Accumulating regions of winding periodic orbits in optically driven lasers

Physica D: Nonlinear Phenomena

Volumn 173, Issue 1-2, 2002, Pages 97-113

  Krauskopf, Bernd ^a   Wieczorek, Sebastian ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Bifurcation diagrams; Lasers with optical injection; Saddle node Hopf bifurcation; Transition to locking

Indexed keywords

BIFURCATION (MATHEMATICS); CARBON DIOXIDE LASERS; CHAOS THEORY; SEMICONDUCTOR LASERS; SOLID STATE LASERS;

HOPF BIFURCATIONS;

OPTICALLY PUMPED LASERS;

EID: 0036888068     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(02)00650-4     Document Type: Article

References (58)

1. Kobayashi S., Kimura T. Injection locking characteristics of an AlGaAs semiconductor laser IEEE J. Quant. Electron. 16 1980 915-917.
2. Lang R. Injection locking properties of a semiconductor laser IEEE J. Quant. Electron. 18 6 1982 976-983.
3. Mogensen F., Olesen H., Jacobsen G. FM noise suppression and linewidth reduction in an injection-locked semiconductor laser Electron. Lett. 21 1985 696-697.
4. Oppo G.L., Politi A., Lippi G.L., Arecchi F.T. Frequency pushing in lasers with injected signal Phys. Rev. A 34 5 1986 4000-4007.
5. Hui R., D'Ottavi A., Mecozzi A., Spano P. Injection locking in distributed feedback semiconductor lasers IEEE J. Quant. Electron. 27 1991 1688.
6. Lugiato L.A., Narducci L.M., Bandy D.K., Pennise C.A. Breathing, spiking and chaos in a laser with injected signal Opt. Commun. 46 1983 64-68.
7. Mogensen F., Jacobsen G., Olesen H. Light intensity pulsations in an injection locked semiconductor laser Opt. Quant. Electron. 16 1984 183-186.
8. Braza P.A., Erneux T. Constant phase, phase drift and phase entrainment in lasers with an injected signal Phys. Rev. A 41 11 1990 6470-6479.
9. Sacher J., Baums D., Panknin P., Elsäßer W., Göbel E.O. Intensity instabilities of semiconductor lasers under current modulation, external light injection and delayed feedback Phys. Rev. A 45 3 1992 1893-1905.
10. Lee E.-K., Pang H.-S., Park J.-D., Lee H. Bistability and chaos in an injection-locked semiconductor laser Phys. Rev. A 47 1 1993 736-739.
11. van Tartwijk G.H.M., Muijres G., Lenstra D., van Exter M.P., Woerdman J.P. The semiconductor laser beyond the locking range of optical injection Electron. Lett. 29 1993 137-138.
12. Lenstra D., van Tartwijk G.H.M., van der Graaf W.A., De Jagher P.C. Multi-wave mixing dynamics in a diode laser, Chaos in Optics Proc. SPIE 2039 1993 11-22.
13. Annovazzi-Lodi V., Donati S., Manna M. Chaos and locking in a semiconductor laser due to external injection IEEE J. Quant. Electron. 30 7 1994 1537-1541.
14. Solari H.G., Oppo G.L. Laser with injected signal: perturbation of an invariant circle Opt. Commun. 111 1994 173-190.
15. Simpson T.B., Liu J.M., Gavrielides A., Kovanis V., Alsing P.M. Period-doubling route to chaos in a semiconductor laser subject to optical injection Appl. Phys. Lett. 64 26 1994 3539-3541.
16. Simpson T.B., Liu J.M., Gavrielides A., Kovanis V., Alsing P.M. Period-doubling cascade and chaos in a semiconductor lasers with optical injection Phys. Rev. A 51 5 1995 4181-4185.
17. Kovanis V., Gavrielides A., Simpson T.B., Liu J.M. Instabilities and chaos in optically injected semiconductor lasers Appl. Phys. Lett. 67 19 1995 2780-2782.
18. de Jagher P.C., van der Graaf W.A., Lenstra D. Relaxation-oscillation phenomena in an injection locked semiconductor laser Quant. Semiclass. Opt. 8 1996 805-822.
19. Erneux T., Kovanis V., Gavrielides A., Alsing P.M. Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection Phys. Rev. A 53 6 1996 4372-4380.
20. Erneux T., Gavrielides A., Kovanis V. Low pump stability of an optically injected diode laser Quant. Semiclass. Opt. 9 5 1997 811-818.
21. Gavrielides A., Kovanis V., Varangis P.M., Erneux T., Lythe G. Coexisting periodic attractors in injection-locked diode lasers Quant. Semiclass. Opt. 9 5 1997 785-796.
22. Simpson T.B., Liu J.M., Huang K.F., Tai K. Nonlinear dynamics induced by external optical injection in semiconductor lasers Quant. Semiclass. Opt. 9 5 1997 765-784.
23. Zimmermann M.G., Natiello M.A., Solari H. Shilnikov-Saddle-node interaction near a codimension 2 bifurcation: laser with injected signal Physica D 109 3-4 1997 293-314.
24. Krauskopf B., van der Graaf W.A., Lenstra D. Bifurcations of relaxation oscillations in an optically injected diode laser Quant. Semiclass. Opt. 9 1997 797-809.
25. Krauskopf B., Tollenaar N., Lenstra D. Tori and their bifurcations in an optically injected semiconductor laser Opt. Commun. 156 1998 158-169.
26. Yeung M.K.S., Strogatz S.H., Nonlinear dynamics of a solid-state laser with injection, Phys. Rev. E, 58 (4) (1998) 4421-4435. M.K.S., Strogatz S.H. Erratum Phys. Rev. E 61 2 2000 2154.
