Abstract

We demonstrate experimentally that multiple four-wave mixing (FWM) pumped by a dual-frequency input in a single-mode fiber is modulationally unstable. This collective type of instability leads, in the anomalous dispersion regime, to sideband growth around all orders of FWM. This is in contrast with the normal dispersion regime where our measurements show that FWM exhibits no instability. Our conclusions are based on the first systematic mapping of the phenomenon as a function of the dual-pump input frequency separation.

© 2013 Optical Society of America

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    [CrossRef]
  2. K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. G. Millot, S. Pitois, and P. Tchofo-Dinda, J. Opt. Soc. Am. B 19, 454 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. V. Eckhouse, I. Cestier, G. Eisenstein, S. Combrié, P. Colman, A. De Rossi, M. Santagiustina, C. G. Someda, and G. Vadalà, Opt. Lett. 35, 1440 (2010).
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    [CrossRef]
  18. C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, IEEE J. Sel. Topics Quantum Electron. 8, 538 (2002).
    [CrossRef]
  19. J. Fatome, S. Pitois, and G. Millot, IEEE J. Quantum Electron. 42, 1038 (2006).
    [CrossRef]
  20. J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
    [CrossRef]
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2012 (1)

2011 (3)

2010 (3)

2006 (1)

J. Fatome, S. Pitois, and G. Millot, IEEE J. Quantum Electron. 42, 1038 (2006).
[CrossRef]

2002 (2)

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, IEEE J. Sel. Topics Quantum Electron. 8, 538 (2002).
[CrossRef]

G. Millot, S. Pitois, and P. Tchofo-Dinda, J. Opt. Soc. Am. B 19, 454 (2002).
[CrossRef]

2001 (1)

E. Ciaramella, F. Curti, and S. Trillo, IEEE Photon. Technol. Lett. 13, 142 (2001).
[CrossRef]

1998 (1)

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

1997 (3)

S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897(1997).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 56, 1048 (1997).
[CrossRef]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

1994 (3)

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[CrossRef]

P. V. Mamyshev, C. Bosshard, and G. I. Stegeman, J. Opt. Soc. Am. B 11, 1254 (1994).
[CrossRef]

1991 (1)

J. R. Thompson and R. Roy, Phys. Rev. A 43, 4987(1991).
[CrossRef]

1990 (2)

J. E. Rothenberg, Phys. Rev. A 42, 682 (1990).
[CrossRef]

J. E. Rothenberg, Phys. Rev. Lett. 64, 813 (1990).
[CrossRef]

1989 (1)

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 39, 3406 (1989).
[CrossRef]

1987 (1)

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef]

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 39, 3406 (1989).
[CrossRef]

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef]

Akhmediev, N.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 107, 253901 (2011).
[CrossRef]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

Alfano, R. R.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 39, 3406 (1989).
[CrossRef]

Armaroli, A.

Baboiu, D. M.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Baldeck, P. L.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 39, 3406 (1989).
[CrossRef]

Beletic, J. W.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

Biancalana, F.

Bosshard, C.

Cestier, I.

Chraplyvy, A. R.

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, IEEE J. Sel. Topics Quantum Electron. 8, 538 (2002).
[CrossRef]

Ciaramella, E.

E. Ciaramella, F. Curti, and S. Trillo, IEEE Photon. Technol. Lett. 13, 142 (2001).
[CrossRef]

Colman, P.

Combrié, S.

Courde, C.

J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
[CrossRef]

Curti, F.

E. Ciaramella, F. Curti, and S. Trillo, IEEE Photon. Technol. Lett. 13, 142 (2001).
[CrossRef]

De Rossi, A.

Dudley, J. M.

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 107, 253901 (2011).
[CrossRef]

Eckhouse, V.

Eisenstein, G.

Erkintalo, M.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 107, 253901 (2011).
[CrossRef]

Fatome, J.

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
[CrossRef]

J. Fatome, S. Pitois, and G. Millot, IEEE J. Quantum Electron. 42, 1038 (2006).
[CrossRef]

Finot, C.

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 107, 253901 (2011).
[CrossRef]

J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
[CrossRef]

Fortier, C.

J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
[CrossRef]

Fuerst, R. A.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Genty, G.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 107, 253901 (2011).
[CrossRef]

Hammani, K.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 107, 253901 (2011).
[CrossRef]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

Hart, D. L.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef]

Judy, A. F.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

Kennedy, T. A. B.

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[CrossRef]

Kibler, B.

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 107, 253901 (2011).
[CrossRef]

J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
[CrossRef]

Lawrence, B.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Lintz, M.

J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
[CrossRef]

Mamyshev, P. V.

McKinstrie, C. J.

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, IEEE J. Sel. Topics Quantum Electron. 8, 538 (2002).
[CrossRef]

Millot, G.

