Abstract

We show that second-harmonic generation in the regime of weak dispersion/diffraction can exhibit a coexistence of wave breaking mechanisms, such that a gradient catastrophe yielding a dispersive shock wave competes with modulational instability, leading to the generation of wavetrains with incommensurate frequencies and eventually to the destruction of the shock wave-train.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. J. Lighthill, J. Inst. Math. Appl. 1, 269 (1965).
    [CrossRef]
  2. T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
    [CrossRef]
  3. K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
    [CrossRef]
  4. A. V. Gurevich and A. L. Krylov, J. Exp. Theor. Phys. 65, 944 (1987).
  5. J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
    [CrossRef]
  6. W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
    [CrossRef]
  7. N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Rev. Lett. 99, 043903 (2007).
    [CrossRef]
  8. S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
    [CrossRef]
  9. C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
    [CrossRef]
  10. S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995).
    [CrossRef]
  11. 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]
  12. M. Conforti, F. Baronio, and S. Trillo, Opt. Lett. 37, 1082 (2012).
    [CrossRef]
  13. C. Etrich, F. Lederer, B. A. Malomed, T. Peschel, and U. Peschel, Prog. Opt. 41, 483 (2000).
    [CrossRef]
  14. A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
    [CrossRef]
  15. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef]
  16. J. E. Rothenberg, Opt. Lett. 16, 18 (1991).
    [CrossRef]

2012 (1)

2009 (1)

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

2007 (3)

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

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

S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
[CrossRef]

2002 (1)

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

2000 (1)

C. Etrich, F. Lederer, B. A. Malomed, T. Peschel, and U. Peschel, Prog. Opt. 41, 483 (2000).
[CrossRef]

1997 (1)

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]

1995 (2)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995).
[CrossRef]

1991 (1)

1989 (1)

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

1987 (1)

A. V. Gurevich and A. L. Krylov, J. Exp. Theor. Phys. 65, 944 (1987).

1986 (1)

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

1967 (1)

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

1965 (1)

M. J. Lighthill, J. Inst. Math. Appl. 1, 269 (1965).
[CrossRef]

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]

Baronio, F.

Benjamin, T. B.

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

Buryak, A. V.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

Conforti, M.

Conti, C.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

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

Di Trapani, P.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

Etrich, C.

C. Etrich, F. Lederer, B. A. Malomed, T. Peschel, and U. Peschel, Prog. Opt. 41, 483 (2000).
[CrossRef]

Feir, J. E.

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

Ferro, P.

Fleischer, J. W.

S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
[CrossRef]

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

Fratalocchi, A.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[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]

Ghofraniha, N.

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Rev. Lett. 99, 043903 (2007).
[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, J. Exp. Theor. Phys. 65, 944 (1987).

Hagan, D. J.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Hasegawa, A.

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

Jia, S.

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

S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
[CrossRef]

Krylov, A. L.

A. V. Gurevich and A. L. Krylov, J. Exp. Theor. Phys. 65, 944 (1987).

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]

Lederer, F.

C. Etrich, F. Lederer, B. A. Malomed, T. Peschel, and U. Peschel, Prog. Opt. 41, 483 (2000).
[CrossRef]

Lighthill, M. J.

M. J. Lighthill, J. Inst. Math. Appl. 1, 269 (1965).
[CrossRef]

Malomed, B. A.

C. Etrich, F. Lederer, B. A. Malomed, T. Peschel, and U. Peschel, Prog. Opt. 41, 483 (2000).
[CrossRef]

Peccianti, M.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

Peschel, T.

C. Etrich, F. Lederer, B. A. Malomed, T. Peschel, and U. Peschel, Prog. Opt. 41, 483 (2000).
[CrossRef]

Peschel, U.

C. Etrich, F. Lederer, B. A. Malomed, T. Peschel, and U. Peschel, Prog. Opt. 41, 483 (2000).
[CrossRef]

Rothenberg, J. E.

J. E. Rothenberg, Opt. Lett. 16, 18 (1991).
[CrossRef]

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

Ruocco, G.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

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

Skryabin, D. V.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

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]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Tai, K.

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

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Trillo, S.

M. Conforti, F. Baronio, and S. Trillo, Opt. Lett. 37, 1082 (2012).
[CrossRef]

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

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

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[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 P. Ferro, Opt. Lett. 20, 438 (1995).
[CrossRef]

VanStryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

Wabnitz, S.

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]

Wan, W.

S. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
[CrossRef]

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

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef]

J. Exp. Theor. Phys. (1)

A. V. Gurevich and A. L. Krylov, J. Exp. Theor. Phys. 65, 944 (1987).

J. Fluid Mech. (1)

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

J. Inst. Math. Appl. (1)

M. J. Lighthill, J. Inst. Math. Appl. 1, 269 (1965).
[CrossRef]

Nat. Phys. (1)

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

Opt. Lett. (3)

Phys. Rep. (1)

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

Phys. Rev. Lett. (6)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, and G. I. Stegeman, Phys. Rev. Lett. 74, 5036 (1995).
[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. Jia, W. Wan, and J. W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007).
[CrossRef]

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef]

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

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

Prog. Opt. (1)

C. Etrich, F. Lederer, B. A. Malomed, T. Peschel, and U. Peschel, Prog. Opt. 41, 483 (2000).
[CrossRef]

Rev. Lett. (1)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

(a) Equivalent fluid density μ and (b) velocity v at distance z=1.4zs from numerical integration of Eq. (5) with δk=4 (solid blue curves), compared with SH amplitude |u2| and chirp S2x from Eqs. (1) to (2) with ε=0.05 (dots), and input (dashed line).

Fig. 2.
Fig. 2.

(a),(c) Color level plot of FF field |u1|, ruled by Eqs. (1) and (2) (the SH, not shown, is similar); (b),(d) snapshots of output amplitudes |u1| (FF, solid red) and |u2| (SH, solid blue). Dashed curves are the input. Here, ε=0.05 and (a),(b) δk=4 or (c),(d) δk=0.

Fig. 3.
Fig. 3.

(a) Color level plot of MI gain versus scaled wavenumber εq and phase mismatch δk, for μ=1. Intersecting white line indicates the estimated wavenumber qSH from the DSW and (b) critical mismatch δkc[value at intersection between qSH and the gain bandwidth in (a)] versus μ. Shaded (red) region gives stable DSW.

Fig. 4.
Fig. 4.

Evolution of spatial spectra for stable DSWs at δk=4: (a) FF, (b) SH and competing MI at δk=0, (c) FF, and (d) SH. Double arrow indicates the estimated DSW frequency qSH (see text). Dashed vertical lines refers to the peak of MI gain g(q).

Equations (5)

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

iεu1z+β1ε22u1xx+u2u1*=0,
iεu2z+β2ε22u2xxδku2+u12=0,
ρ1z+β1(v1ρ1)x=0,ρ2z+β2(v2ρ2)x=0,(1+ρ12ρ2)vz+(2β2+β1ρ12ρ2)vvxs2ρ1xρ2=0,
ρ1=μ(z,x)[2μ(z,x)+sδk],ρ2=μ2(z,x).
μz+(vμ)xg(μ)μvx=0;vz+vvxsμx=0.

Metrics