Abstract

The nonlinear dynamics of lasers with frequency-shifted delayed feedback are investigated. Resonant excitation of sustained relaxation oscillations by harmonic resonance is demonstrated. Self-induced switching between sustained relaxation oscillation and spiking oscillation is observed as the feedback coefficient is increased. Observed instabilities are well reproduced by numerical simulations of proposed model equations. A statistical analysis of this switching phenomenon is carried out numerically, and the results indicate that an inverse-power relation with the feedback coefficient determines the periods over which the system dwells in its relaxation-oscillation state.

© 2001 Optical Society of America

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    [CrossRef] [PubMed]
  2. M. C. Mackay and L. Glass, Science 197, 287 (1977).
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    [CrossRef] [PubMed]
  4. K. Ikeda, Opt. Commun. 30, 257 (1979).
    [CrossRef]
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    [CrossRef]
  6. See, for example, K. Peterman, IEEE J. Sel. Top. Quantum Electron. 1, 480 (1995), and references therein.
    [CrossRef]
  7. K. Otsuka, Jpn. J. Appl. Phys. 31, 1546 (1992).
    [CrossRef]
  8. K. Otsuka, IEEE J. Quantum Electron. QE-15, 655 (1979).
    [CrossRef]
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    [CrossRef]
  10. J.-L. Chern, K. Otsuka, and F. Ishiyama, Opt. Commun. 96, 259 (1993).
    [CrossRef]
  11. K. Otsuka, Nonlinear Dynamics in Optical Complex Systems (Kluwer Academic, Dordrecht, The Netherlands, 1999), pp. 85 and 233.
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  13. H. G. Winful and L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
    [CrossRef] [PubMed]
  14. K. Otsuka, R. Kawai, S.-L. Hwong, J.-Y. Ko, and J.-L. Chern, Phys. Rev. Lett. 84, 3049 (2000).
    [CrossRef] [PubMed]
  15. K. Otsuka, P. Mandel, M. Georgiou, and C. Etric, Jpn. J. Appl. Phys. 32, 318 (1993).
    [CrossRef]

2000 (1)

K. Otsuka, R. Kawai, S.-L. Hwong, J.-Y. Ko, and J.-L. Chern, Phys. Rev. Lett. 84, 3049 (2000).
[CrossRef] [PubMed]

1999 (1)

K. Otsuka, J.-Y. Ko, J.-L. Chern, K. Ohki, and H. Utsu, Phys. Rev. A 60, 3389 (1999).
[CrossRef]

1996 (1)

J. Foss, A. Longtin, B. Mensour, and J. Milton, Phys. Rev. Lett. 76, 708 (1996).
[CrossRef] [PubMed]

1995 (1)

See, for example, K. Peterman, IEEE J. Sel. Top. Quantum Electron. 1, 480 (1995), and references therein.
[CrossRef]

1993 (2)

J.-L. Chern, K. Otsuka, and F. Ishiyama, Opt. Commun. 96, 259 (1993).
[CrossRef]

K. Otsuka, P. Mandel, M. Georgiou, and C. Etric, Jpn. J. Appl. Phys. 32, 318 (1993).
[CrossRef]

1992 (1)

K. Otsuka, Jpn. J. Appl. Phys. 31, 1546 (1992).
[CrossRef]

1990 (1)

H. G. Winful and L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
[CrossRef] [PubMed]

1980 (1)

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

1979 (2)

K. Otsuka, IEEE J. Quantum Electron. QE-15, 655 (1979).
[CrossRef]

K. Ikeda, Opt. Commun. 30, 257 (1979).
[CrossRef]

1977 (1)

M. C. Mackay and L. Glass, Science 197, 287 (1977).
[CrossRef]

1976 (1)

R. M. May, Nature 261, 459 (1976).
[CrossRef] [PubMed]

Chern, J.-L.

