Dynamics of a large array of globally coupled lasers with distributed frequencies

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 11, Issue 9, 2001, Pages 2359-2374

  Oliva, Ricardo A ^a   Strogatz, Steven H ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035438236     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401003450     Document Type: Article

References (43)

1. Aronson, D. G., Ermentrout, G. B. & Kopell, N. [1990] "Amplitude response of coupled oscillators," Physica D41(3), 403-449.
2. Bel'dyugin, I. M., Zolotarev, M. V. & Shinkareva, I. V. [1991] "Phase-locking of optically coupled lasers in the presence of resonant frequency spread and external noise," Opt. Commun. 85(4), 338-342.
3. Botez, D. & Scifres, D. R. (Eds.) [1994] Diode Laser Arrays (Cambridge University Press, Cambridge, England).
4. Braiman, Y., Kennedy, T. A. B., Wiesenfeld, K. & Khibnik, A. [1995] "Entrainment of solid-state laser arrays," Phys. Rev. A52(2), 1500-1506.
5. Ermentrout, G. B. [1990] "Oscillator death in populations of all to all coupled nonlinear oscillators," Physica D41(2), 219-231.
6. Fabiny, L., Colet, P., Roy, R. & Lenstra, D. [1993] "Coherence and phase dynamics of spatially coupled solid-state lasers," Phys. Rev. A47(5), 4287-4296.
7. Garcia-Ojalvo, J., Casademont, J., Torrent, M. C., Mirasso, C. R. & Sancho, J. M. [1999] "Coherence and synchronization in diode-laser arrays with delayed global coupling," Int. J. Bifurcation and Chaos 9(11), 2225-2229.
8. Golubentsev, A. A., Likhanskii, V. V. & Napartovich, A. P. [1990] "Phase-locking of a two-dimensional laser array with random detuning of eigenfrequencies," Proc. SPIE - Int. Soc. Opt. Eng. 1219, 220-226.
9. Hairer, E., Norsett, S. P. & Wanner, G. [1993] Solving Ordinary Differential Equations I (Springer-Verlag, Berlin).
10. Herrero, R., Figueras, M., Rius, J., Pi, F. & Orriols, G. [2000] "Experimental observation of the amplitude death effect in two coupled nonlinear oscillators," Phys. Rev. Lett. 84(23), 5312-5315.
11. Hohl, A., Gavrielides, A., Erneux, T. & Kovanis, V. [1997] "Localized synchronization in two nonidentical coupled lasers," Phys. Rev. Lett. 23(25), 4745-4748.
12. Hohl, A., Erneux, T., Gavrielides, A. & Kovanis, V. [1998] "Synchronization of coupled semiconductor lasers," Proc. SPIE - Int. Soc. Opt. Eng. 3283, 546-554.
13. Hohl, A., Gavrielides, A., Erneux, T. & Kovanis, V. [1999] "Quasiperiodic synchronization for two delay-coupled semiconductor lasers," Phys. Rev. A59(5), 3941-3949.
14. Jiang, Z. P. & McCall, M. [1993] "Numerical simulation of a large number of coupled lasers," J. Opt. Soc. Am. B10(1), 155-163.
15. Kandidov, V. P., Kondrat'ev, A. V. & Surovitskii, M. B. [1998] "Collective modes of two-dimensional laser arrays in a Talbot cavity," Quant. Electron. 28(8), 692-696.
16. Khibnik, A., Braiman, Y., Kennedy, T. A. B. & Wiesenfeld, K. [1998] "Phase model analysis of two lasers with injected field," Physica D111(1-4), 295-310.
17. Kourtchatov, S. Y., Likhanskii, V. V., Napartovich, A. P., Arecchi, F. T. & Lapucci, A. [1995] "Theory of phase locking of globally coupled laser arrays," Phys. Rev. A52(5), 4089-4094.
18. Kozyreff, G., Vladimirov, A. G. & Mandel P. [2000] "Global coupling with time delay in an array of semiconductor lasers," Phys. Rev. Lett. 85(18), 3809-3812.
19. Kuramoto, Y. [1984] Chemical Oscillations, Waves and Turbulence (Springer-Verlag, Berlin).