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, Opt. Lett. 36, 2140 (2011).
[CrossRef]

J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
[CrossRef]

J. Fatome, S. Pitois, and G. Millot, IEEE J. Quantum Electron. 42, 1038 (2006).
[CrossRef]

G. Millot, S. Pitois, and P. Tchofo-Dinda, J. Opt. Soc. Am. B 19, 454 (2002).
[CrossRef]

Pitois, S.

J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
[CrossRef]

J. Fatome, S. Pitois, and G. Millot, IEEE J. Quantum Electron. 42, 1038 (2006).
[CrossRef]

G. Millot, S. Pitois, and P. Tchofo-Dinda, J. Opt. Soc. Am. B 19, 454 (2002).
[CrossRef]

Radic, S.

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, IEEE J. Sel. Topics Quantum Electron. 8, 538 (2002).
[CrossRef]

Rothenberg, J. E.

J. E. Rothenberg, Phys. Rev. A 42, 682 (1990).
[CrossRef]

J. E. Rothenberg, Phys. Rev. Lett. 64, 813 (1990).
[CrossRef]

Roy, R.

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

J. R. Thompson and R. Roy, Phys. Rev. A 43, 4987(1991).
[CrossRef]

Samain, E.

J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
[CrossRef]

Santagiustina, M.

Someda, C. G.

Stegeman, G. I.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

P. V. Mamyshev, C. Bosshard, and G. I. Stegeman, J. Opt. Soc. Am. B 11, 1254 (1994).
[CrossRef]

Stoev, K.

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef]

Tchofo-Dinda, P.

Thompson, J. R.

J. R. Thompson and R. Roy, Phys. Rev. A 43, 4987(1991).
[CrossRef]

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef]

Torruellas, W. E.

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Trillo, S.

A. Armaroli and S. Trillo, Opt. Lett. 36, 1999 (2011).
[CrossRef]

S. Trillo and A. Valiani, Opt. Lett. 35, 3967 (2010).
[CrossRef]

E. Ciaramella, F. Curti, and S. Trillo, IEEE Photon. Technol. Lett. 13, 142 (2001).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897(1997).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 56, 1048 (1997).
[CrossRef]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[CrossRef]

Vadalà, G.

Valiani, A.

Wabnitz, S.

S. Trillo and S. Wabnitz, Phys. Rev. E 56, 1048 (1997).
[CrossRef]

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897(1997).
[CrossRef]

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[CrossRef]

Wetzel, B.

IEEE J. Quantum Electron. (1)

J. Fatome, S. Pitois, and G. Millot, IEEE J. Quantum Electron. 42, 1038 (2006).
[CrossRef]

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

C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, IEEE J. Sel. Topics Quantum Electron. 8, 538 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

E. Ciaramella, F. Curti, and S. Trillo, IEEE Photon. Technol. Lett. 13, 142 (2001).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

J. Fatome, S. Pitois, C. Fortier, B. Kibler, C. Finot, G. Millot, C. Courde, M. Lintz, and E. Samain, Opt. Commun. 283, 2425 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (5)

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Phys. Rev. A 39, 3406 (1989).
[CrossRef]

J. E. Rothenberg, Phys. Rev. A 42, 682 (1990).
[CrossRef]

J. R. Thompson and R. Roy, Phys. Rev. A 43, 4987(1991).
[CrossRef]

D. L. Hart, A. F. Judy, T. A. B. Kennedy, R. Roy, and K. Stoev, Phys. Rev. A 50, 1807 (1994).
[CrossRef]

S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A 50, 1732 (1994).
[CrossRef]

Phys. Rev. E (3)

D. L. Hart, A. F. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897(1997).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 56, 1048 (1997).
[CrossRef]

Phys. Rev. Lett. (5)

R. A. Fuerst, D. M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

J. E. Rothenberg, Phys. Rev. Lett. 64, 813 (1990).
[CrossRef]

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987).
[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 107, 253901 (2011).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup. External cavity laser (ECL), phase modulator (PM), and optical spectrum analyzer (OSA).

Fig. 2.
Fig. 2.

Experimental output spectra showing MI developing over mFWM for balanced (a) and imbalanced (c) pumps at Δfp=100GHz and P=800mW, color maps of output spectrum as a function of detuning Δfp ranging from 10 to 250 GHz, measured in the balanced (b), and imbalanced case (d). Open dots correspond to the most unstable frequency fMI from theory.

Fig. 3.
Fig. 3.

Output spectrum calculated from Eq. (1) with same parameters as in Fig. 2(a) (a). The MI gain is also reported around the pumps for comparison (thin red line, vertical a.u.) (b). Corresponding evolution along the fiber of the power of one of the pumps.

Fig. 4.
Fig. 4.

Same as in Figs. 2(a) and 2(b) for balanced input in the normal GVD regime.

Equations (1)

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iEZk22ET2+γ|E|2E=iα2E,

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