Abstract

We experimentally investigate the nonlinear reshaping of a continuous wave that leads to chirp-free and flat-top intense pulses or flaticons exhibiting strong temporal oscillations at their edges and a stable self-similar expansion upon propagation of their central region. This study was performed in the normal dispersion regime of a nonzero dispersion-shifted fiber and involved a sinusoidal phase modulation of the continuous wave. Our fiber optics experiment is analogous to considering the collision between oppositely directed currents near the beach, and it may open the way to new investigations in the field of hydrodynamics.

© 2013 Optical Society of America

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  1. J. J. Stoker, Comm. Pure Appl. Math. 1, 1 (1948).
    [CrossRef]
  2. G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).
  3. J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
    [CrossRef]
  4. V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).
  5. T. B. Benjamin and J. F. Feir, J. Fluid Mech. 27, 417 (1967).
    [CrossRef]
  6. A. Ritter, Z. Ver. Deutscher Ingen. 36, 947 (1982).
  7. Y. Kodama and S. Wabnitz, Opt. Lett. 20, 2291 (1995).
    [CrossRef]
  8. P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, Opt. Commun. 62, 374 (1987).
    [CrossRef]
  9. A. Chabchoub, O. Kimmoun, H. Branger, N. Hoffmann, D. Proment, M. Onorato, and N. Akhmediev, Phys. Rev. Lett. 110, 124101 (2013).
    [CrossRef]
  10. A. Slunyaev, I. Didenkulova, and E. Pelinovsky, Cont. Phy. 52, 571 (2011).
    [CrossRef]
  11. D. H. Peregrine, J. Austral. Math. Soc. Ser. B 25, 16 (1983).
    [CrossRef]
  12. K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
    [CrossRef]
  13. I. Didenkulova and E. Pelinovsky, Nonlinearity 24, R1 (2011).
    [CrossRef]
  14. S. Wabnitz, C. Finot, J. Fatome, and G. Millot, Phys. Lett. A 377, 932 (2013).
    [CrossRef]
  15. S. Wabnitz, J. Opt. 15, 064002 (2013).
    [CrossRef]
  16. G. Biondini and Y. Kodama, J. Nonlinear Sci. 16, 435 (2006).
    [CrossRef]
  17. S. Pitois, C. Finot, J. Fatome, and G. Millot, Opt. Commun. 260, 301 (2006).
    [CrossRef]

2013 (3)

A. Chabchoub, O. Kimmoun, H. Branger, N. Hoffmann, D. Proment, M. Onorato, and N. Akhmediev, Phys. Rev. Lett. 110, 124101 (2013).
[CrossRef]

S. Wabnitz, C. Finot, J. Fatome, and G. Millot, Phys. Lett. A 377, 932 (2013).
[CrossRef]

S. Wabnitz, J. Opt. 15, 064002 (2013).
[CrossRef]

2011 (3)

I. Didenkulova and E. Pelinovsky, Nonlinearity 24, R1 (2011).
[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
[CrossRef]

A. Slunyaev, I. Didenkulova, and E. Pelinovsky, Cont. Phy. 52, 571 (2011).
[CrossRef]

2006 (2)

G. Biondini and Y. Kodama, J. Nonlinear Sci. 16, 435 (2006).
[CrossRef]

S. Pitois, C. Finot, J. Fatome, and G. Millot, Opt. Commun. 260, 301 (2006).
[CrossRef]

1995 (1)

1989 (1)

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

1987 (1)

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

1983 (1)

D. H. Peregrine, J. Austral. Math. Soc. Ser. B 25, 16 (1983).
[CrossRef]

1982 (1)

A. Ritter, Z. Ver. Deutscher Ingen. 36, 947 (1982).

1967 (1)

T. B. Benjamin and J. F. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

1966 (1)

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

1948 (1)

J. J. Stoker, Comm. Pure Appl. Math. 1, 1 (1948).
[CrossRef]

Akhmediev, N.

A. Chabchoub, O. Kimmoun, H. Branger, N. Hoffmann, D. Proment, M. Onorato, and N. Akhmediev, Phys. Rev. Lett. 110, 124101 (2013).
[CrossRef]

Barthelemy, A.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Benjamin, T. B.

