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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 9 — Apr. 27, 2009
  • pp: 7592–7608

Automated correlation dimension analysis of optically injected solid state lasers

J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg  »View Author Affiliations


Optics Express, Vol. 17, Issue 9, pp. 7592-7608 (2009)
http://dx.doi.org/10.1364/OE.17.007592


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Abstract

Nonlinear lasers are excellent systems from which to obtain high signal-to-noise experimental data of nonlinear dynamical variables to be used to develop and demonstrate robust nonlinear dynamics analysis techniques. Here we investigate the dynamical complexity of such a system: an optically injected Nd:YVO4 solid state laser. We show that a map of the correlation dimension as a function of the injection strength and frequency detuning, extracted from the laser output power time-series data, is an excellent mirror of the dynamics map generated from a theoretical model of the system. An automated computational protocol has been designed and implemented to achieve this. The correlation dimension map is also contrasted with prior research that mapped the peak intensity of the output power as an experimentally accessible measurand reflecting the dynamical state of the system [Valling et al., Phys. Rev. A 72, 033810 (2005)].

© 2009 Optical Society of America

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.1540) Lasers and laser optics : Chaos
(140.3580) Lasers and laser optics : Lasers, solid-state
(190.0190) Nonlinear optics : Nonlinear optics
(190.3100) Nonlinear optics : Instabilities and chaos

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: February 12, 2009
Revised Manuscript: April 3, 2009
Manuscript Accepted: April 4, 2009
Published: April 23, 2009

Citation
J. P. Toomey, D. M. Kane, S. Valling, and A. M. Lindberg, "Automated correlation dimension analysis of optically injected solid state lasers," Opt. Express 17, 7592-7608 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7592


