Abstract

We show that pulses undergoing wave breaking in nonlinear weakly dispersive fibers radiate, owing to phase-matching (assisted by higher-order dispersion) of linear dispersive waves with the shock-wave front. Our theoretical results perfectly explain the radiation observed recently from pulses propagating in the normal dispersion (i.e., nonsolitonic) regime.

© 2013 Optical Society of America

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2013 (1)

2012 (2)

P. Colman, S. Combrié, G. Lehoucq, A. de Rossi, and S. Trillo, Phys. Rev. Lett. 109, 093901 (2012).
[CrossRef]

E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C. E. Kuklevicz, and U. Leonhardt, Phys. Rev. Lett. 108, 253901 (2012).
[CrossRef]

2010 (1)

D. V. Skryabin and A. V. Gorbach, Rev. Mod. Phys. 82, 1287 (2010).
[CrossRef]

2009 (1)

2007 (2)

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

2005 (1)

2004 (1)

1996 (2)

1995 (1)

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).

1992 (1)

1989 (1)

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

1987 (2)

A. V. Gurevich and A. L. Krylov, Sov. Phys. JETP 65, 944 (1987).

P. K. A. Wai, C. R. Menyuk, Y. C. Lee, and H. H. Chen, Opt. Lett. 12, 628 (1987).
[CrossRef]

1986 (1)

1985 (1)

Afanasjev, V. V.

Akhmediev, N.

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).

Anderson, D.

Belgiorno, F.

E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C. E. Kuklevicz, and U. Leonhardt, Phys. Rev. Lett. 108, 253901 (2012).
[CrossRef]

Chen, H. H.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Colman, P.

P. Colman, S. Combrié, G. Lehoucq, A. de Rossi, and S. Trillo, Phys. Rev. Lett. 109, 093901 (2012).
[CrossRef]

Combrié, S.

P. Colman, S. Combrié, G. Lehoucq, A. de Rossi, and S. Trillo, Phys. Rev. Lett. 109, 093901 (2012).
[CrossRef]

Conti, C.

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Cristiani, I.

de Rossi, A.

P. Colman, S. Combrié, G. Lehoucq, A. de Rossi, and S. Trillo, Phys. Rev. Lett. 109, 093901 (2012).
[CrossRef]

Degiorgio, V.

Desaix, M.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Erkintalo, M.

Ferrando, A.

Fleischer, J. W.

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Ghofraniha, N.

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Gorbach, A. V.

D. V. Skryabin and A. V. Gorbach, Rev. Mod. Phys. 82, 1287 (2010).
[CrossRef]

Grischkowsky, D.

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

Gurevich, A. V.

A. V. Gurevich and A. L. Krylov, Sov. Phys. JETP 65, 944 (1987).

Jia, S.

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

Johnson, A. M.

Karlsson, M.

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).

Kehr, S. C.

E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C. E. Kuklevicz, and U. Leonhardt, Phys. Rev. Lett. 108, 253901 (2012).
[CrossRef]

Kivshar, Y. S.

Kodama, Y.

Kolesik, M.

Krylov, A. L.

A. V. Gurevich and A. L. Krylov, Sov. Phys. JETP 65, 944 (1987).

Kuklevicz, C. E.

E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C. E. Kuklevicz, and U. Leonhardt, Phys. Rev. Lett. 108, 253901 (2012).
[CrossRef]

Lee, Y. C.

Lehoucq, G.

P. Colman, S. Combrié, G. Lehoucq, A. de Rossi, and S. Trillo, Phys. Rev. Lett. 109, 093901 (2012).
[CrossRef]

Leonhardt, U.

E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C. E. Kuklevicz, and U. Leonhardt, Phys. Rev. Lett. 108, 253901 (2012).
[CrossRef]

Leveque, R. J.

R. J. Leveque, Finite-Volume Methods for Hyperbolic Problems (Cambridge, 2004).

Lisak, M.

McLenaghan, J.

E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C. E. Kuklevicz, and U. Leonhardt, Phys. Rev. Lett. 108, 253901 (2012).
[CrossRef]

Menyuk, C. R.

Milian, C.

Moloney, J. V.

Murdoch, S. G.

Quiroiga-Teixeiro, M. L.

Rohr, S.

E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C. E. Kuklevicz, and U. Leonhardt, Phys. Rev. Lett. 108, 253901 (2012).
[CrossRef]

Rothenberg, J. E.

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

Rubino, E.

E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C. E. Kuklevicz, and U. Leonhardt, Phys. Rev. Lett. 108, 253901 (2012).
[CrossRef]

Ruocco, G.

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Skryabin, D. V.

