Abstract

We report the experimental and theoretical verification that, in a diode-pumped Nd:YAG+Cr:YAG Q-switched laser, the instabilities in the pulse spacing (“jitter”) are ruled by low-dimensional deterministic chaos. From our experimental time series, we determine the embedding and fractal dimensions of the attractor, as well as the values of the Lyapunov exponents. We also present a simplified theoretical description in terms of a map of the same universality class as the logistic map, which explains the bifurcations’ cascade and the period-three window of stability observed. The achieved characterization of the dynamics and its main parameters opens a door to effective ways to reduce the jitter, which is of practical interest, through mechanisms of control of chaos. Conversely, the difficulty in the prediction of the interpulse spacing makes this system attractive for high power, robust FM chaotic laser cryptography in free-space propagation.

© 2010 Optical Society of America

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References

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2009 (1)

L. Zunino, M. Soriano, A. Figliola, D. Pérez, M. Garavaglia, C. Mirasso, and O. Rosso, Opt. Commun. 282, 4587 (2009).
[CrossRef]

2004 (2)

2003 (1)

2002 (1)

M. Larotonda, A. Hnilo, J. Méndez, and A. Yacomotti, Phys. Rev. A 65, 033812 (2002).
[CrossRef]

2001 (1)

1996 (1)

H. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, 1996).
[CrossRef]

1994 (1)

1986 (1)

A. Siegman, in Lasers (University Science, 1986), Chap. 26.

1985 (1)

TISEAN software is based on M. Sano and Y. Sawada, Phys. Rev. Lett. 55, 1082 (1985); it is freely available at http://www.mpipks-dresden.mpg.de/~tisean.
[CrossRef] [PubMed]

1984 (1)

P. Hauser, C. Tsallis, and E. Curado, Phys. Rev. A 30, 2074 (1984).
[CrossRef]

1981 (1)

E. Ott, Rev. Mod. Phys. 53, 655 (1981).
[CrossRef]

1978 (1)

A. Haken, Synergetics (Springer-Verlag, 1978).

Abarbanel, H.

H. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, 1996).
[CrossRef]

Chen, C.-H.

Curado, E.

P. Hauser, C. Tsallis, and E. Curado, Phys. Rev. A 30, 2074 (1984).
[CrossRef]

Dill, C.

Figliola, A.

L. Zunino, M. Soriano, A. Figliola, D. Pérez, M. Garavaglia, C. Mirasso, and O. Rosso, Opt. Commun. 282, 4587 (2009).
[CrossRef]

Garavaglia, M.

L. Zunino, M. Soriano, A. Figliola, D. Pérez, M. Garavaglia, C. Mirasso, and O. Rosso, Opt. Commun. 282, 4587 (2009).
[CrossRef]

Haken, A.

A. Haken, Synergetics (Springer-Verlag, 1978).

Hauser, P.

P. Hauser, C. Tsallis, and E. Curado, Phys. Rev. A 30, 2074 (1984).
[CrossRef]

Hnilo, A.

M. Kovalsky and A. Hnilo, Phys. Rev. A 70, 043813 (2004).
[CrossRef]

M. Larotonda, A. Hnilo, J. Méndez, and A. Yacomotti, Phys. Rev. A 65, 033812 (2002).
[CrossRef]

A. Hnilo and M. Larotonda, J. Opt. Soc. Am. B 18, 1451 (2001).
[CrossRef]

Kovalsky, M.

M. Kovalsky and A. Hnilo, Phys. Rev. A 70, 043813 (2004).
[CrossRef]

Larotonda, M.

M. Larotonda, A. Hnilo, J. Méndez, and A. Yacomotti, Phys. Rev. A 65, 033812 (2002).
[CrossRef]

A. Hnilo and M. Larotonda, J. Opt. Soc. Am. B 18, 1451 (2001).
[CrossRef]

Luna, A. E.

A. E. Luna, “Láser de estado totalmente sólido pulsado con técnicas de Q-switch pasivo,” M.Sc. thesis final report (Facultad de Ciencias Exactas, Universidad de Buenos Aires, 2006) (in Spanish, available upon request to the corresponding author).

Méndez, J.

M. Larotonda, A. Hnilo, J. Méndez, and A. Yacomotti, Phys. Rev. A 65, 033812 (2002).
[CrossRef]

Meng, X. L.

Mirasso, C.

L. Zunino, M. Soriano, A. Figliola, D. Pérez, M. Garavaglia, C. Mirasso, and O. Rosso, Opt. Commun. 282, 4587 (2009).
[CrossRef]

Ng, S. P.