T. B. Benjamin and J. F. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Biondini, G.

G. Biondini and Y. Kodama, J. Nonlinear Sci. 16, 435 (2006).
[CrossRef]

Branger, H.

A. Chabchoub, O. Kimmoun, H. Branger, N. Hoffmann, D. Proment, M. Onorato, and N. Akhmediev, Phys. Rev. Lett. 110, 124101 (2013).
[CrossRef]

Chabchoub, A.

A. Chabchoub, O. Kimmoun, H. Branger, N. Hoffmann, D. Proment, M. Onorato, and N. Akhmediev, Phys. Rev. Lett. 110, 124101 (2013).
[CrossRef]

Didenkulova, I.

I. Didenkulova and E. Pelinovsky, Nonlinearity 24, R1 (2011).
[CrossRef]

A. Slunyaev, I. Didenkulova, and E. Pelinovsky, Cont. Phy. 52, 571 (2011).
[CrossRef]

Dudley, J. M.

Emplit, P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Fatome, J.

S. Wabnitz, C. Finot, J. Fatome, and G. Millot, Phys. Lett. A 377, 932 (2013).
[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
[CrossRef]

S. Pitois, C. Finot, J. Fatome, and G. Millot, Opt. Commun. 260, 301 (2006).
[CrossRef]

Feir, J. F.

T. B. Benjamin and J. F. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Finot, C.

S. Wabnitz, C. Finot, J. Fatome, and G. Millot, Phys. Lett. A 377, 932 (2013).
[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
[CrossRef]

S. Pitois, C. Finot, J. Fatome, and G. Millot, Opt. Commun. 260, 301 (2006).
[CrossRef]

Froehly, C.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Grischkowsky, D.

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

Hamaide, J. P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Hammani, K.

Hoffmann, N.

A. Chabchoub, O. Kimmoun, H. Branger, N. Hoffmann, D. Proment, M. Onorato, and N. Akhmediev, Phys. Rev. Lett. 110, 124101 (2013).
[CrossRef]

Kibler, B.

Kimmoun, O.

A. Chabchoub, O. Kimmoun, H. Branger, N. Hoffmann, D. Proment, M. Onorato, and N. Akhmediev, Phys. Rev. Lett. 110, 124101 (2013).
[CrossRef]

Kodama, Y.

G. Biondini and Y. Kodama, J. Nonlinear Sci. 16, 435 (2006).
[CrossRef]

Y. Kodama and S. Wabnitz, Opt. Lett. 20, 2291 (1995).
[CrossRef]

Millot, G.

S. Wabnitz, C. Finot, J. Fatome, and G. Millot, Phys. Lett. A 377, 932 (2013).
[CrossRef]

K. Hammani, B. Kibler, C. Finot, P. Morin, J. Fatome, J. M. Dudley, and G. Millot, Opt. Lett. 36, 112 (2011).
[CrossRef]

S. Pitois, C. Finot, J. Fatome, and G. Millot, Opt. Commun. 260, 301 (2006).
[CrossRef]

Morin, P.

Onorato, M.

A. Chabchoub, O. Kimmoun, H. Branger, N. Hoffmann, D. Proment, M. Onorato, and N. Akhmediev, Phys. Rev. Lett. 110, 124101 (2013).
[CrossRef]

Pelinovsky, E.

I. Didenkulova and E. Pelinovsky, Nonlinearity 24, R1 (2011).
[CrossRef]

A. Slunyaev, I. Didenkulova, and E. Pelinovsky, Cont. Phy. 52, 571 (2011).
[CrossRef]

Peregrine, D. H.

D. H. Peregrine, J. Austral. Math. Soc. Ser. B 25, 16 (1983).
[CrossRef]

Pitois, S.

S. Pitois, C. Finot, J. Fatome, and G. Millot, Opt. Commun. 260, 301 (2006).
[CrossRef]

Proment, D.

A. Chabchoub, O. Kimmoun, H. Branger, N. Hoffmann, D. Proment, M. Onorato, and N. Akhmediev, Phys. Rev. Lett. 110, 124101 (2013).
[CrossRef]

Reynaud, F.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Ritter, A.

A. Ritter, Z. Ver. Deutscher Ingen. 36, 947 (1982).

Rothenberg, J. E.

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

Slunyaev, A.