K. Otsuka, R. Kawai, S.-L. Hwong, J.-Y. Ko, and J.-L. Chern, Phys. Rev. Lett. 84, 3049 (2000).
[CrossRef] [PubMed]

K. Otsuka, J.-Y. Ko, J.-L. Chern, K. Ohki, and H. Utsu, Phys. Rev. A 60, 3389 (1999).
[CrossRef]

J.-L. Chern, K. Otsuka, and F. Ishiyama, Opt. Commun. 96, 259 (1993).
[CrossRef]

Cohen, L.

L. Cohen, Time-Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1995).

Etric, C.

K. Otsuka, P. Mandel, M. Georgiou, and C. Etric, Jpn. J. Appl. Phys. 32, 318 (1993).
[CrossRef]

Foss, J.

J. Foss, A. Longtin, B. Mensour, and J. Milton, Phys. Rev. Lett. 76, 708 (1996).
[CrossRef] [PubMed]

Georgiou, M.

K. Otsuka, P. Mandel, M. Georgiou, and C. Etric, Jpn. J. Appl. Phys. 32, 318 (1993).
[CrossRef]

Glass, L.

M. C. Mackay and L. Glass, Science 197, 287 (1977).
[CrossRef]

Hwong, S.-L.

K. Otsuka, R. Kawai, S.-L. Hwong, J.-Y. Ko, and J.-L. Chern, Phys. Rev. Lett. 84, 3049 (2000).
[CrossRef] [PubMed]

Ikeda, K.

K. Ikeda, Opt. Commun. 30, 257 (1979).
[CrossRef]

Ishiyama, F.

J.-L. Chern, K. Otsuka, and F. Ishiyama, Opt. Commun. 96, 259 (1993).
[CrossRef]

Kawai, R.

K. Otsuka, R. Kawai, S.-L. Hwong, J.-Y. Ko, and J.-L. Chern, Phys. Rev. Lett. 84, 3049 (2000).
[CrossRef] [PubMed]

Ko, J.-Y.

K. Otsuka, R. Kawai, S.-L. Hwong, J.-Y. Ko, and J.-L. Chern, Phys. Rev. Lett. 84, 3049 (2000).
[CrossRef] [PubMed]

K. Otsuka, J.-Y. Ko, J.-L. Chern, K. Ohki, and H. Utsu, Phys. Rev. A 60, 3389 (1999).
[CrossRef]

Kobayashi, K.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Longtin, A.

J. Foss, A. Longtin, B. Mensour, and J. Milton, Phys. Rev. Lett. 76, 708 (1996).
[CrossRef] [PubMed]

Mackay, M. C.

M. C. Mackay and L. Glass, Science 197, 287 (1977).
[CrossRef]

Mandel, P.

K. Otsuka, P. Mandel, M. Georgiou, and C. Etric, Jpn. J. Appl. Phys. 32, 318 (1993).
[CrossRef]

May, R. M.

R. M. May, Nature 261, 459 (1976).
[CrossRef] [PubMed]

Mensour, B.

J. Foss, A. Longtin, B. Mensour, and J. Milton, Phys. Rev. Lett. 76, 708 (1996).
[CrossRef] [PubMed]

Milton, J.

J. Foss, A. Longtin, B. Mensour, and J. Milton, Phys. Rev. Lett. 76, 708 (1996).
[CrossRef] [PubMed]

Ohki, K.

K. Otsuka, J.-Y. Ko, J.-L. Chern, K. Ohki, and H. Utsu, Phys. Rev. A 60, 3389 (1999).
[CrossRef]

Otsuka, K.

K. Otsuka, R. Kawai, S.-L. Hwong, J.-Y. Ko, and J.-L. Chern, Phys. Rev. Lett. 84, 3049 (2000).
[CrossRef] [PubMed]

K. Otsuka, J.-Y. Ko, J.-L. Chern, K. Ohki, and H. Utsu, Phys. Rev. A 60, 3389 (1999).
[CrossRef]

K. Otsuka, P. Mandel, M. Georgiou, and C. Etric, Jpn. J. Appl. Phys. 32, 318 (1993).
[CrossRef]

J.-L. Chern, K. Otsuka, and F. Ishiyama, Opt. Commun. 96, 259 (1993).
[CrossRef]

K. Otsuka, Jpn. J. Appl. Phys. 31, 1546 (1992).
[CrossRef]

K. Otsuka, IEEE J. Quantum Electron. QE-15, 655 (1979).
[CrossRef]

K. Otsuka, Nonlinear Dynamics in Optical Complex Systems (Kluwer Academic, Dordrecht, The Netherlands, 1999), pp. 85 and 233.

