Abstract

A period-doubling route to chaos with nonstationary transverse pattern is observed in a diode-pumped Nd:YAG laser with a Cr4+:YAG saturable absorber. The nonlinear behavior results from the multitransverse-mode competition with gradually adding the number of the transverse modes. By analyzing the transverse pattern, we find that the bifurcation accompanies with the increase of the higher-order family of transverse modes in sequence. Moreover, a series of period-doubling route to chaos beginning from the low period is attained by varying the pump power at specific cavity configurations.

© 2004 Optical Society of America

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References

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Eur. Phys. J. (1)

Q. Zhang, B. Ozygus, and H. Weber, �??Degeneration effects in laser cavities,�?? Eur. Phys. J. AP 6, 293-298 (1999).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (2)

H.-H. Wu, C.-C. Sheu, T.-W. Chen, M.-D. Wei, and W.-F. Hsieh, �??Observation of power drop and low threshold due to beam waist shrinkage around critical configurations in an an pumped Nd:YVO4 laser,�?? Opt. Commun. 165, 225-229 (1999).
[CrossRef]

M.-D. Wei, W.-F. Hsieh, and C. C. Sung, �??Dynamics of an optical resonator determined by its iterative map of beam parameters,�?? Opt. Commun. 146, 201-207 (1998).
[CrossRef]

Opt. Lett. (3)

Phy. Rev. (1)

K. Tanii, T. Tohei, T. Sugawara, M. Tachikawa, and T. Shimizu, �??Two different routes to chaos in a twomode CO2 laser with a saturable absorber,�?? Phy. Rev. E 59, 1600-1604 (1999).
[CrossRef]

Phy. Rev. A (2)

L. A. Lugiato, F. Prati, L. M. Narducci, P. Ru, J. R. Tredicce, and D. K. Bandy, �??Role of transverse effects in laser instabilities,�?? Phy. Rev. A 37, 3847-3866 (1988).
[CrossRef]

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, �?? Transverse laser patterns. I. Phase singularity crystals,�?? Phy. Rev. A 43, 5090-5113 (1991).
[CrossRef]

Phy. Rev. Lett. (1)

M. Tachikawa, F.-L. Hong, K. Tanii, and T. Shimizu, �??Deterministic chaos in passive Q-switching pulsation of a CO2 laser with saturable absorber,�?? Phy. Rev. Lett. 60, 2266-2268 (1988).
[CrossRef]

Phys. Rep. (2)

F. T. Arecchi, S. Boccaletti, and P. Ramazza, �??Pattern formation and competition in nonlinear optics,�?? Phys. Rep. 318, 1-83 (1999).
[CrossRef]

M. Vasnetsov and K. Staliunas, Optical Vortices (Nova Science, New York, 1999).

Phys. Rev. A (1)

K. Klische, C. O. Weiss, and B. Wellegehausen, �??Spatiotemporal chaos from a continue Na2 laser,�?? Phys. Rev. A 39, 919-922 (1989).
[CrossRef] [PubMed]

Other (2)

A. E. Siegman, Lasers (University Science, Mill Valley, CA., 1986).

R. L. Devaney, A First Course in Chaotic Dynamical Systems �?? Theory and Experiment (Addison-Wesley, Sydney, 1992), Chap. 8.

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Figures (8)

Fig. 1.
Fig. 1.

Experimental setup

Fig. 2.
Fig. 2.

The evolutions of pulse trains at the cavity length of 64.13 mm. The pump powers with (a) 2.10 W, (b) 2.49 W, (c) 2.68 W, and (d) 3.66 W show period 1, period 2, period 4, and chaos, respectively.

Fig. 3.
Fig. 3.

Bifurcation diagram at the cavity length of 64.13 mm. We only show the peak frequency less or equal to the repetition rate, which is labeled by solid circle.

Fig. 4.
Fig. 4.

The transverse pattern as period 2 at the pump power of 2.2 W. The experimental patterns are shown an (a) and (b), and (c) corresponds to the numerical reconstructed patter of (b).

Fig. 5.
Fig. 5.

The transverse pattern as period 2 at the pump power of 2.68 W. The experimental results are shown in the upper row and numerically reconstructed patterns are plotted under the experimental ones. The corresponding parameters concluding the amplitude and the relative phase of the participating transverse modes in simulation are listed under the pictures.

Fig. 6.
Fig. 6.

The period-4 pulse train detected at the different spatial positions

Fig. 7.
Fig. 7.

The dark-dot patterns

Fig. 8.
Fig. 8.

The period-doubling route beginning from period 3 at the cavity length of 64.17 mm. The pump powers are (a) 2.58 W, (b) 2.88 W, and (c) 3.30W.

Equations (1)

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H G mn ( x , y ) = 1 ( 2 m + n 1 π m ! n ! ) 1 w 0 H m ( 2 x w 0 ) H n ( 2 y w 0 ) exp ( x 2 + y 2 w 0 2 ) ,

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