Transformations of continuously self-focusing and continuously self-defocusing dissipative solitons
Optics Express, Vol. 16, Issue 20, pp. 15388-15401 (2008)
http://dx.doi.org/10.1364/OE.16.015388
Acrobat PDF (934 KB)
Abstract
Dissipative media admit the existence of two types of stationary self-organized beams: continuously self-focused and continuously self-defocused. Each beam is stable inside of a certain region of its existence. Beyond these two regions, beams loose their stability, and new dynamical behaviors appear. We present several types of instabilities related to each beam configuration and give examples of beam dynamics in the areas adjacent to the two regions. We observed that, in one case beams loose the radial symmetry while in the other one the radial symmetry is conserved during complicated beam transformations.
© 2008 Optical Society of America
1. Introduction
1. (Eds.)N. Akhmediev and A. Ankiewicz, Dissipative solitons Lecture Notes in Physics, V. 661 (Springer, Heidelberg, 2005). [CrossRef]
3. M. Tlidi, M. Taki, and T. Kolokolnikov, “Dissipative Localized Structures in Extended Systems,” Chaos 17, 037101, 2007. [CrossRef] [PubMed]
4. M. Tlidi, A. Vladimirov, and P. Mandel, “Curvature instability in passive diffractive resonators,” Phys. Rev. Lett. 98, 233901, (2002). [CrossRef]
5. I. S. Aranson and L. Kramer, “The world of the complex Ginzburg-Landau equation,” Rev. Mod. Phys. 74, 99 (2002). [CrossRef]
6. O. Descalzi, G. Düring, and E. Tirapegui, “On the stable hole solutions in the complex Ginzburg-Landau equation,” Physica A 356, 66–71 (2005). [CrossRef]
7. H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE Journ. of Quantum Electron. , QE-11 (9), 736 (1975). [CrossRef]
8. W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814 (2008). [CrossRef]
9. A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604(R) (2005). [CrossRef]
10. M. Taki, N. Ouarzazi, H. Ward, and P. Glorieux, “Nonlinear front propagation in optical parametric oscillators,” J. Opt. Soc. Am. B 17, 997 (2000). [CrossRef]
12. E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, “Stable dissipative solitons in semiconductor optical amplifiers,” Phys. Rev. Lett. 90, 253903 (2003). [CrossRef] [PubMed]
13. C. Montes, A. Mikhailov, A. Picozzi, and F. Ginovart, “Dissipative three-wave structures in stimulated backscattering. I. A subluminous solitary attractor,” Phys. Rev. E 55, 1086 (1997). [CrossRef]
14. R. J. Deissler and H. R. Brand, “Periodic, quasiperiodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation,” Phys. Rev. Lett. 72, 478–481 (1994). [CrossRef] [PubMed]
15. X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, “Cavity solitons in a driven VCSEL above threshold,” J. of Sel. Topics on Quant. Electr. 12, 339–351 (2006). [CrossRef]
16. A. Ankiewicz, N. Devine, N. Akhmediev, and J. M. Soto-Crespo “Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media,” Phys. Rev. A 77, 033840 (2008). [CrossRef]
17. J. M. Soto-Crespo, N. Akhmediev, and y A. Ankiewicz. “Pulsating, creeping and erupting solitons in dissipative systems,” hys. Rev. Lett. 85, 2937 (2000). [CrossRef]
18. Akhmediev. J. M. Soto-Crespo and G. Town “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation,” Phys. Rev. E. 63, 056602 (2001). [CrossRef]
2. Statement of the problem
16. A. Ankiewicz, N. Devine, N. Akhmediev, and J. M. Soto-Crespo “Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media,” Phys. Rev. A 77, 033840 (2008). [CrossRef]
16. A. Ankiewicz, N. Devine, N. Akhmediev, and J. M. Soto-Crespo “Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media,” Phys. Rev. A 77, 033840 (2008). [CrossRef]
16. A. Ankiewicz, N. Devine, N. Akhmediev, and J. M. Soto-Crespo “Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media,” Phys. Rev. A 77, 033840 (2008). [CrossRef]
16. A. Ankiewicz, N. Devine, N. Akhmediev, and J. M. Soto-Crespo “Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media,” Phys. Rev. A 77, 033840 (2008). [CrossRef]
16. A. Ankiewicz, N. Devine, N. Akhmediev, and J. M. Soto-Crespo “Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media,” Phys. Rev. A 77, 033840 (2008). [CrossRef]
3. Bifurcation diagrams
4. Period-1 pulsating solitons
18. Akhmediev. J. M. Soto-Crespo and G. Town “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation,” Phys. Rev. E. 63, 056602 (2001). [CrossRef]
22. E. Tsoy and N. Akhmediev, “Bifurcations from stationary to pulsating solitons in the cubic quintic complex Ginzburg Landau equation,” Phys. Lett. A 343, 417–422 (2005). [CrossRef]
5. Elliptic beam oscillations
6. More complicated pulsations
7. Beam evolution around the region of continuously self-defocusing beams
17. J. M. Soto-Crespo, N. Akhmediev, and y A. Ankiewicz. “Pulsating, creeping and erupting solitons in dissipative systems,” hys. Rev. Lett. 85, 2937 (2000). [CrossRef]
