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

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  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).
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    [CrossRef]
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    [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]
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    [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]
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    [CrossRef] [PubMed]

2007 (1)

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]

2006 (1)

2005 (4)

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]

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, "The dynamical complexity of optically injected semiconductor lasers," Phys. Rep.  416, 1-128 (2005).

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]

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]

2004 (2)

T. Fordell and A. M. Lindberg, "Numerical stability maps of an optically injected semiconductor laser," Opt. Commun. 242, 613-622 (2004).
[CrossRef]

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]

2003 (2)

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]

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]

2002 (4)

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]

S. Donati and C. R. Mirasso, "Feature section on optical chaos and applications to cryptography," IEEE J. Quantum Electron. 38, 1138-1204 (2002).
[CrossRef]

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]

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]

2001 (1)

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]

2000 (1)

T. Schreiber and A. Schmitz, "Surrogate time series," Physica D 142, 346-382 (2000).
[CrossRef]

1999 (1)

1998 (2)

G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef] [PubMed]

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]

1997 (2)

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]

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]

1994 (3)

H. Kantz, "A robust method to estimate the maximal Lyapunov exponent of a time-series," Phys. Lett. A 185, 77-87 (1994).
[CrossRef]

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]

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]

1993 (2)

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]

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]

1992 (3)

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]

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]

T. Buzug and G. Pfister, "Comparison of algorithms calculating optimal embedding parameters for delay time coordinates," Physica D 58, 127-137 (1992).
[CrossRef]

1991 (1)

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]

1990 (2)

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]

L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

1986 (3)

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]

A. M. Fraser and H. L. Swinney, "Independent coordinates for strange attractors from mutual information," Phys. Rev. A 33, 1134-1140 (1986).
[CrossRef] [PubMed]

J. Theiler, "Spurious dimension from correlation algorithms applied to limited time-series data," Phys. Rev. A 34, 2427-2432 (1986).
[CrossRef] [PubMed]

1985 (1)

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]

1983 (1)

P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors," Physica D 9, 189-208 (1983).
[CrossRef]

1981 (1)

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]

1966 (1)

H. L. Stover and W. H. Steier, "Locking of laser oscillators by light injection," Appl. Phys. Lett. 8, 91-93 (1966).
[CrossRef]

1963 (1)

E. N. Lorenz, "Deterministic Nonperiodic Flow," J. Atmos. Sci. 20, 130-141 (1963).
[CrossRef]

Abarbanel, H. D. I.

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]

Adams, M. J.

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]

Albano, A. M.

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]

Alsing, P. M.

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]

Annovazzi-Lodi, V.

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]

Arecchi, F. T.

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]

Argyris, A.

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]

Bortolan, G.

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]

Buzug, T.

T. Buzug and G. Pfister, "Comparison of algorithms calculating optimal embedding parameters for delay time coordinates," Physica D 58, 127-137 (1992).
[CrossRef]

Cameron, K. H.

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]

Carroll, T. L.

L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

Casaleggio, A.

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]

Casdagli, M.

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]

Chlouverakis, K. E.

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]

Chusseau, L.

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]

Colet, P.

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]

Collins, J. J.

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]

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]

Corana, A.

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]

Deluca, C. J.

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]

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]

Donati, S.

S. Donati and C. R. Mirasso, "Feature section on optical chaos and applications to cryptography," IEEE J. Quantum Electron. 38, 1138-1204 (2002).
[CrossRef]

Eriksson, S.

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]

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]

Eubank, S.

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]

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]

Farmer, J. D.

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]

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]

Farwell, L. A.

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]

Fischer, I.

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]

Fordell, T.

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]

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]

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]

T. Fordell and A. M. Lindberg, "Numerical stability maps of an optically injected semiconductor laser," Opt. Commun. 242, 613-622 (2004).
[CrossRef]

Fraser, A. M.

A. M. Fraser and H. L. Swinney, "Independent coordinates for strange attractors from mutual information," Phys. Rev. A 33, 1134-1140 (1986).
[CrossRef] [PubMed]

Gadomski, W.

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]

Galdrikian, B.

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]

Garcia-Ojalvo, J.

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]

Gavrielides, A.

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]

Gibson, J.

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]

Gills, Z.

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]

Goedgebuer, J. P.

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]

Grassberger, P.

P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors," Physica D 9, 189-208 (1983).
[CrossRef]

Hemery, E.

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]

Huang, K. F.

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]

Kane, D. M.

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]

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]

Kannari, F.

Kantz, H.

H. Kantz, "A robust method to estimate the maximal Lyapunov exponent of a time-series," Phys. Lett. A 185, 77-87 (1994).
[CrossRef]

Klische, W.

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]

Kovanis, V.

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]

Krauskopf, B.

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]

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, "The dynamical complexity of optically injected semiconductor lasers," Phys. Rep.  416, 1-128 (2005).

Larger, L.