20. Kuske, R. & Erneux, T. [1997] "Localized synchronization of two coupled solid state lasers," Opt. Commun. 139(1-3), 125-131.
21. Li, R. & Erneux, T. [1992] "Preferential instability in arrays of coupled lasers," Phys. Rev. A46(7), 4252-4260.
22. Li, R. & Erneux, T. [1993] "Stability conditions for coupled lasers: series coupling versus parallel coupling," Opt. Commun. 99(3&4), 196-200.
23. Li, R. & Erneux, T. [1994] "Bifurcations to standing and traveling waves in large arrays of coupled lasers," Phys. Rev. A49(2), 1301-1312.
24. Matthews, P. C. & Strogatz, S. H. [1990] "Phase diagram for the collective behavior of limit-cycle oscillators," Phys. Rev. Lett. 65(14), 1701-1704.
25. Matthews, P. C., Mirollo, R. E. & Strogatz, S. H. [1991] "Dynamics of a large system of coupled nonlinear oscilators," Physica D52(2&3), 293-331.
26. Mirollo, R. E. & Strogatz, S. H. [1990] "Amplitude death in an array of limit-cycle oscillators," J. Stat. Phys. 60(1&2), 245-262.
27. Moller, M., Forsmann, B. & Lange, W. [1998] "Instabilities in coupled Nd:YVO4 microchip lasers," Quant. Semicl. Opt. 10(6), 839-848.
28. Moller, M., Forsmann, B. & Lange, W. [1999] "Amplitude instability in coupled Nd:YVO4 microchip lasers," Chaos Solit. Fract. 10(4&5), 825-829.
29. Moller, M., Forsmann, B. & Lange, W. [2000] "Dynamics of three coupled Nd:YVO4 microchip lasers," J. Opt. B. Quant. S O 2(3), 371-374.
30. Rahman, L. & Winful, H. G. [1994] "Nonlinear dynamics of semiconductor laser arrays: A mean field model," IEEE J. Quant. Electron. 30(6), 1405-1416.
31. Reddy, D. V. R., Sen, A. & Johnston, G. L. [2000] "Experimental evidence of time-delay-induced death in coupled limit-cycle oscillators," Phys. Rev. Lett. 85(16), 3381-3384.
32. Schönnagel, H. & Glas, P. [1996] "Coherent coupling of mutually nonresonant waveguide lasers by synchronization of supermodes from locally composed mode clusters," J. Opt. Soc. Am. B13(5), 938-945.
33. Silber, M., Fabiny, L. & Wiesenfeld, K. [1993] "Stability results for in-phase and splay-phase states of solid-state laser arrays," J. Opt. Soc. Am. B10(6), 1121-1129.
34. Strogatz, S. H. [2000] "From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators," Physica D143(1-4), 1-20.
35. Thornburg, K. S., Moller, M., Roy, R., Carr, T. W., Li, R. D. & Erneux, T. [1997] "Chaos and coherence in coupled lasers," Phys. Rev. E55(4), 3865-3869.
36. Tsacoyeanes, J. [1988] "Phase locking and stability properties for two coupled semiconductor lasers," J. Appl. Phys. 64(1), 32-36.
37. Wang, S. S. & Winful, H. G. [1998] "Dynamics of phase-locked semiconductor laser arrays," Appl. Phys. Lett. 52(21), 1774-1776.
38. Winfree, A. T. [1980] Geometry of Biological Time (Springer-Verlag, NY).
39. Winful, H. G. & Wang, S. S. [1988] "Stability of phase locking in semiconductor laser arrays," Appl. Phys. Lett. 53(20), 1894-1896.
40. Winful, H. G. & Rahman, L. [1990] "Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers," Phys. Rev. Lett. 65(13), 1575-1578.
41. Winful, H. G. [1992] "Instability threshold for an array of coupled semiconductor lasers," Phys. Rev. A46(9), 6093-6094.
42. Winful, H. G., Allen, S. & Rahman, L. [1993] "Validity of the coupled-oscillator model for laser-array dynamics," Opt. Lett. 18(21), 1810-1812.
43. Zehnle, V. [2000] "Theoretical model for coupled solid-state lasers," Phys. Rev. A62(3), 033814/1-10.