Abstract

We unveil theoretically the bifurcations to chaotic low-frequency fluctuations (LFF) in a laser diode with phase-conjugate feedback (PCF). LFF occur from a chaotic itinerancy among destabilized limit-cycle attractors that correspond to the external-cavity modes (ECMs) of the PCF laser system and with a directional motion toward a self-pulsating dynamics of increasing frequency and larger output power. When increasing the feedback strength, the frequency of the fast-pulsing dynamics changes about a multiple of the external-cavity frequency, which is a unique feature of LFF in a laser diode with PCF.

© 2014 Optical Society of America

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  1. C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
    [CrossRef]
  2. T. Sano, Phys. Rev. A 50, 2719 (1994).
    [CrossRef]
  3. G. H. M. Van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995).
    [CrossRef]
  4. I. Fischer, G. H. M. Van Tartwijk, A. M. Levine, W. Elsaesser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
    [CrossRef]
  5. J. S. Lawrence and D. M. Kane, Phys. Rev. A 63, 033805 (2001).
    [CrossRef]
  6. A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Europhys. Lett. 101, 24001 (2013).
    [CrossRef]
  7. G. P. Agrawal and J. T. Klaus, Opt. Lett. 16, 1325 (1991).
    [CrossRef]
  8. T. Erneux, A. Gavrielides, K. Green, and B. Krauskopf, Phys. Rev. E 68, 066205 (2003).
    [CrossRef]
  9. M. Virte, A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Phys. Rev. A 84, 043836 (2011).
    [CrossRef]
  10. D. O’Brien, G. Huyet, and J. G. McInerney, Phys. Rev. A 64, 025802 (2001).
    [CrossRef]
  11. A. Hohl, H. J. C. van der Linden, and R. Roy, Opt. Lett. 20, 2396 (1995).
    [CrossRef]
  12. J. Zamora-Munt, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 81, 033820 (2010).
    [CrossRef]
  13. A. Torcini, S. Barland, G. Giacomelli, and F. Marin, Phys. Rev. A 74, 063801 (2006).
    [CrossRef]

2013 (1)

A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Europhys. Lett. 101, 24001 (2013).
[CrossRef]

2011 (1)

M. Virte, A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Phys. Rev. A 84, 043836 (2011).
[CrossRef]

2010 (1)

J. Zamora-Munt, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 81, 033820 (2010).
[CrossRef]

2006 (1)

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, Phys. Rev. A 74, 063801 (2006).
[CrossRef]

2003 (1)

T. Erneux, A. Gavrielides, K. Green, and B. Krauskopf, Phys. Rev. E 68, 066205 (2003).
[CrossRef]

2001 (2)

D. O’Brien, G. Huyet, and J. G. McInerney, Phys. Rev. A 64, 025802 (2001).
[CrossRef]

J. S. Lawrence and D. M. Kane, Phys. Rev. A 63, 033805 (2001).
[CrossRef]

1996 (1)

I. Fischer, G. H. M. Van Tartwijk, A. M. Levine, W. Elsaesser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef]

1995 (2)

G. H. M. Van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995).
[CrossRef]

A. Hohl, H. J. C. van der Linden, and R. Roy, Opt. Lett. 20, 2396 (1995).
[CrossRef]

1994 (1)

T. Sano, Phys. Rev. A 50, 2719 (1994).
[CrossRef]

1991 (1)

1977 (1)

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Agrawal, G. P.

Barland, S.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, Phys. Rev. A 74, 063801 (2006).
[CrossRef]

Elsaesser, W.

I. Fischer, G. H. M. Van Tartwijk, A. M. Levine, W. Elsaesser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef]

Erneux, T.

T. Erneux, A. Gavrielides, K. Green, and B. Krauskopf, Phys. Rev. E 68, 066205 (2003).
[CrossRef]

Fischer, I.

I. Fischer, G. H. M. Van Tartwijk, A. M. Levine, W. Elsaesser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef]

Garcia-Ojalvo, J.

J. Zamora-Munt, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 81, 033820 (2010).
[CrossRef]

Gavrielides, A.

T. Erneux, A. Gavrielides, K. Green, and B. Krauskopf, Phys. Rev. E 68, 066205 (2003).
[CrossRef]

Giacomelli, G.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, Phys. Rev. A 74, 063801 (2006).
[CrossRef]

Gobel, E.

I. Fischer, G. H. M. Van Tartwijk, A. M. Levine, W. Elsaesser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef]

Green, K.

T. Erneux, A. Gavrielides, K. Green, and B. Krauskopf, Phys. Rev. E 68, 066205 (2003).
[CrossRef]

Hohl, A.

Huyet, G.

D. O’Brien, G. Huyet, and J. G. McInerney, Phys. Rev. A 64, 025802 (2001).
[CrossRef]

Kane, D. M.

J. S. Lawrence and D. M. Kane, Phys. Rev. A 63, 033805 (2001).
[CrossRef]

Karsaklian Dal Bosco, A.

A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Europhys. Lett. 101, 24001 (2013).
[CrossRef]

M. Virte, A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Phys. Rev. A 84, 043836 (2011).
[CrossRef]

Klaus, J. T.

Krauskopf, B.

T. Erneux, A. Gavrielides, K. Green, and B. Krauskopf, Phys. Rev. E 68, 066205 (2003).
[CrossRef]

Lawrence, J. S.

