Abstract

We investigate wave-breaking and dispersive shock wave formation driven by a pulse undergoing second-harmonic generation in a quadratic medium. We show that the process is accessible in the regime of high phase-mismatch (cascading limit) and weak dispersion. Insight into the phenomenon is obtained by means of a suitable hydrodynamic reduction of the equations that govern the mixing.

© 2012 Optical Society of America

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References

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  1. C. R. Menuyk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).
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    [CrossRef]
  6. W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2007).
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  7. N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
    [CrossRef]
  8. C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 102, 083902 (2009).
    [CrossRef]
  9. F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, J. Opt. Soc. Am. B 21, 376 (2004).
    [CrossRef]
  10. J. Moses and F. W. Wise, Phys. Rev. Lett. 97, 073903 (2006).
    [CrossRef]
  11. F. Baronio, C. De Angelis, M. Marangoni, C. Manzoni, R. Ramponi, and G. Cerullo, Opt. Express 14, 4774 (2006).
    [CrossRef]
  12. J. Moses, B. Malomed, and F. W. Wise, Phys. Rev. A 76, 021802(R) (2007).
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    [CrossRef]
  15. Y. Kodama and S. Wabnitz, Opt. Lett. 20, 2291 (1995).
    [CrossRef]
  16. M. G. Forest and K. T.-R. McLaughlin, J. Nonlinear Sci. 7, 43 (1998).
    [CrossRef]
  17. D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey (Springer, 2005).

2009 (2)

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

M. G. Forest, C.-J. Rosenberg, and O. C. Wright, Nonlinearity 22, 2287 (2009).
[CrossRef]

2007 (3)

J. Moses, B. Malomed, and F. W. Wise, Phys. Rev. A 76, 021802(R) (2007).
[CrossRef]

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 (2)

2004 (1)

2002 (1)

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

1998 (1)

M. G. Forest and K. T.-R. McLaughlin, J. Nonlinear Sci. 7, 43 (1998).
[CrossRef]

1995 (1)

1994 (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, Sov. Phys. JETP 65, 944 (1987).

1979 (1)

H. H. Chen, Y. C. Lee, and C. S. Liu, Phys. Scr. 20, 490 (1979).
[CrossRef]

1974 (1)

A. V. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974).

Baronio, F.

Beckwitt, K.

Buryak, A. V.

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

Cerullo, G.

Chen, H. H.

H. H. Chen, Y. C. Lee, and C. S. Liu, Phys. Scr. 20, 490 (1979).
[CrossRef]

Chen, Y.

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, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

De Angelis, C.

Di Trapani, P.

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

Fleischer, J. W.

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

Forest, M. G.

M. G. Forest, C.-J. Rosenberg, and O. C. Wright, Nonlinearity 22, 2287 (2009).
[CrossRef]

M. G. Forest and K. T.-R. McLaughlin, J. Nonlinear Sci. 7, 43 (1998).
[CrossRef]

Fratalocchi, A.

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

Ghofraniha, N.

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. 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, Sov. Phys. JETP 65, 944 (1987).

A. V. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974).

Ilday, F.

Jia, S.

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

Kodama, Y.

Krylov, A. L.

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

Lee, Y. C.

H. H. Chen, Y. C. Lee, and C. S. Liu, Phys. Scr. 20, 490 (1979).
[CrossRef]

Lim, H.

Liu, C. S.

H. H. Chen, Y. C. Lee, and C. S. Liu, Phys. Scr. 20, 490 (1979).
[CrossRef]

Malomed, B.

J. Moses, B. Malomed, and F. W. Wise, Phys. Rev. A 76, 021802(R) (2007).
[CrossRef]

Manzoni, C.

Marangoni, M.

McLaughlin, K. T.-R.

M. G. Forest and K. T.-R. McLaughlin, J. Nonlinear Sci. 7, 43 (1998).
[CrossRef]

Menuyk, C. R.

Moses, J.

J. Moses, B. Malomed, and F. W. Wise, Phys. Rev. A 76, 021802(R) (2007).
[CrossRef]

J. Moses and F. W. Wise, Phys. Rev. Lett. 97, 073903 (2006).
[CrossRef]

Nikogosyan, D. N.

D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey (Springer, 2005).

Peccianti, M.

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

Pitaevskii, L. P.

A. V. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974).

Ramponi, R.

Rosenberg, C.-J.

M. G. Forest, C.-J. Rosenberg, and O. C. Wright, Nonlinearity 22, 2287 (2009).
[CrossRef]

Rothenberg, J. E.

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, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

Schiek, R.

Skryabin, D.

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

Torner, L.

Trillo, S.

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, Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef]

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

Wabnitz, S.

Wan, W.

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

Wise, F.

Wise, F. W.

J. Moses, B. Malomed, and F. W. Wise, Phys. Rev. A 76, 021802(R) (2007).
[CrossRef]

J. Moses and F. W. Wise, Phys. Rev. Lett. 97, 073903 (2006).
[CrossRef]

Wright, O. C.

M. G. Forest, C.-J. Rosenberg, and O. C. Wright, Nonlinearity 22, 2287 (2009).
[CrossRef]

J. Nonlinear Sci. (1)

M. G. Forest and K. T.-R. McLaughlin, J. Nonlinear Sci. 7, 43 (1998).
[CrossRef]

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

Nat. Phys. (1)

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

Nonlinearity (1)

M. G. Forest, C.-J. Rosenberg, and O. C. Wright, Nonlinearity 22, 2287 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rep. (1)

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

Phys. Rev. A (1)

J. Moses, B. Malomed, and F. W. Wise, Phys. Rev. A 76, 021802(R) (2007).
[CrossRef]

Phys. Rev. Lett. (4)

J. Moses and F. W. Wise, Phys. Rev. Lett. 97, 073903 (2006).
[CrossRef]

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

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

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

Phys. Scr. (1)

H. H. Chen, Y. C. Lee, and C. S. Liu, Phys. Scr. 20, 490 (1979).
[CrossRef]

Sov. Phys. JETP (2)

A. V. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP 38, 291 (1974).

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

Other (1)

D. N. Nikogosyan, Nonlinear Optical Crystals: A Complete Survey (Springer, 2005).

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Figures (3)

Fig. 1.
Fig. 1.

Shock capture window (shaded area) versus GVM parameter σ: (a) Gaussian input; (b) Gaussian on pedestal, ν=0.1. The bullets give the shock distance obtained via direct numerical integration of Eq. (4).

Fig. 2.
Fig. 2.

(a), (b) Color level plot of FF field |a1| (a) and SH field (b), ruled by Eq. (2); (c) same for FF field |u| from Eq. (3); (d) Snapshots of output field moduli |a1| (FF, solid black) and |a2| (SH, solid red) from Eq. (2), compared with |u| (FF, dashed red) from Eq. (3). The solid blue curve is the input. Here η=σ=0, ε=0.05.

Fig. 3.
Fig. 3.

As in Fig. 2, with nonvanishing GVM such that η=30 [Eq. (2)] and σ=0.15 [Eq. (3)].

Equations (5)

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

iwZβ12wTT+χvw*eiΔkZ=0,ivZ+iδvTβ22vTT+χw2eiΔkZ=0,
iεa1zε22a1tt+|δk|εa2a1*=0,iεa2z+iεηa2tγε22a2ttεδka2+|δk|εa12=0.
iεuzε22utt+s|u|2u+2iεσ|u|2ut=0,
ρz+(vρ+σρ2)t=0,vz+vvt+ρt+2σ(ρv)t=0,
P=Δk2χ2|δk|ε,T0=1χε|Δk|β1P,L=|δk||Δk|.

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