D. V. Skryabin and A. V. Gorbach, Rev. Mod. Phys. 82, 1287 (2010).
[CrossRef]

C. Milian, D. V. Skryabin, and A. Ferrando, Opt. Lett. 34, 2096 (2009).
[CrossRef]

Stolen, R. H.

Tanaka, K.

Tartara, L.

Tediosi, R.

Tomlinson, W. J.

Townsend, D.

E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C. E. Kuklevicz, and U. Leonhardt, Phys. Rev. Lett. 108, 253901 (2012).
[CrossRef]

Trillo, S.

P. Colman, S. Combrié, G. Lehoucq, A. de Rossi, and S. Trillo, Phys. Rev. Lett. 109, 093901 (2012).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Wabnitz, S.

Wai, P. K. A.

Wan, W.

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

Webb, K. E.

Wright, E. M.

Xu, Y. Q.

J. Opt. Soc. Am. B (1)

Nat. Phys. (1)

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (7)

Phys. Rev. A (1)

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).

Phys. Rev. Lett. (4)

P. Colman, S. Combrié, G. Lehoucq, A. de Rossi, and S. Trillo, Phys. Rev. Lett. 109, 093901 (2012).
[CrossRef]

E. Rubino, J. McLenaghan, S. C. Kehr, F. Belgiorno, D. Townsend, S. Rohr, C. E. Kuklevicz, and U. Leonhardt, Phys. Rev. Lett. 108, 253901 (2012).
[CrossRef]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

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

Rev. Mod. Phys. (2)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

D. V. Skryabin and A. V. Gorbach, Rev. Mod. Phys. 82, 1287 (2010).
[CrossRef]

Sov. Phys. JETP (1)

A. V. Gurevich and A. L. Krylov, Sov. Phys. JETP 65, 944 (1987).

Other (1)

R. J. Leveque, Finite-Volume Methods for Hyperbolic Problems (Cambridge, 2004).

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Figures (5)

Fig. 1.
Fig. 1.

Power profiles ρ=|A|2 at z=20m, comparing the numerical solutions of Eqs. (2) and (3) (green dots) with those of the full GNLSE [Eq. (1)] (solid blue curve), and GNLSE with only β3 perturbation (τs=fR=β4=0; dashed red curve). The thin black curve is the input sech-shaped pulse at λp=1568.5nm. Here ε=0.077.

Fig. 2.
Fig. 2.

(a) Temporal and (c) spectral evolution of an input sech pulse with P0=600W and T0=850fs, at λp=1568.5nm (normal GVD). (b) and (d) Same with anomalous GVD (λp=1661nm) at P0=40W. In (c) and (d), A/N indicates anomalous/normal GVD regions and the dashed red lines indicate the DW detuning predicted by Eq. (4), with inverse velocity Δk1 (of shock and soliton, respectively) shown by the oblique dashed lines in (a) and (b).

Fig. 3.
Fig. 3.

Phase-matching curves: D(Δω)=n=24(βn/n!)ΔωnΔωΔk1 [left-hand side of Eq. (4), representing the DW wavenumber in the moving frame] versus Δf=Δω/2π. The DW frequency (red marker) is given by the intersection with the red horizontal line, which indicates kNL (in the normal GVD case, kNL also accounts for cross phase modulation (XPM) between the pump and the DW). (a) Normal GVD regime (λp=1568.5nm, 6.7 THz from the ZDW). (b) Anomalous GVD regime (λp=1661nm, 4THz from the ZDW). The vertical dashed line indicates the ZDW.

Fig. 4.
Fig. 4.

DW detuning as a function of pump detuning (both from the ZDW), contrasting numerical simulations (filled circles) with the prediction from Eq. (6) (dashed blue line) and Eq. (4) with Δk1=0 (solid red curve). The solid black line refers to the prediction from Eq. (4), with inverse velocity Δk1 shown in Fig. 5.

Fig. 5.
Fig. 5.

Inverse-velocity shifts Δk1=Vs1Vg1 (filled circles) versus pump detuning from the ZDW for the shock (positive detunings) and solitons (negative detunings). Solid blue line: linear best-fit for Δk1.

Equations (6)

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

izA+d(t)A+γ(1+iτst)(AR(t)|A(tt)|2)=0,
ρz+[β2ρu+β32ρu2+β46ρu3]t=0,
(ρu)z+[β2ρu2+β32ρu3+β46ρu4+γ2ρ2]t=0.
n=24βnn!ΔωnΔωΔk1=kNL,
ΔωDW=3β22β3(1+1+8β3Δk13β22),
ΔωDW3β2β3.

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