A. Slunyaev, I. Didenkulova, and E. Pelinovsky, Cont. Phy. 52, 571 (2011).
[CrossRef]

Stoker, J. J.

J. J. Stoker, Comm. Pure Appl. Math. 1, 1 (1948).
[CrossRef]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Wabnitz, S.

S. Wabnitz, J. Opt. 15, 064002 (2013).
[CrossRef]

S. Wabnitz, C. Finot, J. Fatome, and G. Millot, Phys. Lett. A 377, 932 (2013).
[CrossRef]

Y. Kodama and S. Wabnitz, Opt. Lett. 20, 2291 (1995).
[CrossRef]

Whitham, G. B.

G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).

Comm. Pure Appl. Math. (1)

J. J. Stoker, Comm. Pure Appl. Math. 1, 1 (1948).
[CrossRef]

Cont. Phy. (1)

A. Slunyaev, I. Didenkulova, and E. Pelinovsky, Cont. Phy. 52, 571 (2011).
[CrossRef]

J. Austral. Math. Soc. Ser. B (1)

D. H. Peregrine, J. Austral. Math. Soc. Ser. B 25, 16 (1983).
[CrossRef]

J. Fluid Mech. (1)

T. B. Benjamin and J. F. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

J. Nonlinear Sci. (1)

G. Biondini and Y. Kodama, J. Nonlinear Sci. 16, 435 (2006).
[CrossRef]

J. Opt. (1)

S. Wabnitz, J. Opt. 15, 064002 (2013).
[CrossRef]

JETP Lett. (1)

V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 307 (1966).

Nonlinearity (1)

I. Didenkulova and E. Pelinovsky, Nonlinearity 24, R1 (2011).
[CrossRef]

Opt. Commun. (2)

S. Pitois, C. Finot, J. Fatome, and G. Millot, Opt. Commun. 260, 301 (2006).
[CrossRef]

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, Opt. Commun. 62, 374 (1987).
[CrossRef]

Opt. Lett. (2)

Phys. Lett. A (1)

S. Wabnitz, C. Finot, J. Fatome, and G. Millot, Phys. Lett. A 377, 932 (2013).
[CrossRef]

Phys. Rev. Lett. (2)

A. Chabchoub, O. Kimmoun, H. Branger, N. Hoffmann, D. Proment, M. Onorato, and N. Akhmediev, Phys. Rev. Lett. 110, 124101 (2013).
[CrossRef]

J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
[CrossRef]

Z. Ver. Deutscher Ingen. (1)

A. Ritter, Z. Ver. Deutscher Ingen. 36, 947 (1982).

Other (1)

G. B. Whitham, Linear and Nonlinear Waves (Wiley, 1974).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Experimental setup. (b) Optical spectrum of the continuous seed for an average pump power of 25 dBm. Experimental results (black solid line) are compared with analytical results of CW with a sinusoidal phase modulation of 7.3 rad [gray-dashed line (red online)]. (c) Experimental evolution of the amplitude of the phase modulation according to the pump power in the HNLF. Experimental results (circles) are compared with a linear fit (gray-dashed line).

Fig. 2.
Fig. 2.

Temporal intensity profiles at the output of the NZ-DSF obtained at a phase modulation of 6.75 rad and at three different input powers: (1) 19 dBm, (2) 24 dBm and (3) 28 dBm. Experimental results (subplots a) are compared with results of numerical integration of the NLSE (subplots b).

Fig. 3.
Fig. 3.

Evolution of the temporal intensity profile as a function of the input average power injected into the NZ-DSF for a phase modulation of 6.75 rad. Experimental results (panel a) are compared with numerical simulations (panel b).

Fig. 4.
Fig. 4.

Evolution of the temporal intensity profile as a function of the amplitude of the initial phase modulation. Experimental results (panel a) are compared with numerical simulations (panel b). The dotted line (blue online) denotes the phase amplitude leading to the frequency jump of 2.4fc.

Fig. 5.
Fig. 5.

Impact of a Gaussian OBPF of a flaticon pulse generated from an average signal power of 25 dBm and an initial phase amplitude of 8 rad. The filtered pulse (solid black line) is compared with the flaticon pulse (gray-dotted line). Experimental results (panel a) are compared with numerical results (panel b).

Equations (1)

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iψzβ222ψt2+γ|ψ|2ψ+iα2ψ=0,

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