Stable bound states of one-dimensional autosolitons in a bistable laser

A. G. Vladimirov; G. V. Khodova; N. N. Rosanov

doi:10.1103/PhysRevE.63.056607

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Stable bound states of one-dimensional autosolitons in a bistable laser

A. G. Vladimirov¹, G. V. Khodova², and N. N. Rosanov²

¹Physics Faculty, St. Petersburg State University, 1 Ulianovskaya Street, 198904 St. Petersburg, Russia
²Institute for Laser Physics, Birzhevaya line 12, 199034 St. Petersburg, Russia

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Phys. Rev. E 63, 056607 – Published 16 April, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.056607

Abstract

Differential equations describing the interaction of two weakly overlapping autosolitons in the transverse section of a wide-aperture laser with a saturable absorber are derived and analyzed. The existence of in-phase and out-of-phase stable bound autosoliton states is predicted analytically and confirmed numerically.

References (21)

N. N. Rosanov, Optical Bistability and Hysteresis in Distributed Nonlinear Systems (Nauka, Moscow, 1997).
N. N. Rosanov and G. V. Khodova, Opt. Spectrosk. 64, 1375 (1988) [Opt. Spectrosc. 64, 449 (1988)]; J. Opt. Soc. Am. 7, 1075 (1990).
M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 73, 640 (1994); M. Tlidi and P. Mandel, Chaos, Solitons Fractals 4, 1475 (1994).
W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).
M. Saffman, D. Montgomery, and D. Z. Andreson, Opt. Lett. 19, 518 (1994).
V. B. Taranenko, K. Staliunas, and C. O. Weiss, Phys. Rev. A 56, 1582 (1997).
H. R. Brand and R. J. Deissler, Phys. Rev. Lett. 63, 2801 (1989).
B. A. Malomed, Phys. Rev. A 44, 6954 (1991).
B. A. Malomed, Phys. Rev. E 58, 7928 (1998).
V. V. Afanasjev, B. A. Malomed, and P. L. Chu, Phys. Rev. E 56, 6020 (1997).
V. V. Afanasjev and N. Akhmediev, Phys. Rev. E 53, 6471 (1996).
N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. Lett. 79, 4047 (1997); J. Opt. Soc. Am. B 15, 515 (1998).
M. Brambilla, L. A. Lugiato, and M. Stefani, Europhys. Lett. 34, 109 (1996).
A. G. Vladimirov, N. N. Rosanov, S. V. Fedorov, and G. V. Khodova, Quantum Electron. 27, 949 (1997); ibid.28, 55 (1998); A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, and N. N. Rosanov, J. Opt. B: Quantum Semiclassical Opt. 1, 101 (1999).
E. A. Ostrovskaya and Y. S. Kivshar, J. Opt. B: Quantum Semiclassical Opt. 1, 77 (1999); E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
D. V. Skryabin and W. J. Firth, Opt. Lett. 24, 1056 (1999).
B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).
N. V. Vyssotina, L. A. Nesterov, N. N. Rosanov, and V. A. Smirnov, Opt. Spektrosk. 85, 239 (1998) [Opt. Spectrosc. 85, 218 (1998)].
K. Staliunas, Phys. Rev. A 48, 1573 (1993).
K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981); ibid.I. S. Aranson, K. A. Gorshkov, A. S. Lomov, and M. I. Rabinovich, 43, 435 (1990).
V. V. Afanasjev, Opt. Lett. 18, 790 (1993).

[c1] N. N. Rosanov, Optical Bistability and Hysteresis in Distributed Nonlinear Systems (Nauka, Moscow, 1997).

[c2] N. N. Rosanov and G. V. Khodova, Opt. Spectrosk. 64, 1375 (1988) [Opt. Spectrosc. 64, 449 (1988)]; J. Opt. Soc. Am. 7, 1075 (1990).

[c3] M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 73, 640 (1994); M. Tlidi and P. Mandel, Chaos, Solitons Fractals 4, 1475 (1994).

[c4] W. J. Firth and A. J. Scroggie, Phys. Rev. Lett. 76, 1623 (1996).

[c5] M. Saffman, D. Montgomery, and D. Z. Andreson, Opt. Lett. 19, 518 (1994).

[c6] V. B. Taranenko, K. Staliunas, and C. O. Weiss, Phys. Rev. A 56, 1582 (1997).

[c7] H. R. Brand and R. J. Deissler, Phys. Rev. Lett. 63, 2801 (1989).

[c8] B. A. Malomed, Phys. Rev. A 44, 6954 (1991).

[c9] B. A. Malomed, Phys. Rev. E 58, 7928 (1998).

[c10] V. V. Afanasjev, B. A. Malomed, and P. L. Chu, Phys. Rev. E 56, 6020 (1997).

[c11] V. V. Afanasjev and N. Akhmediev, Phys. Rev. E 53, 6471 (1996).

[c12] N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. Lett. 79, 4047 (1997); J. Opt. Soc. Am. B 15, 515 (1998).

[c13] M. Brambilla, L. A. Lugiato, and M. Stefani, Europhys. Lett. 34, 109 (1996).

[c14] A. G. Vladimirov, N. N. Rosanov, S. V. Fedorov, and G. V. Khodova, Quantum Electron. 27, 949 (1997); ibid.28, 55 (1998); A. G. Vladimirov, S. V. Fedorov, N. A. Kaliteevskii, G. V. Khodova, and N. N. Rosanov, J. Opt. B: Quantum Semiclassical Opt. 1, 101 (1999).

[c15] E. A. Ostrovskaya and Y. S. Kivshar, J. Opt. B: Quantum Semiclassical Opt. 1, 77 (1999); E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).

[c16] D. V. Skryabin and W. J. Firth, Opt. Lett. 24, 1056 (1999).

[c17] B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, Phys. Rev. Lett. 85, 748 (2000).

[c18] N. V. Vyssotina, L. A. Nesterov, N. N. Rosanov, and V. A. Smirnov, Opt. Spektrosk. 85, 239 (1998) [Opt. Spectrosc. 85, 218 (1998)].

[c19] K. Staliunas, Phys. Rev. A 48, 1573 (1993).

[c20] K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981); ibid.I. S. Aranson, K. A. Gorshkov, A. S. Lomov, and M. I. Rabinovich, 43, 435 (1990).

[c21] V. V. Afanasjev, Opt. Lett. 18, 790 (1993).

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Stable bound states of one-dimensional autosolitons in a bistable laser

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