27. Yeung M.K.S., Strogatz S.H. Nonlinear dynamics of a solid-state laser with injection Phys. Rev. E 58 4 1998 4421-4435 Yeung M.K.S., Strogatz S.H. Erratum Phys. Rev. E 61 2 2000 2154.
28. Kovanis V., Erneux T., Gavrielides A. Largely detuned injection-locked semiconductor lasers Opt. Commun. 159 1999 177-183.
29. Nizette M., Erneux T., Gavrielides A., Kovanis V. Injection locked semiconductor laser dynamics from large to small detunings Proc. SPIE 3625 1999 679-689.
30. Wieczorek S., Krauskopf B., Lenstra D. A unifying view of bifurcations in a semiconductor laser subject to optical injection Opt. Commun. 172 1-6 1999 279-295.
31. Wieczorek S., Krauskopf B., Lenstra D. Mechanisms for multistability in a semiconductor laser with optical injection Opt. Commun. 183 1-4 2000 215-226.
32. Krauskopf B., Wieczorek S.M., Lenstra D. Different types of chaos in an optically injected semiconductor laser Appl. Phys. Lett. 77 11 2000 1611-1613.
33. Hwang S.K., Liu J.M. Dynamical Characteristics of an optically injected semiconductor laser Opt. Commun. 183 2000 195-205.
34. Wieczorek S., Krauskopf B., Lenstra D. Sudden chaotic transitions in an optically injected semiconductor laser Opt. Lett. 26 11 2001 816-818.
35. S. Wieczorek, B. Krauskopf, D. Lenstra, Unneseted islands of period-doublings in an injected semiconductor laser, Phys. Rev. E 64 056204 (2001) 1-9.
36. Eriksson S., Lindberg A.M. Periodic oscillations within the chaotic region in a semiconductor laser subject to optical injection Opt. Lett. 26 3 2001 142-144.
37. Mayol C., Natiello M.A., Zimmermann M.G. Resonance structure in a weakly detuned laser with injected signal Int. J. Bifurcat. Chaos 11 2001 2587-2605.
38. S. Wieczorek, T.B. Simpson, B. Krauskopf, D. Lenstra, Global quantitative predictions of complex laser dynamics, Phys. Rev. E 65 (4) 045207 (R) (2002) 1-4.
39. Nizette M., Erneux T., Gavrielides A., Kovanis V. Averaged equations for injection locked semiconductor lasers Physica D 161 2002 220-236.
40. Zimmermann M.G., Natiello M.A., Solari H. Global bifurcations in a laser with injected signal: beyond Adler's approximation Chaos 11 2001 500-513.
41. Van Tartwijk G.H.M., Lenstra D. Semiconductor lasers with optical injection and feedback Quant. Semiclass. Opt. 7 1995 87-143.
42. Van Tartwijk G.H.M., Agrawal G.P. Laser instabilities: a modern perspective Prog. Quant. Electron. 22 1998 43-122.
43. B. Krauskopf, D. Lenstra (Eds.), Fundamental Issues of Nonlinear Laser Dynamics, AIP Conference Proceedings, vol. 548, 2000.
44. Chen H.F., Liu J.M. Open loop chaotic synchronization of injection locked semiconductor lasers with gigahertz range modulation IEEE. J. Quant. Electron. 36 2000 27-34.
45. G.P. Agrawal, N.K. Dutta, Semiconductor Lasers, 2nd ed., Van Nostrand, New York, 1993.
46. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, 2nd ed., Springer, Berlin, 1986.
47. Yu.A. Kuznetsov, Elements of applied bifurcation theory, Applied Mathematical Sciences, vol. 112, Springer, Berlin, 1995.
48. Thornburg K.S. Jr., Möller M., Roy R., Carr T.W., Li R.-D., Erneux T. Chaos and coherence in coupled lasers Phys. Rev. E 55 1997 3865-3869.
49. Brun E., Derighetti B., Meier D., Holzner R., Ravani M. Observation of order and chaos in a nuclear spin-flip laser J. Opt. Soc. Am. B 2 1 1985 156-167.
50. Tredicce J.R., Arecchi F.T., Lippi G.L., Puccioni G.P. Instabilities in lasers with an injected signal J. Opt. Soc. Am. B 2 1 1985 173-183.
51. 2 ring laser with an injected signal, Opt. Commun. 58 (1986) 124-129.
52. W. Lauterborn, I. Eick, Numerical investigation of a periodically driven laser with an intracavity saturable absorber, J. Opt. Soc. Am. B 5 (5) (1988) 1089-1096.
53. M. Sargent III, M.O. Scully, W.E. Lamb Jr., Laser Physics, Addison-Wesley, Reading, MA, 1974.
54. F.T. Arecchi, G. Lippi, G. Puccioni, J. Tredicce, in: L. Mandel, E. Wolf (Eds.), Coherence in Quantum Optics, vol. V, Plenum Press, New York, 1984, p. 1227.
55. E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Yu. Kuznetsov, X. Wang, AUTO 97: Continuation and bifurcation software for ordinary differential equations. http://indy.cs.concordia.ca/auto/main.html.
56. Back A., Guckenheimer J., Myers M.R., Wicklin F.J., Worfolk P.A. DsTool: computer assisted exploration of dynamical systems Notices Am. Math. Soc. 39 1992 303-309.
57. Krauskopf B., Osinga H.M. Growing 1D and quasi 2D unstable manifolds of maps J. Comp. Phys. 146 1 1998 404-419.
58. B. Krauskopf, H.M. Osinga, Investigating torus bifurcations in the forced Van der Pol oscillator, in: E.J. Doedel, L.S. Tuckerman (Eds.), Numerical Methods for Bifurcation Problems and Large-scale Dynamical Systems, IMA Volumes in Mathematics and its Applications, vol. 119, Springer, Berlin, 2000, pp. 199-208.