Abstract

We investigate a nonlinear dynamical behavior of the stimulated Brillouin scattering (SBS) near the threshold in the presence of feedback. When a cw Nd:YAG laser is injected into a single mode optical fiber, the SBS signal exhibits intermittently appearing irregular self-pulsations near the threshold. By examining the time series of the SBS signals, we verify that spontaneous Brillouin scattering having a stochastic property is dramatically suppressed due to the feedback. We explain the chaotic phenomenon of SBS in the presence of feedback in comparison with that in the absence of feedback.

© 2007 Optical Society of America

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  1. R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, "Evidence of chaotic stimulated Brillouin scattering in optical fibers," Phys. Rev. Lett. 65, 167 (1990).
    [CrossRef] [PubMed]
  2. W. Lu, A. Johnstone, and R. G. Harrison, "Deterministic dynamics of stimulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114 (1992).
    [CrossRef] [PubMed]
  3. D. Yu, W. Lu, and R. G. Harrison, "Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback," Phys. Rev. A 51, 669 (1995).
    [CrossRef] [PubMed]
  4. A. L. Gaeta and R. W. Boyd, "Stochastic dynamics of stimulated Brillouin scattering in an optcal fiber," Phys. Rev. A 44, 3205 (1991).
    [CrossRef] [PubMed]
  5. M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301 (1993).
    [CrossRef] [PubMed]
  6. R. G. Harrison, P. M. Ripley, and W. Lu, "Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback," Phys. Rev. A 49, R24 (1994).
    [CrossRef] [PubMed]
  7. S. H. Lee and C. M. Kim, "Chaotic stimulated Brillouin scattering near the threshold in a fiber," Opt. Lett. 31, 3131 (2006).
    [CrossRef] [PubMed]
  8. N. Platt, E. A. Spiegel, and C. Tresser, "On-off intermittency: A mechanism of bursting," Phy. Rev. Lett. 70, 279 (1993).
    [CrossRef]
  9. N. Platt, S. M. Hammel, and J. F. Heagy, "Effects of additive noise on on-off intermittency," Phy. Rev. Lett. 72, 3498 (1994).
    [CrossRef]
  10. P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, "Experimental observation of on-off intermittency," Phy. Rev. Lett 73, 1095 (1994).
    [CrossRef]

2006

1995

D. Yu, W. Lu, and R. G. Harrison, "Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback," Phys. Rev. A 51, 669 (1995).
[CrossRef] [PubMed]

1994

R. G. Harrison, P. M. Ripley, and W. Lu, "Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback," Phys. Rev. A 49, R24 (1994).
[CrossRef] [PubMed]

N. Platt, S. M. Hammel, and J. F. Heagy, "Effects of additive noise on on-off intermittency," Phy. Rev. Lett. 72, 3498 (1994).
[CrossRef]

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, "Experimental observation of on-off intermittency," Phy. Rev. Lett 73, 1095 (1994).
[CrossRef]

1993

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301 (1993).
[CrossRef] [PubMed]

N. Platt, E. A. Spiegel, and C. Tresser, "On-off intermittency: A mechanism of bursting," Phy. Rev. Lett. 70, 279 (1993).
[CrossRef]

1992

W. Lu, A. Johnstone, and R. G. Harrison, "Deterministic dynamics of stimulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114 (1992).
[CrossRef] [PubMed]

1991

A. L. Gaeta and R. W. Boyd, "Stochastic dynamics of stimulated Brillouin scattering in an optcal fiber," Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

1990

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, "Evidence of chaotic stimulated Brillouin scattering in optical fibers," Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, "Stochastic dynamics of stimulated Brillouin scattering in an optcal fiber," Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Dämmig, M.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301 (1993).
[CrossRef] [PubMed]

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, "Stochastic dynamics of stimulated Brillouin scattering in an optcal fiber," Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

Hammel, S. M.

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, "Experimental observation of on-off intermittency," Phy. Rev. Lett 73, 1095 (1994).
[CrossRef]

N. Platt, S. M. Hammel, and J. F. Heagy, "Effects of additive noise on on-off intermittency," Phy. Rev. Lett. 72, 3498 (1994).
[CrossRef]

Hammer, P. W.

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, "Experimental observation of on-off intermittency," Phy. Rev. Lett 73, 1095 (1994).
[CrossRef]

Harrison, R. G.

D. Yu, W. Lu, and R. G. Harrison, "Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback," Phys. Rev. A 51, 669 (1995).
[CrossRef] [PubMed]

R. G. Harrison, P. M. Ripley, and W. Lu, "Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback," Phys. Rev. A 49, R24 (1994).
[CrossRef] [PubMed]

W. Lu, A. Johnstone, and R. G. Harrison, "Deterministic dynamics of stimulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114 (1992).
[CrossRef] [PubMed]

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, "Evidence of chaotic stimulated Brillouin scattering in optical fibers," Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

Heagy, J. F.

N. Platt, S. M. Hammel, and J. F. Heagy, "Effects of additive noise on on-off intermittency," Phy. Rev. Lett. 72, 3498 (1994).
[CrossRef]

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, "Experimental observation of on-off intermittency," Phy. Rev. Lett 73, 1095 (1994).
[CrossRef]

Johnstone, A.

