Abstract

We experimentally demonstrate diffraction from a straight edge in a medium with self-focusing nonlinearity. Diffraction into the shadow region is suppressed with increasing nonlinearity, but mode coupling leads to excitations and traveling waves on the high-intensity side. Theoretically, we interpret these modulations as spatially dispersive shock waves with negative pressure.

© 2010 Optical Society of America

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  1. I. Freund, Phys. Rev. Lett. 21, 1404 (1968).
    [CrossRef]
  2. R. Reinisch and M. Neviere, Phys. Rev. B 28, 1870 (1983).
    [CrossRef]
  3. P. Vincent, N. Paraire, M. Neviere, A. Koster, and R. Reinisch, J. Opt. Soc. Am. B 2, 1106 (1985).
    [CrossRef]
  4. O. Manela and M. Segev, Opt. Express 15, 10863 (2007).
    [CrossRef] [PubMed]
  5. W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46(2007).
    [CrossRef]
  6. N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
    [CrossRef] [PubMed]
  7. E. G. Khamis, A. Gammal, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 78, 013829 (2008).
    [CrossRef]
  8. S. Chavez-Cerda, M. D. Iturbe-Castillo, and J. M. Hickmann, in Self-Focusing: Past and Present, Vol. 114 of Topics in Applied Physics (2009), pp. 517–545.
    [CrossRef]
  9. M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
    [CrossRef] [PubMed]
  10. D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
    [CrossRef] [PubMed]
  11. D. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903(2008).
    [CrossRef] [PubMed]
  12. C. Sun, D. V. Dylov, and J. W. Fleischer, Opt. Lett. 34, 3003(2009).
    [CrossRef] [PubMed]
  13. V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, J. Exp. Theor. Phys. 84, 388 (1997).
    [CrossRef]
  14. S. Jia, W. Wan, and J. W. Fleischer, Opt. Lett. 32, 1668(2007).
    [CrossRef] [PubMed]
  15. C. Sun, C. Barsi, and J. W. Fleischer, Opt. Express 16, 20676(2008).
    [CrossRef] [PubMed]
  16. A. M. Kamchatnov, A. Gammal, F. K. Abdullaev, and R. A. Kraenkel, Phys. Lett. A 319, 406 (2003).
    [CrossRef]
  17. G. Assanto, T. R. Marchant, and N. F. Smyth, Phys. Rev. A 78, 063808 (2008).
    [CrossRef]
  18. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
    [CrossRef]
  19. C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
    [CrossRef]
  20. D.V. Dylov and J. W. Fleischer, Nat. Photonics 4, 323 (2010).
    [CrossRef]

2010 (1)

D.V. Dylov and J. W. Fleischer, Nat. Photonics 4, 323 (2010).
[CrossRef]

2009 (2)

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

C. Sun, D. V. Dylov, and J. W. Fleischer, Opt. Lett. 34, 3003(2009).
[CrossRef] [PubMed]

2008 (4)

C. Sun, C. Barsi, and J. W. Fleischer, Opt. Express 16, 20676(2008).
[CrossRef] [PubMed]

G. Assanto, T. R. Marchant, and N. F. Smyth, Phys. Rev. A 78, 063808 (2008).
[CrossRef]

E. G. Khamis, A. Gammal, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 78, 013829 (2008).
[CrossRef]

D. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903(2008).
[CrossRef] [PubMed]

2007 (4)

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] [PubMed]

S. Jia, W. Wan, and J. W. Fleischer, Opt. Lett. 32, 1668(2007).
[CrossRef] [PubMed]

O. Manela and M. Segev, Opt. Express 15, 10863 (2007).
[CrossRef] [PubMed]

2003 (1)

A. M. Kamchatnov, A. Gammal, F. K. Abdullaev, and R. A. Kraenkel, Phys. Lett. A 319, 406 (2003).
[CrossRef]

2000 (2)

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

1997 (2)

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, J. Exp. Theor. Phys. 84, 388 (1997).
[CrossRef]

1985 (1)

1983 (1)

R. Reinisch and M. Neviere, Phys. Rev. B 28, 1870 (1983).
[CrossRef]

1968 (1)

I. Freund, Phys. Rev. Lett. 21, 1404 (1968).
[CrossRef]

Abdullaev, F. K.

