Abstract
The nonlinear dynamics of a vector two-component optical pulse propagating in quasi-resonance conditions in a medium of nonsymmetric quantum objects is investigated for Stark splitting of quantum energy levels by an external electric field. We consider the case when the ordinary component of the optical pulse induces σ transitions, while the extraordinary component induces the π transition and shifts the frequencies of the allowed transitions due to the dynamic Stark effect. It is found that under Zakharov-Benney resonance conditions, the propagation of the optical pulse is accompanied by generation of an electromagnetic pulse in the terahertz band and is described by the vector generalization of the nonlinear Yajima-Oikawa system. It is shown that this system (as well as its formal generalization with an arbitrary number of optical components) is integrable by the inverse scattering transformation method. The corresponding Darboux transformations are found for obtaining multisoliton solutions. The influence of transverse effects on the propagation of vector solitons is investigated. The conditions under which transverse dynamics leads to self-focusing (defocusing) of solitons are determined.
Similar content being viewed by others
References
G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1995; Mir, Moscow, 1996).
Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, New York, 2003; Fizmatlit, Moscow, 2005).
N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman and Hall, London, 1997; Fizmatlit, Moscow, 2003).
A. I. Maimistov, Pramana 57, 953 (2001).
S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (Nauka, Moscow, 1988; American Institute of Physics, New York, 1991).
A. M. Basharov and A. I. Maimistov, Opt. Spectrosc. 88(3), 380 (2000).
A. I. Maimistov, Kvantovaya Electron. (Moscow) 22, 936 (1995).
S. P. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method (Nauka, Moscow, 1980; Springer, New York, 1984).
G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980; Mir, Moscow, 1983).
Solitons, Ed. by R. Bullough and Ph. Caudry (Springer, Heidelberg, 1980; Mir, Moscow, 1983).
R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, New York, 1984; Mir, Moscow, 1988).
S. V. Manakov, Sov. Phys. JETP 40(2), 269 (1974).
D. A. Bagdasaryan, A. O. Makaryan, and P. S. Pogosyan, JETP Lett. 37(10), 594 (1983).
D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984).
P. G. Kryukov, Femtosecond Pulses (Fizmatlit, Moscow, 2008) [in Russian].
U. A. Abdullin, G. A. Lyakhov, O. V. Rudenko, and A. S. Chirkin, Sov. Phys. JETP 39(4), 633 (1974).
S. V. Sazonov and A. F. Sobolevskii, JETP Lett. 75(12), 621 (2002).
S. V. Sazonov and A. F. Sobolevskii, JETP 96(6), 1019 (2003).
S. V. Sazonov and A. F. Sobolevskii, Kvantovaya Elektron. (Moscow) 35, 1019 (2005).
N. Yajima and M. Oikawa, Prog. Theor. Phys. 56, 1719 (1976).
Y. C. Ma, Stud. Appl. Math. 59, 201 (1978).
V. E. Zakharov, Sov. Phys. JETP 35(5), 908 (1972).
S. Kočinac, Z. Ikonić, and V. Milanović, Opt. Commun. 140, 89 (1997).
L. W. Casperson, Phys. Rev. A: At., Mol., Opt. Phys. 57, 609 (1998).
M. Agrotis, N. M. Ercolani, S. V. Glasgow, and G. V. Moloney, Physica D (Amsterdam) 138, 134 (2000).
A. A. Zabolotskii, JETP 94(5), 869 (2002).
A. I. Maimistov and J.-G. Caputo, Opt. Spectrosc. 94(2), 245 (2003).
S. V. Sazonov, JETP 97(4), 722 (2003).
H. Vogt, Phys. Rev. B: Condens. Matter 58, 9916 (1998).
W. Yang, S. Gong, R. Li, and Z. Xu, Phys. Rev. A: At., Mol., Opt. Phys. 74, 013407 (2006).
I. I. Sobel’man, Introduction to the Theory of Atomic Spectra (Pergamon, Oxford, 1972; Nauka, Moscow, 1977).
L. Allen and J. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975; Mir, Moscow, 1978).
S. V. Sazonov and N. V. Ustinov, JETP 100(2), 256 (2005).
J. D. Gibbon, P. J. Caudrey, J. C. Eilbeck, and R. K. Bullough, J. Phys. A: Math. Gen. 6, 1237 (1973).
M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, Theory of Waves (Nauka, Moscow, 1990) [in Russian].
V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer, Berlin, 1991).
A. G. Stepanov, A. A. Mel’nikov, V. O. Kompanets, and S. V. Chekalin, JETP Lett. 85(5), 227 (2007).
A. N. Bugai and S. V. Sazonov, JETP Lett. 87(8), 403 (2008).
S. K. Zhdanov and B. A. Trubnikov, Sov. Phys. JETP 65(5), 904 (1987).
S. K. Zhdanov and B. A. Trubnikov, Quasi-Gaseous Unstable Media (Nauka, Moscow, 1991) [in Russian].
S. V. Sazonov, JETP 98(6), 1237 (2004).
N. V. Karlov and N. A. Kirichenko, Vibrations, Waves, and Structures (Nauka, Moscow, 2001) [in Russian].
R. E. Slusher and H. H. Gibbs, Phys. Rev. Lett. 24, 638 (1970).
S. N. Vlasov, V. I. Talanov, and V. A. Petrishchev, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 14, 1353 (1971).
L. A. Bol’shov, V. V. Likhanskii, and M. I. Persiantsev, Sov. Phys. JETP 57(3), 524 (1983).
A. I. Maimistov, Kvantovaya Elektron. (Moscow) 11, 567 (1984).
L. A. Bol’shov and V. V. Likhanskii, Kvantovaya Elektron. (Moscow) 12, 1339 (1985).
A. M. Basharov and A. I. Maimistov, Sov. Phys. JETP 67(12), 2426 (1988).
H. Steudel, J. Mod. Opt. 35, 693 (1988).
A. N. Bugay and S. V. Sazonov, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 74, 066608 (2006).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.V. Sazonov, N.V. Ustinov, 2012, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2012, Vol. 142, No. 5, pp. 842–861.
Rights and permissions
About this article
Cite this article
Sazonov, S.V., Ustinov, N.V. Propagation of vector solitons in a quasi-resonant medium with stark deformation of quantum states. J. Exp. Theor. Phys. 115, 741–758 (2012). https://doi.org/10.1134/S1063776112090117
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776112090117