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]

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]

Lawrence, J. S.

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]

Lee, M. W.

Lenstra, D.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, "The dynamical complexity of optically injected semiconductor lasers," Phys. Rep.  416, 1-128 (2005).

Lin, F. Y.

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]

Lindberg, A. M.

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]

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]

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]

T. Fordell and A. M. Lindberg, "Numerical stability maps of an optically injected semiconductor laser," Opt. Commun. 242, 613-622 (2004).
[CrossRef]

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]

Liu, C.

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]

Liu, J. M.

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]

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]

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]

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]

Longtin, A.

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]

Lorenz, E. N.

E. N. Lorenz, "Deterministic Nonperiodic Flow," J. Atmos. Sci. 20, 130-141 (1963).
[CrossRef]

Lourtioz, J. M.

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]

Meucci, R.

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]

Mirasso, C. R.

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]

S. Donati and C. R. Mirasso, "Feature section on optical chaos and applications to cryptography," IEEE J. Quantum Electron. 38, 1138-1204 (2002).
[CrossRef]

Murante, G.

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]

Nunes, K.

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]

Ogawa, T.

Pecora, L. M.

L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

Pesquera, L.

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]

Pfister, G.

T. Buzug and G. Pfister, "Comparison of algorithms calculating optimal embedding parameters for delay time coordinates," Physica D 58, 127-137 (1992).
[CrossRef]

Porte, H.

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]

Preston, K. R.

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]

Procaccia, I.

P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors," Physica D 9, 189-208 (1983).
[CrossRef]

Provenzale, A.

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]

Rapp, P. E.

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]

Rosenstein, M. T.

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]

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]

Roy, R.

G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef] [PubMed]

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]

Schmah, T. I.

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]

Schmitz, A.

T. Schreiber and A. Schmitz, "Surrogate time series," Physica D 142, 346-382 (2000).
[CrossRef]

Schreiber, T.

T. Schreiber and A. Schmitz, "Surrogate time series," Physica D 142, 346-382 (2000).
[CrossRef]

Shinozuka, H.

Shore, K. A.

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]

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]

Simpson, T. B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, "The dynamical complexity of optically injected semiconductor lasers," Phys. Rep.  416, 1-128 (2005).

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]

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]

Smith, L. A.

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]

Steier, W. H.

H. L. Stover and W. H. Steier, "Locking of laser oscillators by light injection," Appl. Phys. Lett. 8, 91-93 (1966).
[CrossRef]

Stover, H. L.

H. L. Stover and W. H. Steier, "Locking of laser oscillators by light injection," Appl. Phys. Lett. 8, 91-93 (1966).
[CrossRef]

Swinney, H. L.

A. M. Fraser and H. L. Swinney, "Independent coordinates for strange attractors from mutual information," Phys. Rev. A 33, 1134-1140 (1986).
[CrossRef] [PubMed]

Syvridis, D.

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]

Tai, K.

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]

Tang, S.

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]

Theiler, J.

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]

J. Theiler, "Spurious dimension from correlation algorithms applied to limited time-series data," Phys. Rev. A 34, 2427-2432 (1986).
[CrossRef] [PubMed]

Toomey, J. P.

Uchida, A.

Valling, S.

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]

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]

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]

VanWiggeren, G. D.

G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef] [PubMed]

Vio, R.

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]

Weiss, C. O.

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]

Wieczorek, S.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, "The dynamical complexity of optically injected semiconductor lasers," Phys. Rep.  416, 1-128 (2005).

Woollard, K. C.

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]

Appl. Phys. Lett. (2)

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]

H. L. Stover and W. H. Steier, "Locking of laser oscillators by light injection," Appl. Phys. Lett. 8, 91-93 (1966).
[CrossRef]

Chaos, Solitons Fractals (1)

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]

Electron. Lett. (1)

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]

IEEE J. Quantum Electron. (4)

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]

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]

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]

S. Donati and C. R. Mirasso, "Feature section on optical chaos and applications to cryptography," IEEE J. Quantum Electron. 38, 1138-1204 (2002).
[CrossRef]

J. Atmos. Sci. (1)

E. N. Lorenz, "Deterministic Nonperiodic Flow," J. Atmos. Sci. 20, 130-141 (1963).
[CrossRef]

J. Opt. B:Quantum Semiclassical Opt. (1)

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]

Nature (1)

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]

Opt. Commun. (6)

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]

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]

T. Fordell and A. M. Lindberg, "Numerical stability maps of an optically injected semiconductor laser," Opt. Commun. 242, 613-622 (2004).
[CrossRef]

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]

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]

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]

Opt. Lett. (2)

Phys. Lett. A (1)

H. Kantz, "A robust method to estimate the maximal Lyapunov exponent of a time-series," Phys. Lett. A 185, 77-87 (1994).
[CrossRef]

Phys. Rep. (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, "The dynamical complexity of optically injected semiconductor lasers," Phys. Rep.  416, 1-128 (2005).

