+Business Media Dordrecht

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Sukhorukov, A.P. (1999). Diffraction Beam Interaction in Quadratic Nonlinear Media. In: Boardman, A.D., Pavlov, L., Tanev, S. (eds) Advanced Photonics with Second-Order Optically Nonlinear Processes. NATO Science Series, vol 61. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0850-1_6

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  • DOI: https://doi.org/10.1007/978-94-007-0850-1_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5316-4

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