18. Akhmediev. J. M. Soto-Crespo and G. Town “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation,” Phys. Rev. E. 63, 056602 (2001). [CrossRef]
8. Conclusion
Acknowledgments
References and links
1. | (Eds.)N. Akhmediev and A. Ankiewicz, Dissipative solitons Lecture Notes in Physics, V. 661 (Springer, Heidelberg, 2005). [CrossRef] |
2. | Dissipative Solitons: From optics to biology and medicine Lecture Notes in Physics, V 751, (Eds.) N. Akhmediev and A. Ankiewicz, (Springer, Berlin-Heidelberg, 2008). |
3. | M. Tlidi, M. Taki, and T. Kolokolnikov, “Dissipative Localized Structures in Extended Systems,” Chaos 17, 037101, 2007. [CrossRef] [PubMed] |
4. | M. Tlidi, A. Vladimirov, and P. Mandel, “Curvature instability in passive diffractive resonators,” Phys. Rev. Lett. 98, 233901, (2002). [CrossRef] |
5. | I. S. Aranson and L. Kramer, “The world of the complex Ginzburg-Landau equation,” Rev. Mod. Phys. 74, 99 (2002). [CrossRef] |
6. | O. Descalzi, G. Düring, and E. Tirapegui, “On the stable hole solutions in the complex Ginzburg-Landau equation,” Physica A 356, 66–71 (2005). [CrossRef] |
7. | H. A. Haus, “Theory of mode locking with a slow saturable absorber,” IEEE Journ. of Quantum Electron. , QE-11 (9), 736 (1975). [CrossRef] |
8. | W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814 (2008). [CrossRef] |
9. | A. Komarov, H. Leblond, and F. Sanchez, “Quintic complex Ginzburg-Landau model for ring fiber lasers,” Phys. Rev. E 72, 025604(R) (2005). [CrossRef] |
10. | M. Taki, N. Ouarzazi, H. Ward, and P. Glorieux, “Nonlinear front propagation in optical parametric oscillators,” J. Opt. Soc. Am. B 17, 997 (2000). [CrossRef] |
11. | N. N. Rosanov, Solitons in laser systems with saturable absorption, Dissipative solitons Lecture Notes in Physics, V. 661, (Eds.) N. Akhmediev and A. Ankiewicz, (Springer, Heidelberg, 2005). |
12. | E. A. Ultanir, G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, “Stable dissipative solitons in semiconductor optical amplifiers,” Phys. Rev. Lett. 90, 253903 (2003). [CrossRef] [PubMed] |
13. | C. Montes, A. Mikhailov, A. Picozzi, and F. Ginovart, “Dissipative three-wave structures in stimulated backscattering. I. A subluminous solitary attractor,” Phys. Rev. E 55, 1086 (1997). [CrossRef] |
14. | R. J. Deissler and H. R. Brand, “Periodic, quasiperiodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation,” Phys. Rev. Lett. 72, 478–481 (1994). [CrossRef] [PubMed] |
15. | X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, “Cavity solitons in a driven VCSEL above threshold,” J. of Sel. Topics on Quant. Electr. 12, 339–351 (2006). [CrossRef] |
16. | A. Ankiewicz, N. Devine, N. Akhmediev, and J. M. Soto-Crespo “Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media,” Phys. Rev. A 77, 033840 (2008). [CrossRef] |
17. | J. M. Soto-Crespo, N. Akhmediev, and y A. Ankiewicz. “Pulsating, creeping and erupting solitons in dissipative systems,” hys. Rev. Lett. 85, 2937 (2000). [CrossRef] |
18. | Akhmediev. J. M. Soto-Crespo and G. Town “Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation,” Phys. Rev. E. 63, 056602 (2001). [CrossRef] |
19. | J. M. Soto-Crespo, Ph. Grelu, and N. Akhmediev “Optical bullets and “rockets” in nonlinear dissipative systems and their transformations and interactions,” Opt. Express 14, 4013 (2006). [CrossRef] [PubMed] |
20. | J. M. Soto-Crespo, N. Akhmediev, and Ph. Grelu “Optical bullets and double bullet complexes in dissipative systems,” Phys. Rev. E 74, 046612 (2006). [CrossRef] |
21. | N. Akhmediev, J.M. Soto-Crespo, and Ph. Grelu, “Vibrating and shaking soliton pairs in dissipative systems.” Phys. Lett. A 364, 413 (2007). [CrossRef] |
22. | E. Tsoy and N. Akhmediev, “Bifurcations from stationary to pulsating solitons in the cubic quintic complex Ginzburg Landau equation,” Phys. Lett. A 343, 417–422 (2005). [CrossRef] |
OCIS Codes
(190.3100) Nonlinear optics : Instabilities and chaos
(190.6135) Nonlinear optics : Spatial solitons
ToC Category:
Nonlinear Optics
History
Original Manuscript: July 18, 2008
Manuscript Accepted: August 27, 2008
Published: September 15, 2008
Citation
J. M. Soto-Crespo, N. Akhmediev, N. Devine, and C. Mejía-Cortés, "Transformations of continuously self-focusing and continuously self-defocusing dissipative solitons," Opt. Express 16, 15388-15401 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15388
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References
- (Eds.) N. Akhmediev and A. Ankiewicz, Dissipative solitons Lecture Notes in Physics, V. 661 (Springer, Heidelberg, 2005). [CrossRef]
- Dissipative Solitons: From optics to biology and medicine Lecture Notes in Physics, V 751, (Eds.) N. Akhmediev and A. Ankiewicz, (Springer, Berlin-Heidelberg, 2008).