Ott, E.

E. Ott, Rev. Mod. Phys. 53, 655 (1981).
[CrossRef]

Pérez, D.

L. Zunino, M. Soriano, A. Figliola, D. Pérez, M. Garavaglia, C. Mirasso, and O. Rosso, Opt. Commun. 282, 4587 (2009).
[CrossRef]

Qin, L. J.

Rosso, O.

L. Zunino, M. Soriano, A. Figliola, D. Pérez, M. Garavaglia, C. Mirasso, and O. Rosso, Opt. Commun. 282, 4587 (2009).
[CrossRef]

Sano, M.

TISEAN software is based on M. Sano and Y. Sawada, Phys. Rev. Lett. 55, 1082 (1985); it is freely available at http://www.mpipks-dresden.mpg.de/~tisean.
[CrossRef] [PubMed]

Sawada, Y.

TISEAN software is based on M. Sano and Y. Sawada, Phys. Rev. Lett. 55, 1082 (1985); it is freely available at http://www.mpipks-dresden.mpg.de/~tisean.
[CrossRef] [PubMed]

Siegman, A.

A. Siegman, in Lasers (University Science, 1986), Chap. 26.

Soriano, M.

L. Zunino, M. Soriano, A. Figliola, D. Pérez, M. Garavaglia, C. Mirasso, and O. Rosso, Opt. Commun. 282, 4587 (2009).
[CrossRef]

Tang, D. Y.

Tsallis, C.

P. Hauser, C. Tsallis, and E. Curado, Phys. Rev. A 30, 2074 (1984).
[CrossRef]

Tu, K.-C.

Wei, M.-D.

Yacomotti, A.

M. Larotonda, A. Hnilo, J. Méndez, and A. Yacomotti, Phys. Rev. A 65, 033812 (2002).
[CrossRef]

Zayhowsi, J. J.

Zunino, L.

L. Zunino, M. Soriano, A. Figliola, D. Pérez, M. Garavaglia, C. Mirasso, and O. Rosso, Opt. Commun. 282, 4587 (2009).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

L. Zunino, M. Soriano, A. Figliola, D. Pérez, M. Garavaglia, C. Mirasso, and O. Rosso, Opt. Commun. 282, 4587 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (3)

M. Kovalsky and A. Hnilo, Phys. Rev. A 70, 043813 (2004).
[CrossRef]

P. Hauser, C. Tsallis, and E. Curado, Phys. Rev. A 30, 2074 (1984).
[CrossRef]

M. Larotonda, A. Hnilo, J. Méndez, and A. Yacomotti, Phys. Rev. A 65, 033812 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

TISEAN software is based on M. Sano and Y. Sawada, Phys. Rev. Lett. 55, 1082 (1985); it is freely available at http://www.mpipks-dresden.mpg.de/~tisean.
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

E. Ott, Rev. Mod. Phys. 53, 655 (1981).
[CrossRef]

Other (4)

H. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, 1996).
[CrossRef]

A. Siegman, in Lasers (University Science, 1986), Chap. 26.

A. Haken, Synergetics (Springer-Verlag, 1978).

A. E. Luna, “Láser de estado totalmente sólido pulsado con técnicas de Q-switch pasivo,” M.Sc. thesis final report (Facultad de Ciencias Exactas, Universidad de Buenos Aires, 2006) (in Spanish, available upon request to the corresponding author).

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Figures (2)

Fig. 1
Fig. 1

(a) Zoom of one of the raw data files used to calculate d E in the fully developed chaotic regime. The complete file has 8024 pulses. (b) Single sweep oscilloscope trace in the period-three stable region, both in amplitude (high, low, low) and in time spacing (short, long, long). Be aware that the pulse amplitudes displayed do not always correspond exactly to the real ones, because of the uneven sampling.

Fig. 2
Fig. 2

Percentage of false nearest neighbors as a function of the dimension of embedding ( d E ), for the complete file cor responding to Fig. 1a, m = 4 (first minimum of the mutual information). Squares: from the actual series of the time separation between consecutive pulses, a value d E = 5 is clearly determined. Triangles: the same from the surrogated data series. Note that this curve does not decay to zero. It indicates that the scrambled series, in opposition to the actual one, has no defined topological structure.

Equations (3)

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Δ i / Δ f 1 = ( Δ u / Δ f ) ln ( Δ i / Δ f ) ,
σ l g Δ ( τ ) = σ a l s N SA ( τ ) + k ,
Δ n + 1 = a 1 + a 2 Δ n exp ( Δ n / Δ u ) ,

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