Abstract

We consider a semiconductor laser with external optical feedback operating at a regime for which the delay time signature is extremely difficult to identify from the analysis of the intensity time series, using standard techniques. We show that such a delay signature can be successfully retrieved by computing the same quantifiers from the phase, the real or the imaginary part of the field, even in the presence of noise. Therefore, the choice of the observable is the determinant for parameter identification.

© 2011 Optical Society of America

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  1. A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
    [CrossRef] [PubMed]
  2. X. Li, W. Pan, B. Luo, and D. Ma, IEEE J. Quantum Electron. 42, 953 (2006).
    [CrossRef]
  3. R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, Phys. Rev. Lett. 81, 558 (1998).
    [CrossRef]
  4. V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, Phys. Lett. A 308, 54 (2003).
    [CrossRef]
  5. M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, Phys. D 203, 209 (2005).
    [CrossRef]
  6. L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, Phys. Rev. E 82, 046212 (2010).
    [CrossRef]
  7. D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, Opt. Lett. 32, 2960 (2007).
    [CrossRef] [PubMed]
  8. D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortín, IEEE J. Quantum Electron. 45, 879 (2009).
    [CrossRef]
  9. J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, Opt. Express 18, 6661 (2010).
    [CrossRef] [PubMed]
  10. C. Letellier, L. A. Aguirre, and J. Maquet, Phys. Rev. E 71, 066213 (2005).
    [CrossRef]
  11. R. Lang and K. Kobayashi, IEEE J. Quantum Electron. 16, 347 (1980).
    [CrossRef]
  12. H. C. Wang, K. P. Ho, H. K. Chen, and H. C. Lu, J. Lightwave Technol. 24, 5075 (2006).
    [CrossRef]
  13. L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, IEEE Photon. Technol. Lett. 21, 143 (2009).
    [CrossRef]
  14. R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, Phys. Rev. Lett. 107, 034103 (2011).
    [CrossRef] [PubMed]

2011

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, Phys. Rev. Lett. 107, 034103 (2011).
[CrossRef] [PubMed]

2010

J. G. Wu, G. Q. Xia, X. Tang, X. D. Lin, T. Deng, L. Fan, and Z. M. Wu, Opt. Express 18, 6661 (2010).
[CrossRef] [PubMed]

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, Phys. Rev. E 82, 046212 (2010).
[CrossRef]

2009

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortín, IEEE J. Quantum Electron. 45, 879 (2009).
[CrossRef]

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, IEEE Photon. Technol. Lett. 21, 143 (2009).
[CrossRef]

2007

2006

X. Li, W. Pan, B. Luo, and D. Ma, IEEE J. Quantum Electron. 42, 953 (2006).
[CrossRef]

H. C. Wang, K. P. Ho, H. K. Chen, and H. C. Lu, J. Lightwave Technol. 24, 5075 (2006).
[CrossRef]

2005

C. Letellier, L. A. Aguirre, and J. Maquet, Phys. Rev. E 71, 066213 (2005).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, Phys. D 203, 209 (2005).
[CrossRef]

2003

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, Phys. Lett. A 308, 54 (2003).
[CrossRef]

1998

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, Phys. Rev. Lett. 81, 558 (1998).
[CrossRef]

1980

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

Aguirre, L. A.

C. Letellier, L. A. Aguirre, and J. Maquet, Phys. Rev. E 71, 066213 (2005).
[CrossRef]

Annovazzi-Lodi, V.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Argyris, A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Bezruchko, B. P.

M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, Phys. D 203, 209 (2005).
[CrossRef]

Bünner, M. J.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, Phys. Rev. Lett. 81, 558 (1998).
[CrossRef]

Chen, H. K.

Citrin, D. S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortín, IEEE J. Quantum Electron. 45, 879 (2009).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, Opt. Lett. 32, 2960 (2007).
[CrossRef] [PubMed]

Colet, P.

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, Phys. Rev. Lett. 107, 034103 (2011).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Cuenot, J. B.

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, Phys. Lett. A 308, 54 (2003).
[CrossRef]

Deng, T.

Fan, L.

