Abstract

We show theoretically and experimentally that a semiconductor laser driven to chaos by optical feedback may be self-synchronized by reinjection of a delayed replica of its same optical output. The ensuing periodic regularity of the self-synchronized laser output is analyzed.

© 2009 Optical Society of America

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References

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  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, Nature 438, 343 (2005).
    [CrossRef] [PubMed]
  2. V. Annovazzi-Lodi, A. Argyris, M. Benedetti, M. Hamacher, S. Merlo, and D. Syvridis, Opt. Photonics News 19, 36 (2008).
    [CrossRef]
  3. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
    [CrossRef] [PubMed]
  4. F. T. Arecchi, R. Meucci, E. Allaria, A. DiGarbo, and L. S. Tsimring, Phys. Rev. E 65, 046237 (2002).
    [CrossRef]
  5. A. Mecozzi and C. Antonelli, arXiv:0811.0258v2.
  6. R. Vicente, C. R. Mirasso, and I. Fischer, Opt. Lett. 32, 403 (2007).
    [CrossRef] [PubMed]
  7. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
    [CrossRef]
  8. C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
    [CrossRef]

2008 (1)

V. Annovazzi-Lodi, A. Argyris, M. Benedetti, M. Hamacher, S. Merlo, and D. Syvridis, Opt. Photonics News 19, 36 (2008).
[CrossRef]

2007 (1)

2005 (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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

2002 (1)

F. T. Arecchi, R. Meucci, E. Allaria, A. DiGarbo, and L. S. Tsimring, Phys. Rev. E 65, 046237 (2002).
[CrossRef]

1990 (1)

L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
[CrossRef] [PubMed]

1982 (1)

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

1980 (1)

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

Allaria, E.

F. T. Arecchi, R. Meucci, E. Allaria, A. DiGarbo, and L. S. Tsimring, Phys. Rev. E 65, 046237 (2002).
[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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Annovazzi-Lodi, V.

V. Annovazzi-Lodi, A. Argyris, M. Benedetti, M. Hamacher, S. Merlo, and D. Syvridis, Opt. Photonics News 19, 36 (2008).
[CrossRef]

Antonelli, C.

A. Mecozzi and C. Antonelli, arXiv:0811.0258v2.

Arecchi, F. T.

F. T. Arecchi, R. Meucci, E. Allaria, A. DiGarbo, and L. S. Tsimring, Phys. Rev. E 65, 046237 (2002).
[CrossRef]

Argyris, A.

V. Annovazzi-Lodi, A. Argyris, M. Benedetti, M. Hamacher, S. Merlo, and D. Syvridis, Opt. Photonics News 19, 36 (2008).
[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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Benedetti, M.

V. Annovazzi-Lodi, A. Argyris, M. Benedetti, M. Hamacher, S. Merlo, and D. Syvridis, Opt. Photonics News 19, 36 (2008).
[CrossRef]

Carroll, T. L.

L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
[CrossRef] [PubMed]

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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

DiGarbo, A.

F. T. Arecchi, R. Meucci, E. Allaria, A. DiGarbo, and L. S. Tsimring, Phys. Rev. E 65, 046237 (2002).
[CrossRef]

Fischer, I.

R. Vicente, C. R. Mirasso, and I. Fischer, Opt. Lett. 32, 403 (2007).
[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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Hamacher, M.

V. Annovazzi-Lodi, A. Argyris, M. Benedetti, M. Hamacher, S. Merlo, and D. Syvridis, Opt. Photonics News 19, 36 (2008).
[CrossRef]

Henry, C. H.

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[CrossRef]

Kobayashi, K.

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

Lang, R.

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

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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Mecozzi, A.

A. Mecozzi and C. Antonelli, arXiv:0811.0258v2.

Merlo, S.

V. Annovazzi-Lodi, A. Argyris, M. Benedetti, M. Hamacher, S. Merlo, and D. Syvridis, Opt. Photonics News 19, 36 (2008).
[CrossRef]

Meucci, R.

F. T. Arecchi, R. Meucci, E. Allaria, A. DiGarbo, and L. S. Tsimring, Phys. Rev. E 65, 046237 (2002).
[CrossRef]

Mirasso, C. R.

R. Vicente, C. R. Mirasso, and I. Fischer, Opt. Lett. 32, 403 (2007).
[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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Pecora, L. M.

L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Shore, K. 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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Syvridis, D.

V. Annovazzi-Lodi, A. Argyris, M. Benedetti, M. Hamacher, S. Merlo, and D. Syvridis, Opt. Photonics News 19, 36 (2008).
[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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Tsimring, L. S.

F. T. Arecchi, R. Meucci, E. Allaria, A. DiGarbo, and L. S. Tsimring, Phys. Rev. E 65, 046237 (2002).
[CrossRef]

Vicente, R.

IEEE J. Quantum Electron. (2)

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

C. H. Henry, IEEE J. Quantum Electron. 18, 259 (1982).
[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, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Opt. Lett. (1)

Opt. Photonics News (1)

V. Annovazzi-Lodi, A. Argyris, M. Benedetti, M. Hamacher, S. Merlo, and D. Syvridis, Opt. Photonics News 19, 36 (2008).
[CrossRef]

Phys. Rev. E (1)

F. T. Arecchi, R. Meucci, E. Allaria, A. DiGarbo, and L. S. Tsimring, Phys. Rev. E 65, 046237 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
[CrossRef] [PubMed]

Other (1)

A. Mecozzi and C. Antonelli, arXiv:0811.0258v2.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup. The light emitted by a distributed-feedback laser diode (DFB LD) at 1550 nm is focused into one end of a 670 m single-mode (SM) fiber through a system of lenses in a 5 cm air cavity and is backreflected after propagation by a high-reflectivity mirror placed at the other end of the fiber. Forward- and backward-propagating light is 50 50 outcoupled to photodiodes PD1 and PD2, and the corresponding photocurrents are sampled at 20   Gigasamples s with a real-time 6 GHz bandwidth oscilloscope.

Fig. 2
Fig. 2

Time series of the photodetected intensity of the electric field from (a) experiment and (b) numerical simulation in a 25 ns window. Solid curves refer to the detected intensity at time t, i d ( t ) , while dotted–dashed curves refer to the same quantity one round-trip T before, i d ( t T ) . The plotted intensity is normalized to have zero mean and unit root-mean-square value.

Fig. 3
Fig. 3

Normalized autocorrelation function of the detected intensity of the electric field i d ( t ) versus time from (a) experiment and (b) numerical simulation. Circles report an exponential approximation of the decay of the correlation peaks.

Fig. 4
Fig. 4

Enlarged view of the autocorrelation peaks of Fig. 3 centered at (a) t = 0 , (b) t = T , and (c) t = 2 T , versus the scaled time t n T with n = 0 , 1, and 2, respectively. The dashed curves refer to the experiment, and the solid curves refer to numerical simulations. In the same plots, dotted curves show the autocorrelation function of the simulated detected photocurrent in the absence of injection from the distant mirror (i.e., κ = 0 ).

Equations (2)

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d E d t = ( 1 i α ) [ G ( t ) 1 τ p ] E ( t ) 2 + γ E ( t Δ t ) × exp ( i ω 0 Δ t ) + κ E ext ( t ) + R F ( t ) ,
d N d t = I e N ( t ) τ c G ( t ) E ( t ) 2 ,

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