A. M. Kamchatnov, A. Gammal, F. K. Abdullaev, and R. A. Kraenkel, Phys. Lett. A 319, 406 (2003).
[CrossRef]

Assanto, G.

G. Assanto, T. R. Marchant, and N. F. Smyth, Phys. Rev. A 78, 063808 (2008).
[CrossRef]

Barsi, C.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

C. Sun, C. Barsi, and J. W. Fleischer, Opt. Express 16, 20676(2008).
[CrossRef] [PubMed]

Chavez-Cerda, S.

S. Chavez-Cerda, M. D. Iturbe-Castillo, and J. M. Hickmann, in Self-Focusing: Past and Present, Vol. 114 of Topics in Applied Physics (2009), pp. 517–545.
[CrossRef]

Christodoulides, D. N.

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Conti, C.

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

Coskun, T.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

Coskun, T. H.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Dylov, D.

D. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903(2008).
[CrossRef] [PubMed]

Dylov, D. V.

El, G. A.

E. G. Khamis, A. Gammal, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 78, 013829 (2008).
[CrossRef]

Eugenieva, E.

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Fleischer, J. W.

D.V. Dylov and J. W. Fleischer, Nat. Photonics 4, 323 (2010).
[CrossRef]

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

C. Sun, D. V. Dylov, and J. W. Fleischer, Opt. Lett. 34, 3003(2009).
[CrossRef] [PubMed]

D. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903(2008).
[CrossRef] [PubMed]

C. Sun, C. Barsi, and J. W. Fleischer, Opt. Express 16, 20676(2008).
[CrossRef] [PubMed]

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

S. Jia, W. Wan, and J. W. Fleischer, Opt. Lett. 32, 1668(2007).
[CrossRef] [PubMed]

Freund, I.

I. Freund, Phys. Rev. Lett. 21, 1404 (1968).
[CrossRef]

Gammal, A.

E. G. Khamis, A. Gammal, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 78, 013829 (2008).
[CrossRef]

A. M. Kamchatnov, A. Gammal, F. K. Abdullaev, and R. A. Kraenkel, Phys. Lett. A 319, 406 (2003).
[CrossRef]

Ghofraniha, N.

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

Gladush, Y. G.

E. G. Khamis, A. Gammal, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 78, 013829 (2008).
[CrossRef]

Hickmann, J. M.

S. Chavez-Cerda, M. D. Iturbe-Castillo, and J. M. Hickmann, in Self-Focusing: Past and Present, Vol. 114 of Topics in Applied Physics (2009), pp. 517–545.
[CrossRef]

Iturbe-Castillo, M. D.

S. Chavez-Cerda, M. D. Iturbe-Castillo, and J. M. Hickmann, in Self-Focusing: Past and Present, Vol. 114 of Topics in Applied Physics (2009), pp. 517–545.
[CrossRef]

Jia, S.

Kamchatnov, A. M.

E. G. Khamis, A. Gammal, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 78, 013829 (2008).
[CrossRef]

A. M. Kamchatnov, A. Gammal, F. K. Abdullaev, and R. A. Kraenkel, Phys. Lett. A 319, 406 (2003).
[CrossRef]

Khamis, E. G.

E. G. Khamis, A. Gammal, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 78, 013829 (2008).
[CrossRef]

Kip, D.

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Koster, A.

Kraenkel, R. A.

A. M. Kamchatnov, A. Gammal, F. K. Abdullaev, and R. A. Kraenkel, Phys. Lett. A 319, 406 (2003).
[CrossRef]

Kutuzov, V.

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, J. Exp. Theor. Phys. 84, 388 (1997).
[CrossRef]

Manela, O.

Marchant, T. R.

G. Assanto, T. R. Marchant, and N. F. Smyth, Phys. Rev. A 78, 063808 (2008).
[CrossRef]

Mitchell, M.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Neviere, M.

Paraire, N.

Petnikova, V. M.

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, J. Exp. Theor. Phys. 84, 388 (1997).
[CrossRef]

Reinisch, R.

