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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
Sukhorukov, A.P. (1988) Nonlinear Wave Interactions in Optics and Radiophysics, Nauka Publishers, Moscow (in Russian).
Kanashov, A.A and Rubenchik, A.M. (1981) On diffraction and dispersion effects on three wave interaction Physica 4D, 123–134.
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.
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.
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.
Khokhlov, R.V. (1961) On propagation of waves in nonlinear dispersive media, Radiotekh. Elektron. 6, 917–921 (in Russian).
Akhmanov, S.A. and Khokhlov, R.V. (1972) Problems of Nonlinear Optics, Gordon and Breach Publishers, New York (1964, Russian edition).
Bloembergen, N. (1965) Nonlinear Optics, Benjamin Publishers, New York.
Ostrovskii, L.A (1967) Self-action of light in crystals, JETP Lett. 5, 272–275.
Akhmanov, S.A., Sukhorukov, A.P., and Chirkin, A.S. (1969) Nonstationary phenomena and space-time analogy, Sov. Phys. JETP 28, 748–755.
Hayata, K. and Koshiba, M. (1993) Multidimensional solitons in quadratic nonlinear media, Phys Rev. Lett. 71, 3275–3278; (1994), 72, 178 (E).
Werner, Y.J. and Drummond, P.D. (1993) Simulton solitons for the parametric amplifier, J. Opt. Soc. Am. B 10, 2390–2393.
Werner, Y.J. and Drummond, P.D. (1994) Strongly coupled nonlinear parametric solitary waves, Opt. Comm. 19, 613–615.
Kalocsai, A.G. and Haus, J.W. (1994) Nonlinear Schrodinger equation for optical media with quadratic nonlinearity, Phys Rev. A 49, 574–585.
Buryak, A.V. and Kivshar, Yu.S. (1994) Spatial optical solitons governed by quadratic nonlinearity, Opt. Lett. 19, 1612–1614.
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.
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).
Lu, X. and Sukhorukov, A.P. (1996) Three-dimensional spatial solitons in a quadratically nonlinear medium, Bull. RAS, phys. 60(12), 64–69.
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.
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.
Torner, L., Menyuk, C.R., and Stegeman, G.I (1995) Bright solitons with second-order nonlinearities, J. Opt. Soc. Am. B 12, 889–897.
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.
Buryak, A.V. and Kivshar, Yu.S. (1997) Multistability of three-wave parametric self-trapping. Phys. Rev. Lett. 78, 3286–3289.
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.
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.
Zakharov, V.E. and Shabat, A.B. (1971) Sov. Phys. JETP 34, 62.
Kobyakov, A. and Lederer, F. (1996) Cascading of quadratic nonlinearities: An analytical study, Phys. Rev. A 54, 3455–3471.
Danielus, R., Piskarskas, A., Sirutkaitis, V., Stabinis, A., and Jasevichute, J. (1983) Optical parametric oscillators and picosecond spectroscopy, Mokslas Publishers, Vilnius (in Russian).
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.
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.
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.
Lu, X. and Sukhorukov, A.P. (1997) Mutual focusing in media with quadratic nonlinearity, Bull. RAS. phys 61 (in press).
Balashenkov, N.R., Gagarskii, S.V., and Inochkin, M.V. (1989) Nonlinear refraction of light on second harmonic generation, Opt. Spectrosc. 66, 806–808.
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.
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.
Akhmanov, S.A, Vysloukh, V.A., and Chirkin, A.S. (1988) Optics of femtosecond laser pulses, Nauka Publishers, Moscow (in Russian).
Sukhorukov, A.A. On the theory of parametrically coupled solitons with high-order dispersion, Bull. RAS, phys. 61(12) (in press).
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.
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.
Gottwald, G., Grimshaw, R., Malomed, B. (1997) Parametric envelope solitons in coupled Korteweg-de Vries equations, Phys. Lett. A 227, 47–54.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-94-007-0850-1_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-5316-4
Online ISBN: 978-94-007-0850-1
eBook Packages: Springer Book Archive