- M. Tlidi, M. Taki, and T. Kolokolnikov, "Dissipative Localized Structures in Extended Systems," Chaos 17, 037101, 2007. [CrossRef] [PubMed]
- M. Tlidi, A. Vladimirov and P. Mandel, "Curvature instability in passive diffractive resonators," Phys. Rev. Lett. 98, 233901, (2002). [CrossRef]
- I. S. Aranson and L. Kramer, "The world of the complex Ginzburg-Landau equation," Rev. Mod. Phys. 74, 99 (2002). [CrossRef]
- O. Descalzi, G. During and E. Tirapegui, "On the stable hole solutions in the complex Ginzburg-Landau equation," Physica A 356, 66-71 (2005). [CrossRef]
- H. A. Haus, "Theory of mode locking with a slow saturable absorber," IEEE Journ. of Quantum Electron., QE-11 (9), 736 (1975). [CrossRef]
- W. H. Renninger, A. Chong, and F. W. Wise, "Dissipative solitons in normal-dispersion fiber lasers," Phys. Rev. A 77, 023814 (2008). [CrossRef]
- A. Komarov, H. Leblond, and F. Sanchez, "Quintic complex Ginzburg-Landau model for ring fiber lasers," Phys. Rev. E 72, 025604(R) (2005). [CrossRef]
- M. Taki, N. Ouarzazi, H. Ward and P. Glorieux, "Nonlinear front propagation in optical parametric oscillators," J. Opt. Soc. Am. B 17, 997 (2000). [CrossRef]
- N. N. Rosanov, Solitons in laser systems with saturable absorption, Dissipative solitons Lecture Notes in Physics, V. 661, (Eds.) N. Akhmediev and A. Ankiewicz, (Springer, Heidelberg, 2005).
- E. A. Ultanir and G. I. Stegeman, D. Michaelis, C. H. Lange, and F. Lederer, "Stable dissipative solitons in semiconductor optical amplifiers," Phys. Rev. Lett. 90, 253903 (2003). [CrossRef] [PubMed]
- C. Montes, A. Mikhailov, A. Picozzi, and F. Ginovart, "Dissipative three-wave structures in stimulated backscattering. I. A subluminous solitary attractor," Phys. Rev. E 55, 1086 (1997). [CrossRef]
- R. J. Deissler and H. R. Brand, "Periodic, quasiperiodic, and chaotic localized solutions of the quintic complex Ginzburg-Landau equation," Phys. Rev. Lett. 72, 478 - 481 (1994). [CrossRef] [PubMed]
- X. Hachair, F. Pedaci, E. Caboche, S. Barland, M. Giudici, J. R. Tredicce, F. Prati, G. Tissoni, R. Kheradmand, L. A. Lugiato, I. Protsenko, and M. Brambilla, "Cavity solitons in a driven VCSEL above threshold," J. of Sel. Topics on Quant.Electr. 12, 339-351 (2006). [CrossRef]
- A. Ankiewicz, N. Devine, N. Akhmediev and J. M. Soto-Crespo "Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media," Phys. Rev. A 77, 033840 (2008). [CrossRef]
- J. M. Soto-Crespo, N. Akhmediev y A. Ankiewicz. "Pulsating, creeping and erupting solitons in dissipative systems," Phys.Rev. Lett. 85, 2937 (2000). [CrossRef]
- Akhmediev. J. M. Soto-Crespo, and G. Town "Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation,"Phys. Rev. E. 63, 056602 (2001). [CrossRef]
- J. M. Soto-Crespo, Ph. Grelu, and N. Akhmediev"Optical bullets and "rockets" in nonlinear dissipative systems and their transformations and interactions," Opt. Express 14, 4013 (2006). [CrossRef] [PubMed]
- J. M. Soto-Crespo, N. Akhmediev and Ph. Grelu "Optical bullets and double bullet complexes in dissipative systems," Phys. Rev. E 74, 046612 (2006). [CrossRef]
- N. AkhmedievJ.M. Soto-Crespo and Ph. Grelu, "Vibrating and shaking soliton pairs in dissipative systems." Phys. Lett. A 364, 413 (2007). [CrossRef]
- E. Tsoy and N. Akhmediev, "Bifurcations from stationary to pulsating solitons in the cubic quintic complex Ginzburg Landau equation," Phys. Lett. A 343, 417-422 (2005). [CrossRef]
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