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References

  1. F. T. Arecchi, W. Gadomski, and R. Meucci, "Generation of chaotic dynamics by feedback on a laser," Phys. Rev. A 34, 1617-1620 (1986). [CrossRef] [PubMed]
  2. W. Klische and C. O. Weiss, "Instabilities and routes to chaos in a homogeneously broadened one- and two-mode ring laser," Phys. Rev. A 31, 4049-4051 (1985). [CrossRef] [PubMed]
  3. E. Hemery, L. Chusseau, and J. M. Lourtioz, "Dynamic behaviors of semiconductor lasers under strong sinusoidal current modulation: modeling and experiments at 1.3 ?m," IEEE J. Quantum Electron. 26, 633-641 (1990). [CrossRef]
  4. D. M. Kane, and K. A. Shore, eds., Unlocking Dynamical Diversity: Feedback Effects on Semiconductor Lasers (Wiley, 2005). [CrossRef]
  5. T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling route to chaos in a semiconductor-laser subject to optical-injection," Appl. Phys. Lett. 64, 3539-3541 (1994). [CrossRef]
  6. S. Tang and J. M. Liu, "Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback," IEEE J. Quantum Electron. 37, 329-336 (2001). [CrossRef]
  7. F. Y. Lin and J. M. Liu, "Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback," Opt. Commun. 221, 173-180 (2003). [CrossRef]
  8. J. S. Lawrence and D. M. Kane, "Nonlinear dynamics of a laser diode with optical feedback systems subject to modulation," IEEE J. Quantum Electron. 38, 185-192 (2002). [CrossRef]
  9. K. R. Preston, K. C. Woollard, and K. H. Cameron, "External cavity controlled single longitudinal mode laser transmitter module," Electron. Lett. 17, 931-933 (1981). [CrossRef]
  10. H. L. Stover and W. H. Steier, "Locking of laser oscillators by light injection," Appl. Phys. Lett. 8, 91-93 (1966). [CrossRef]
  11. L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990). [CrossRef] [PubMed]
  12. G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998). [CrossRef] [PubMed]
  13. A. Uchida, H. Shinozuka, T. Ogawa, and F. Kannari, "Experiments on chaos synchronization in two separate microchip lasers," Opt. Lett. 24, 890-892 (1999). [CrossRef]
  14. S. Donati and C. R. Mirasso, "Feature section on optical chaos and applications to cryptography," IEEE J. Quantum Electron. 38, 1138-1204 (2002). [CrossRef]
  15. J. P. Goedgebuer, L. Larger, and H. Porte, "Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode," Phys. Rev. Lett. 80, 2249-2252 (1998). [CrossRef]
  16. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, "Chaos-based communications at high bit rates using commercial fibre-optic links," Nature 438, 343-346 (2005). [CrossRef] [PubMed]
  17. T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, "Nonlinear dynamics induced by external optical injection in semiconductor lasers," Quantum Semiclassic. Opt. 9, 765-784 (1997). [CrossRef]
  18. S. Eriksson and A. M. Lindberg, "Observations on the dynamics of semiconductor lasers subjected to external optical injection," J. Opt. B:Quantum Semiclassical Opt. 4, 149-154 (2002). [CrossRef]
  19. S. Eriksson, "Dependence of the experimental stability diagram of an optically injected semiconductor laser on the laser current," Opt. Commun. 210, 343-353 (2002). [CrossRef]
  20. S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, "The dynamical complexity of optically injected semiconductor lasers," Phys. Rep.  416, 1-128 (2005).
  21. S. Valling, T. Fordell, and A. M. Lindberg, "Maps of the dynamics of an optically injected solid-state laser," Phys. Rev. A 72, 033810 (2005). [CrossRef]
  22. S. Valling, B. Krauskopf, T. Fordell, and A. M. Lindberg, "Experimental bifurcation diagram of a solid state laser with optical injection," Opt. Commun. 271, 532-542 (2007). [CrossRef]
  23. H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 2004).
  24. H. Kantz, "A robust method to estimate the maximal Lyapunov exponent of a time-series," Phys. Lett. A 185, 77-87 (1994). [CrossRef]
  25. M. T. Rosenstein, J. J. Collins, and C. J. Deluca, "A practical method for calculating largest Lyapunov exponents from small data sets," Physica D 65, 117-134 (1993). [CrossRef]
  26. K. E. Chlouverakis and M. J. Adams, "Stability maps of injection-locked laser diodes using the largest Lyapunov exponent," Opt. Commun. 216, 405-412 (2003). [CrossRef]
  27. J. P. Toomey and D. M. Kane, "Analysis of chaotic semiconductor laser diodes," in Proceedings of the Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, Perth, Australia, 2006), pp. 164-167. [CrossRef]
  28. C. Liu, R. Roy, H. D. I. Abarbanel, Z. Gills, and K. Nunes, "Influence of noise on chaotic laser dynamics," Phys. Rev. E 55, 6483-6500 (1997). [CrossRef]
  29. P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors," Physica D 9, 189-208 (1983). [CrossRef]
  30. T. Fordell and A. M. Lindberg, "Numerical stability maps of an optically injected semiconductor laser," Opt. Commun. 242, 613-622 (2004). [CrossRef]
  31. F. Takens, "Dynamical systems and turbulence," in Springer Lecture Notes in Mathematics, D. A. Rand, and L.-S. Young, eds., (Springer-Verlag, New York, 1980), pp. 366-381.
  32. M. Casdagli, S. Eubank, J. D. Farmer, and J. Gibson, "State space reconstruction in the presence of noise," Physica D 51, 52-98 (1991). [CrossRef]
  33. A. M. Fraser and H. L. Swinney, "Independent coordinates for strange attractors from mutual information," Phys. Rev. A 33, 1134-1140 (1986). [CrossRef] [PubMed]
  34. M. T. Rosenstein, J. J. Collins, and C. J. Deluca, "Reconstruction expansion as a geometry-based framework for choosing proper delay times," Physica D 73, 82-98 (1994). [CrossRef]
  35. T. Buzug and G. Pfister, "Comparison of algorithms calculating optimal embedding parameters for delay time coordinates," Physica D 58, 127-137 (1992). [CrossRef]
  36. E. N. Lorenz, "Deterministic Nonperiodic Flow," J. Atmos. Sci. 20, 130-141 (1963). [CrossRef]
  37. P. E. Rapp, A. M. Albano, T. I. Schmah, and L. A. Farwell, "Filtered noise can mimic low-dimensional chaotic attractors," Phys. Rev. E 47, 2289-2297 (1993). [CrossRef]
  38. J. Theiler, "Spurious dimension from correlation algorithms applied to limited time-series data," Phys. Rev. A 34, 2427-2432 (1986). [CrossRef] [PubMed]
  39. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, and J. D. Farmer, "Testing for nonlinearity in time-series - The method of surrogate data," Physica D 58, 77-94 (1992). [CrossRef]
  40. A. Provenzale, L. A. Smith, R. Vio, and G. Murante, "Distinguishing between low-dimensional dynamics and randomness in measured time-series," Physica D 58, 31-49 (1992). [CrossRef]
  41. T. Schreiber and A. Schmitz, "Surrogate time series," Physica D 142, 346-382 (2000). [CrossRef]
  42. S. Valling, T. Fordell, and A. M. Lindberg, "Experimental and numerical intensity time series of an optically injected solid state laser," Opt. Commun. 254, 282-289 (2005). [CrossRef]
  43. A. Corana, G. Bortolan, and A. Casaleggio, "Most probable dimension value and most flat interval methods for automatic estimation of dimension from time series," Chaos, Solitons Fractals 20, 779-790 (2004). [CrossRef]
  44. D. M. Kane, J. P. Toomey, M. W. Lee, and K. A. Shore, "Correlation dimension signature of wideband chaos synchronization of semiconductor lasers," Opt. Lett. 31, 20-22 (2006). [CrossRef] [PubMed]

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