Phys. Rev. A (5)

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]

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]

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]

A. M. Fraser and H. L. Swinney, "Independent coordinates for strange attractors from mutual information," Phys. Rev. A 33, 1134-1140 (1986).
[CrossRef] [PubMed]

J. Theiler, "Spurious dimension from correlation algorithms applied to limited time-series data," Phys. Rev. A 34, 2427-2432 (1986).
[CrossRef] [PubMed]

Phys. Rev. E (2)

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]

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]

Phys. Rev. Lett. (2)

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]

L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824 (1990).
[CrossRef] [PubMed]

Physica D (8)

P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors," Physica D 9, 189-208 (1983).
[CrossRef]

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]

T. Buzug and G. Pfister, "Comparison of algorithms calculating optimal embedding parameters for delay time coordinates," Physica D 58, 127-137 (1992).
[CrossRef]

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]

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]

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]

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]

T. Schreiber and A. Schmitz, "Surrogate time series," Physica D 142, 346-382 (2000).
[CrossRef]

Quantum Semiclassic. Opt. (1)

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]

Science (1)

G. D. VanWiggeren and R. Roy, "Communication with chaotic lasers," Science 279, 1198-1200 (1998).
[CrossRef] [PubMed]

Other (4)

D. M. Kane, and K. A. Shore, eds., Unlocking Dynamical Diversity: Feedback Effects on Semiconductor Lasers (Wiley, 2005).
[CrossRef]

H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 2004).

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]

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.

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Figures (11)

Fig. 1.
Fig. 1.

The graph in (a) shows correlation sum as a function of radius and (b) shows the gradient of the correlation sum as a function of radius for values of the embedding dimension m between 2 and 12. Time series analyzed is the x-variable data from the chaotic Lorenz equations [36].

Fig. 2.
Fig. 2.

Experimental setup: LD, laser diode; FI, Faraday isolator; TEC, temperature control; IF, interference filter; BS, beam splitter; AOM, acousto-optic modulator; FP, Fabry-Pérot interferometer; PD, photodetectors. Figure reproduced from [21].

Fig. 3.
Fig. 3.

Structure diagram of the process of the automated computational system.

Fig. 4.
Fig. 4.

Experimental laser intensity time-series trace and corresponding injection strength sweep (inset) for detuning Δω = −1.0.

Fig. 5.
Fig. 5.

Plots of Dm (r) and corresponding histograms for examples of (a) ‘good’ and (b) ‘bad’ scaling regions.

Fig. 6.
Fig. 6.

Correlation dimension map in the (K, Δω) plane for experimental data. Different dynamical region are identified as I: Locked (no data), II: Periodic (CD = 1), III: ‘Spiky’ Output (CD < 1), IV: Chaotic (CD > 2), V: Noisy (CD = ∞).

Fig. 7.
Fig. 7.

Correlation dimension map in the (K, Δω) plane for simulated data without noise.

Fig. 8.
Fig. 8.

(a) Experimental (K, Δω) map of intensity time-series maxima. Reproduced from [21]. (b) Theoretical bifurcation diagram in the (K, Δω) plane. Showing Hopf (H) bifurcations in red, saddle-node (SN) bifurcations in blue, torus (T) bifurcations in black and period doubling (PD) bifurcations in green. Reproduced from [22].

Fig. 9.
Fig. 9.

Typical output power time-series, graphs of Dm(r) versus r and corresponding histograms for regions (a) II, (b) III, (c) IV and (d) V in the (K, Δω) plane.

Fig. 10.
Fig. 10.

Typical output power time-series, graphs of Dm (r) versus r and corresponding histograms (showing scaling region peak width) for data from region III with values of embedding delay (a) T = 1 data point, and (b) T = 7 data points.

Fig. 11.
Fig. 11.

Map of the width of scaling region peaks for experimental OISSL data in the (K, Δω) plane.

Tables (1)

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Table 1. Parameter values used in the simulations*

Equations (7)

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A ( t ) = [ P ( t ) , P ( t + T ) , P ( t + 2 T ) , , P ( t + ( m 1 ) T ) ] .
C m ( r ) = lim N 2 N ( N 1 ) j N j = i + 1 N H ( r y i y j ) ,
lim N lim r 0 C m ( r ) = r D .
D = lim N lim r 0 log C m ( r ) log r .
C m ( r ) = lim N 2 ( N w ) ( N w 1 ) i N j = i + 1 + w N H ( r y i y j ) ,
da dt = [ 1 2 ( 1 ) γ c γ n γ s J ̂ ( n 1 ) 1 2 γ p ( a 2 1 ) + i Ω ] a + κ + F a
dn dt = γ s ( 1 n ) + γ s J ̂ ( 1 a 2 ) + γ n a 2 ( 1 n ) + γ p γ s J ̂ γ c a 2 ( a 2 1 ) + F n .

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