J. S. Lawrence and D. M. Kane, Phys. Rev. A 63, 033805 (2001).
[CrossRef]

Lenstra, D.

I. Fischer, G. H. M. Van Tartwijk, A. M. Levine, W. Elsaesser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef]

G. H. M. Van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995).
[CrossRef]

Levine, A. M.

I. Fischer, G. H. M. Van Tartwijk, A. M. Levine, W. Elsaesser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef]

G. H. M. Van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995).
[CrossRef]

Marin, F.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, Phys. Rev. A 74, 063801 (2006).
[CrossRef]

Masoller, C.

J. Zamora-Munt, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 81, 033820 (2010).
[CrossRef]

McInerney, J. G.

D. O’Brien, G. Huyet, and J. G. McInerney, Phys. Rev. A 64, 025802 (2001).
[CrossRef]

O’Brien, D.

D. O’Brien, G. Huyet, and J. G. McInerney, Phys. Rev. A 64, 025802 (2001).
[CrossRef]

Risch, C.

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Roy, R.

Sano, T.

T. Sano, Phys. Rev. A 50, 2719 (1994).
[CrossRef]

Sciamanna, M.

A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Europhys. Lett. 101, 24001 (2013).
[CrossRef]

M. Virte, A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Phys. Rev. A 84, 043836 (2011).
[CrossRef]

Torcini, A.

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, Phys. Rev. A 74, 063801 (2006).
[CrossRef]

van der Linden, H. J. C.

Van Tartwijk, G. H. M.

I. Fischer, G. H. M. Van Tartwijk, A. M. Levine, W. Elsaesser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef]

G. H. M. Van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995).
[CrossRef]

Virte, M.

M. Virte, A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Phys. Rev. A 84, 043836 (2011).
[CrossRef]

Voumard, C.

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Wolfersberger, D.

A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Europhys. Lett. 101, 24001 (2013).
[CrossRef]

M. Virte, A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Phys. Rev. A 84, 043836 (2011).
[CrossRef]

Zamora-Munt, J.

J. Zamora-Munt, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 81, 033820 (2010).
[CrossRef]

Europhys. Lett. (1)

A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Europhys. Lett. 101, 24001 (2013).
[CrossRef]

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

G. H. M. Van Tartwijk, A. M. Levine, and D. Lenstra, IEEE J. Sel. Top. Quantum Electron. 1, 466 (1995).
[CrossRef]

J. Appl. Phys. (1)

C. Risch and C. Voumard, J. Appl. Phys. 48, 2083 (1977).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (6)

J. S. Lawrence and D. M. Kane, Phys. Rev. A 63, 033805 (2001).
[CrossRef]

T. Sano, Phys. Rev. A 50, 2719 (1994).
[CrossRef]

M. Virte, A. Karsaklian Dal Bosco, D. Wolfersberger, and M. Sciamanna, Phys. Rev. A 84, 043836 (2011).
[CrossRef]

D. O’Brien, G. Huyet, and J. G. McInerney, Phys. Rev. A 64, 025802 (2001).
[CrossRef]

J. Zamora-Munt, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 81, 033820 (2010).
[CrossRef]

A. Torcini, S. Barland, G. Giacomelli, and F. Marin, Phys. Rev. A 74, 063801 (2006).
[CrossRef]

Phys. Rev. E (1)

T. Erneux, A. Gavrielides, K. Green, and B. Krauskopf, Phys. Rev. E 68, 066205 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

I. Fischer, G. H. M. Van Tartwijk, A. M. Levine, W. Elsaesser, E. Gobel, and D. Lenstra, Phys. Rev. Lett. 76, 220 (1996).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Simulated time traces showing low-frequency fluctuations for two different values of the feedback rate: (a) γ=0.03386 and (b) γ=0.04460.

Fig. 2.
Fig. 2.

(a) Bifurcation diagram of the output power versus γ. When increasing γ, the laser dynamics stabilizes on ECMs labeled from A to J. These ECMs are reported in the plane Z versus ΔΦ in (c) where they correspond to limit cycle attractors. The red crosses show the mean values of the state variables corresponding to the ECMs. The dashed box is an inset for Fig. 3. (b) Comparison with the bifurcation diagram in the COF case.

Fig. 3.
Fig. 3.

From left to right, (a) γ=0.03300, (b) γ=0.03384, (c) γ=0.03386, (d) γ=0.03391, and (e) γ=0.03500. Top: system trajectory in the plane Z versus ΔΦ. Middle: corresponding time traces of |Y|2. Bottom: corresponding RF spectrum. The time trace in (c.3) is filtered to show the dropout associated with the LFF regime.

Fig. 4.
Fig. 4.

(a.1) and (b.1) Zoom on the fast-pulsing dynamics accompanying the dropouts indicated with arrows in Figs. 1(a) and 1(b), respectively. (a.2) and (b.2) Corresponding trajectories in the phase plane.

Fig. 5.
Fig. 5.

Evolution of the mean duration of the transient LFF as a function of α. The inset shows the evolution for the lowest values of α.

Equations (2)

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dYdt=(1+iα)ZY+γY*(tθ)+Rξ(t),
TdZdt=PZ(1+2Z)|Y|2,

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