Fischer, I.

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, Phys. Rev. E 82, 046212 (2010).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

García-Ojalvo, J.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Giaquinta, A.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, Phys. Rev. Lett. 81, 558 (1998).
[CrossRef]

Goedgebuer, J. P.

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, Phys. Lett. A 308, 54 (2003).
[CrossRef]

Hegger, R.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, Phys. Rev. Lett. 81, 558 (1998).
[CrossRef]

Ho, K. P.

Kantz, H.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, Phys. Rev. Lett. 81, 558 (1998).
[CrossRef]

Karavaev, A. S.

M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, Phys. D 203, 209 (2005).
[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.

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, Phys. Rev. Lett. 107, 034103 (2011).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, Phys. Lett. A 308, 54 (2003).
[CrossRef]

Letellier, C.

C. Letellier, L. A. Aguirre, and J. Maquet, Phys. Rev. E 71, 066213 (2005).
[CrossRef]

Levy, P.

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, Phys. Lett. A 308, 54 (2003).
[CrossRef]

Li, X.

X. Li, W. Pan, B. Luo, and D. Ma, IEEE J. Quantum Electron. 42, 953 (2006).
[CrossRef]

Lin, X. D.

Locquet, A.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortín, IEEE J. Quantum Electron. 45, 879 (2009).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, Opt. Lett. 32, 2960 (2007).
[CrossRef] [PubMed]

Lu, H. C.

Luo, B.

X. Li, W. Pan, B. Luo, and D. Ma, IEEE J. Quantum Electron. 42, 953 (2006).
[CrossRef]

Ma, D.

X. Li, W. Pan, B. Luo, and D. Ma, IEEE J. Quantum Electron. 42, 953 (2006).
[CrossRef]

Maquet, J.

C. Letellier, L. A. Aguirre, and J. Maquet, Phys. Rev. E 71, 066213 (2005).
[CrossRef]

Mirasso, C. R.

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, Phys. Rev. E 82, 046212 (2010).
[CrossRef]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Nguimdo, R. M.

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, Phys. Rev. Lett. 107, 034103 (2011).
[CrossRef] [PubMed]

Ortín, S.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortín, IEEE J. Quantum Electron. 45, 879 (2009).
[CrossRef]

Pan, W.

X. Li, W. Pan, B. Luo, and D. Ma, IEEE J. Quantum Electron. 42, 953 (2006).
[CrossRef]

Pesquera, L.

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, Phys. Rev. Lett. 107, 034103 (2011).
[CrossRef] [PubMed]

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Petermann, K.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, IEEE Photon. Technol. Lett. 21, 143 (2009).
[CrossRef]

Ponomarenko, V. I.

M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, Phys. D 203, 209 (2005).
[CrossRef]

Prokhorov, M. D.

M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, Phys. D 203, 209 (2005).
[CrossRef]

Rhodes, W. T.

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, Phys. Lett. A 308, 54 (2003).
[CrossRef]

Rontani, D.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortín, IEEE J. Quantum Electron. 45, 879 (2009).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, Opt. Lett. 32, 2960 (2007).
[CrossRef] [PubMed]

Rosso, O. A.

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, Phys. Rev. E 82, 046212 (2010).
[CrossRef]

Sciamanna, M.

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortín, IEEE J. Quantum Electron. 45, 879 (2009).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, Opt. Lett. 32, 2960 (2007).
[CrossRef] [PubMed]

Shore, K. A.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Soriano, M. C.

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, Phys. Rev. E 82, 046212 (2010).
[CrossRef]

Syvridis, D.

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Tang, X.

Udaltsov, V. S.

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, Phys. Lett. A 308, 54 (2003).
[CrossRef]

Voigt, K.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, IEEE Photon. Technol. Lett. 21, 143 (2009).
[CrossRef]

Wang, H. C.

Weinert, C. M.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, IEEE Photon. Technol. Lett. 21, 143 (2009).
[CrossRef]

Winzer, G.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, IEEE Photon. Technol. Lett. 21, 143 (2009).
[CrossRef]

Wu, J. G.

Wu, Z. M.