Ruocco, G.

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

Segev, M.

O. Manela and M. Segev, Opt. Express 15, 10863 (2007).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Shuvalov, V. V.

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, J. Exp. Theor. Phys. 84, 388 (1997).
[CrossRef]

Smyth, N. F.

G. Assanto, T. R. Marchant, and N. F. Smyth, Phys. Rev. A 78, 063808 (2008).
[CrossRef]

Soljacic, M.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Sun, C.

Trillo, S.

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

Vincent, P.

Vishwanath, A.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

Vysloukh, V. A.

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, J. Exp. Theor. Phys. 84, 388 (1997).
[CrossRef]

Wan, W.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

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

S. Jia, W. Wan, and J. W. Fleischer, Opt. Lett. 32, 1668(2007).
[CrossRef] [PubMed]

J. Exp. Theor. Phys. (1)

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, J. Exp. Theor. Phys. 84, 388 (1997).
[CrossRef]

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

Nat. Photonics (2)

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photonics 3, 211 (2009).
[CrossRef]

D.V. Dylov and J. W. Fleischer, Nat. Photonics 4, 323 (2010).
[CrossRef]

Nat. Phys. (1)

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

Opt. Express (2)

Opt. Lett. (2)

Phys. Lett. A (1)

A. M. Kamchatnov, A. Gammal, F. K. Abdullaev, and R. A. Kraenkel, Phys. Lett. A 319, 406 (2003).
[CrossRef]

Phys. Rev. A (2)

G. Assanto, T. R. Marchant, and N. F. Smyth, Phys. Rev. A 78, 063808 (2008).
[CrossRef]

E. G. Khamis, A. Gammal, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 78, 013829 (2008).
[CrossRef]

Phys. Rev. B (1)

R. Reinisch and M. Neviere, Phys. Rev. B 28, 1870 (1983).
[CrossRef]

Phys. Rev. Lett. (5)

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

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903(2008).
[CrossRef] [PubMed]

I. Freund, Phys. Rev. Lett. 21, 1404 (1968).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Science (1)

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Other (1)

S. Chavez-Cerda, M. D. Iturbe-Castillo, and J. M. Hickmann, in Self-Focusing: Past and Present, Vol. 114 of Topics in Applied Physics (2009), pp. 517–545.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Simulation of Fresnel diffraction from a sharp edge. Shown are top-view evolutions and output cross sections of (a) linear diffraction, (b) nonlinear diffraction without noise, (c) modulation instability without an edge, and (d) nonlinear edge diffraction with noise. Insets show power spectra of output.

Fig. 2
Fig. 2

Experiment of nonlinear Fresnel diffraction from a sharp edge. (a) Laser light at 532 nm is made partially spatially incoherent by passing it through a rotating diffuser and is then imaged onto an SBN:75 photorefractive crystal. At the input face, half the light is blocked by a razor blade. Light exiting the crystal is imaged into a CCD camera. (b) Initial stepped intensity at the input face. (c) Linear diffraction at output. (d) Nonlinear diffraction.

Fig. 3
Fig. 3

Influence of edge width on nonlinear diffraction. Left column, simulation; right column, experiment. (a)–(c) Results for a sharp edge of 5 μm width. (d)–(f) Results for a soft edge of 50 μm width. (a), (d) Top views of numerical propagation; (b), (e) experimental input; (c), (f) experimental output for nonlinear diffraction.

Fig. 4
Fig. 4

Nonlinear diffraction as a function of nonlinearity and coherence length. (a), (b) Simulation results for shock width as a function of (a) coherence length and (b) nonlinearity. Solid curves are guides to guide the eye. (c), (d) Experimental output pictures for shock width as a function of (c) coherence length and (d) nonlinearity. Solid lines are linear fits to the data.

Equations (4)

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

i ψ z + 1 2 k 0 2 ψ + k 0 Δ n ( | ψ | 2 ) n 0 ψ = 0 ,
ψ ( x , 0 ) = { a x < 0 0 x > 0 ,
ρ z + ( ρ v ) = 0 ,
v z + v v = 1 ρ P + 1 2 ( 1 ρ 2 ρ ) .

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