Peterman, K.

See, for example, K. Peterman, IEEE J. Sel. Top. Quantum Electron. 1, 480 (1995), and references therein.
[CrossRef]

Rahman, L.

H. G. Winful and L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
[CrossRef] [PubMed]

Utsu, H.

K. Otsuka, J.-Y. Ko, J.-L. Chern, K. Ohki, and H. Utsu, Phys. Rev. A 60, 3389 (1999).
[CrossRef]

Winful, H. G.

H. G. Winful and L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

K. Otsuka, IEEE J. Quantum Electron. QE-15, 655 (1979).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

See, for example, K. Peterman, IEEE J. Sel. Top. Quantum Electron. 1, 480 (1995), and references therein.
[CrossRef]

Jpn. J. Appl. Phys. (2)

K. Otsuka, Jpn. J. Appl. Phys. 31, 1546 (1992).
[CrossRef]

K. Otsuka, P. Mandel, M. Georgiou, and C. Etric, Jpn. J. Appl. Phys. 32, 318 (1993).
[CrossRef]

Nature (1)

R. M. May, Nature 261, 459 (1976).
[CrossRef] [PubMed]

Opt. Commun. (2)

K. Ikeda, Opt. Commun. 30, 257 (1979).
[CrossRef]

J.-L. Chern, K. Otsuka, and F. Ishiyama, Opt. Commun. 96, 259 (1993).
[CrossRef]

Phys. Rev. A (1)

K. Otsuka, J.-Y. Ko, J.-L. Chern, K. Ohki, and H. Utsu, Phys. Rev. A 60, 3389 (1999).
[CrossRef]

Phys. Rev. Lett. (3)

J. Foss, A. Longtin, B. Mensour, and J. Milton, Phys. Rev. Lett. 76, 708 (1996).
[CrossRef] [PubMed]

H. G. Winful and L. Rahman, Phys. Rev. Lett. 65, 1575 (1990).
[CrossRef] [PubMed]

K. Otsuka, R. Kawai, S.-L. Hwong, J.-Y. Ko, and J.-L. Chern, Phys. Rev. Lett. 84, 3049 (2000).
[CrossRef] [PubMed]

Science (1)

M. C. Mackay and L. Glass, Science 197, 287 (1977).
[CrossRef]

Other (2)

K. Otsuka, Nonlinear Dynamics in Optical Complex Systems (Kluwer Academic, Dordrecht, The Netherlands, 1999), pp. 85 and 233.

L. Cohen, Time-Frequency Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1995).

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Figures (4)

Fig. 1
Fig. 1

Experimental arrangement of a laser-diode- (LD-) pumped LNP laser with frequency-shifted feedback.

Fig. 2
Fig. 2

Typical waveforms and the corresponding joint time–frequency analysis patterns, as observed for n=2. Periodic RO: (a) feedback ratio, -65 dB. Switching between RO and SO: (b) feedback ratio, -50 dB; (c) feedback ratio, -45 dB.

Fig. 3
Fig. 3

Numerical bifurcation diagram of lasers with frequency-shifted delayed feedback, as a function of feedback coefficient. Delay time tD=1, w=1.1125, K=2000, and ΔΩ=2ΩR=0.02086.

Fig. 4
Fig. 4

Typical waveforms in regions A and B of Fig.  3 and the corresponding joint time–frequency analysis patterns. The parameter values are the same as were used for Fig.  3. Sustained RO: (a) m=0.0012. Switching between RO and SO: (b) m=0.0089, (c) m=0.0150.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

dNt/dt=w-1-Nt-1+2NtEt2/K,
dEt/dt=NtEt+mEt-tDcosΨ,
dϕt/dt=mEt-tD/EtsinΨ,
Ψt=ΔΩt-ϕt+ϕt-tD-Ωo+ΔΩ/2tD,

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