W. Lu, A. Johnstone, and R. G. Harrison, "Deterministic dynamics of stimulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114 (1992).
[CrossRef] [PubMed]

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, "Evidence of chaotic stimulated Brillouin scattering in optical fibers," Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

Kim, C. M.

Lee, B. D.

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, "Experimental observation of on-off intermittency," Phy. Rev. Lett 73, 1095 (1994).
[CrossRef]

Lee, S. H.

Lu, W.

D. Yu, W. Lu, and R. G. Harrison, "Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback," Phys. Rev. A 51, 669 (1995).
[CrossRef] [PubMed]

R. G. Harrison, P. M. Ripley, and W. Lu, "Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback," Phys. Rev. A 49, R24 (1994).
[CrossRef] [PubMed]

W. Lu, A. Johnstone, and R. G. Harrison, "Deterministic dynamics of stimulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114 (1992).
[CrossRef] [PubMed]

Mitschke, F.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301 (1993).
[CrossRef] [PubMed]

Moloney, J. V.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, "Evidence of chaotic stimulated Brillouin scattering in optical fibers," Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

Platt, N.

N. Platt, S. M. Hammel, and J. F. Heagy, "Effects of additive noise on on-off intermittency," Phy. Rev. Lett. 72, 3498 (1994).
[CrossRef]

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, "Experimental observation of on-off intermittency," Phy. Rev. Lett 73, 1095 (1994).
[CrossRef]

N. Platt, E. A. Spiegel, and C. Tresser, "On-off intermittency: A mechanism of bursting," Phy. Rev. Lett. 70, 279 (1993).
[CrossRef]

Ripley, P. M.

R. G. Harrison, P. M. Ripley, and W. Lu, "Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback," Phys. Rev. A 49, R24 (1994).
[CrossRef] [PubMed]

Spiegel, E. A.

N. Platt, E. A. Spiegel, and C. Tresser, "On-off intermittency: A mechanism of bursting," Phy. Rev. Lett. 70, 279 (1993).
[CrossRef]

Tresser, C.

N. Platt, E. A. Spiegel, and C. Tresser, "On-off intermittency: A mechanism of bursting," Phy. Rev. Lett. 70, 279 (1993).
[CrossRef]

Uppal, J. S.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, "Evidence of chaotic stimulated Brillouin scattering in optical fibers," Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

Welling, H.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301 (1993).
[CrossRef] [PubMed]

Yu, D.

D. Yu, W. Lu, and R. G. Harrison, "Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback," Phys. Rev. A 51, 669 (1995).
[CrossRef] [PubMed]

Zinner, G.

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301 (1993).
[CrossRef] [PubMed]

Opt. Lett.

Phy. Rev. Lett

P. W. Hammer, N. Platt, S. M. Hammel, J. F. Heagy, and B. D. Lee, "Experimental observation of on-off intermittency," Phy. Rev. Lett 73, 1095 (1994).
[CrossRef]

Phy. Rev. Lett.

N. Platt, E. A. Spiegel, and C. Tresser, "On-off intermittency: A mechanism of bursting," Phy. Rev. Lett. 70, 279 (1993).
[CrossRef]

N. Platt, S. M. Hammel, and J. F. Heagy, "Effects of additive noise on on-off intermittency," Phy. Rev. Lett. 72, 3498 (1994).
[CrossRef]

Phys. Rev. A

W. Lu, A. Johnstone, and R. G. Harrison, "Deterministic dynamics of stimulated scattering phenomena with external feedback," Phys. Rev. A 46, 4114 (1992).
[CrossRef] [PubMed]

D. Yu, W. Lu, and R. G. Harrison, "Physical origin of dynamical stimulated Brillouin scattering in optical fibers with feedback," Phys. Rev. A 51, 669 (1995).
[CrossRef] [PubMed]

A. L. Gaeta and R. W. Boyd, "Stochastic dynamics of stimulated Brillouin scattering in an optcal fiber," Phys. Rev. A 44, 3205 (1991).
[CrossRef] [PubMed]

M. Dämmig, G. Zinner, F. Mitschke, and H. Welling, "Stimulated Brillouin scattering in fibers with and without external feedback," Phys. Rev. A 48, 3301 (1993).
[CrossRef] [PubMed]

R. G. Harrison, P. M. Ripley, and W. Lu, "Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback," Phys. Rev. A 49, R24 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, "Evidence of chaotic stimulated Brillouin scattering in optical fibers," Phys. Rev. Lett. 65, 167 (1990).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental setup. F.I. is the Faraday isolator, N.D. is the neutral density filter and D1, D2, D3 are the photo-detectors. B.S. is the beam splitter, H. P. is the half wave plate, L1, L2, L4, L5 are the focusing lenses, and L3 is the 10× microscope lens.

Fig. 2.
Fig. 2.

Experimentally obtained time series of SBS near the threshold depending on the pump power for (a) 258, (b) 174, (c) 155, and (d) 129 mW. (e) is the temporal behavior of the pump laser.

Fig. 3.
Fig. 3.

The time series and its time-delayed phase portraits of the back scattered SBS signals for τ= 0.1Tr . (a) and (b) are for the average pump power of 174 mW, and (c) and (d) for 309 mW.

Fig. 4.
Fig. 4.

Probability distribution of laminar phases versus laminar length. The circles represent the experimental results and the solid line is a slope of -3/2.

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