Xia, G. Q.

Zimmermann, L.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, IEEE Photon. Technol. Lett. 21, 143 (2009).
[CrossRef]

Zunino, L.

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, Phys. Rev. E 82, 046212 (2010).
[CrossRef]

IEEE J. Quantum Electron.

X. Li, W. Pan, B. Luo, and D. Ma, IEEE J. Quantum Electron. 42, 953 (2006).
[CrossRef]

D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortín, IEEE J. Quantum Electron. 45, 879 (2009).
[CrossRef]

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

IEEE Photon. Technol. Lett.

L. Zimmermann, K. Voigt, G. Winzer, K. Petermann, and C. M. Weinert, IEEE Photon. Technol. Lett. 21, 143 (2009).
[CrossRef]

J. Lightwave Technol.

Nature

A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, Nature 438, 343 (2005).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. D

M. D. Prokhorov, V. I. Ponomarenko, A. S. Karavaev, and B. P. Bezruchko, Phys. D 203, 209 (2005).
[CrossRef]

Phys. Lett. A

V. S. Udaltsov, J. P. Goedgebuer, L. Larger, J. B. Cuenot, P. Levy, and W. T. Rhodes, Phys. Lett. A 308, 54 (2003).
[CrossRef]

Phys. Rev. E

L. Zunino, M. C. Soriano, I. Fischer, O. A. Rosso, and C. R. Mirasso, Phys. Rev. E 82, 046212 (2010).
[CrossRef]

C. Letellier, L. A. Aguirre, and J. Maquet, Phys. Rev. E 71, 066213 (2005).
[CrossRef]

Phys. Rev. Lett.

R. Hegger, M. J. Bünner, H. Kantz, and A. Giaquinta, Phys. Rev. Lett. 81, 558 (1998).
[CrossRef]

R. M. Nguimdo, P. Colet, L. Larger, and L. Pesquera, Phys. Rev. Lett. 107, 034103 (2011).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

AC (left) and DMI (right) computed from I ( t ) disregarding noise ( β = 0 ) for κ = 2.5 ns 1 , (a), (d)  κ = 5 ns 1 (b), (e) and κ = 10 ns 1 . (c), (f) Vertical dashes indicate the delay time T = 1 ns . We have used a time series with 5 × 10 6 data points sampled every 10 ps .

Fig. 2
Fig. 2

AC (left) and DMI (right), as in Fig. 1, but computed from φ ( t ) (solid line) and R e [ E ( t ) ] (dotted line) and considering β = 10 3 s 1 .

Fig. 3
Fig. 3

Size of the DMI peak signaling the delay computed from (a), (d)  I ( t ) , (b), (e)  φ ( t ) , and (c), (f)  R e [ E ( t ) ] , considering β = 10 3 s 1 . For the left column, T = 1 ns , while for the right column, κ = 2.5 ns 1 . Solid lines and bars indicate the background mean value and standard deviation.

Fig. 4
Fig. 4

DMI peak location computed from I ( t ) (•), φ ( t ) (▾) and R e ( E ( t ) ) (+) for (a)  T = 1 ns and (b)  5 ns . (b) Horizontal dashed lines indicate the delay time. β = 0 .

Fig. 5
Fig. 5

(a) Power and (b) optical spectra for κ = 2.5 ns 1 , T = 1 ns and for (a)  β = 0 and (b)  β = 10 3 s 1 .

Equations (5)

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

d E d t = 1 + i α 2 ( G 1 τ p ) E ( t ) + κ E T e i ω 0 T + F ( t ) ,
d N d t = J 0 N τ e G | E | 2 ,
C ( s ) = [ x ( t ) x ( t ) ] [ x s ( t ) x ( t ) ] [ x ( t ) x ( t ) ] 2 ,
D ( s ) = x ( t ) , x s ( t ) p ( x ( t ) , x s ( t ) ) ln p ( x ( t ) , x s ( t ) ) p ( x ( t ) ) p ( x s ( t ) ) ,
d φ d t = α 2 ( G 1 τ p ) + κ | E T | | E | sin ( φ T φ ω 0 T ) .

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