Abstract

We study generation of two-dimensional dispersive shock waves and oblique dark solitons upon interaction of tilted plane waves with negative refractive index defects embedded into defocusing material with linear gain and two-photon absorption. Different evolution regimes are encountered, including the formation of well-localized disturbances for input tilts below critical one, generation of extended shock waves containing multiple intensity oscillations in the “upstream” region, and gradually vanishing oblique dark solitons in the “downstream” region for input tilts exceeding critical one. The generation of stable dispersive shock waves is possible only below certain critical defect strength.

© 2013 Optical Society of America

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  1. W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, Opt. Lett. 10, 457 (1985).
    [CrossRef]
  2. J. E. Rothenberg and D. Grischkowsky, Phys. Rev. Lett. 62, 531 (1989).
    [CrossRef]
  3. J. E. Rothenberg and H. K. Heinrich, Opt. Lett. 17, 261 (1992).
    [CrossRef]
  4. G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Opt. Lett. 14, 137 (1989).
    [CrossRef]
  5. W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
    [CrossRef]
  6. N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. 99, 043903 (2007).
    [CrossRef]
  7. C. Barsi, W. Wan, C. Sun, and J. W. Fleischer, Opt. Lett. 32, 2930 (2007).
    [CrossRef]
  8. A. M. Kamchatnov, A. Gammal, and R. A. Kraenkel, Phys. Rev. A 69, 063604 (2004).
    [CrossRef]
  9. M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhardt, Phys. Rev. A 74, 023623 (2006).
    [CrossRef]
  10. G. A. El, A. Gammal, and A. M. Kamchatnov, Phys. Rev. Lett. 97, 180405 (2006).
    [CrossRef]
  11. I. Carusotto, S. X. Hu, L. A. Collins, and A. Smerzi, Phys. Rev. Lett. 97, 260403 (2006).
    [CrossRef]
  12. P. Engels, and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007).
    [CrossRef]
  13. A. M. Leszczyszyn, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 79, 063608 (2009).
    [CrossRef]
  14. E. G. Khamis, A. Gammal, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 78, 013829 (2008).
    [CrossRef]
  15. A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
    [CrossRef]
  16. G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, Phys. Rev. Lett. 107, 245301 (2011).
    [CrossRef]
  17. J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401 (2008).
    [CrossRef]
  18. Y. V. Kartashov and A. M. Kamchatnov, Opt. Lett. 37, 389 (2012).
    [CrossRef]

2012 (1)

2011 (2)

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

2009 (1)

A. M. Leszczyszyn, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 79, 063608 (2009).
[CrossRef]

2008 (2)

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

J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401 (2008).
[CrossRef]

2007 (3)

P. Engels, and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007).
[CrossRef]

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

C. Barsi, W. Wan, C. Sun, and J. W. Fleischer, Opt. Lett. 32, 2930 (2007).
[CrossRef]

2006 (4)

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
[CrossRef]

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhardt, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

G. A. El, A. Gammal, and A. M. Kamchatnov, Phys. Rev. Lett. 97, 180405 (2006).
[CrossRef]

I. Carusotto, S. X. Hu, L. A. Collins, and A. Smerzi, Phys. Rev. Lett. 97, 260403 (2006).
[CrossRef]

2004 (1)

A. M. Kamchatnov, A. Gammal, and R. A. Kraenkel, Phys. Rev. A 69, 063604 (2004).
[CrossRef]

1992 (1)

1989 (2)

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, Opt. Lett. 14, 137 (1989).
[CrossRef]

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

1985 (1)

Ablowitz, M. J.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhardt, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Agrawal, G. P.

Alfano, R. R.

Amo, A.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Atherton, C.

P. Engels, and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007).
[CrossRef]

Baldeck, P. L.

Barsi, C.

Berloff, N. G.

J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401 (2008).
[CrossRef]

Bramati, A.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Carusotto, I.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

I. Carusotto, S. X. Hu, L. A. Collins, and A. Smerzi, Phys. Rev. Lett. 97, 260403 (2006).
[CrossRef]

Ciuti, C.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Coddington, I.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhardt, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Collins, L. A.

I. Carusotto, S. X. Hu, L. A. Collins, and A. Smerzi, Phys. Rev. Lett. 97, 260403 (2006).
[CrossRef]

Conti, C.

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

Cornell, E. A.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhardt, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Deveaud-Plédran, B.

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

El, G. A.

A. M. Leszczyszyn, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 79, 063608 (2009).
[CrossRef]

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

G. A. El, A. Gammal, and A. M. Kamchatnov, Phys. Rev. Lett. 97, 180405 (2006).
[CrossRef]

Engels, P.

P. Engels, and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007).
[CrossRef]

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhardt, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Fleischer, J. W.

C. Barsi, W. Wan, C. Sun, and J. W. Fleischer, Opt. Lett. 32, 2930 (2007).
[CrossRef]

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
[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]

G. A. El, A. Gammal, and A. M. Kamchatnov, Phys. Rev. Lett. 97, 180405 (2006).
[CrossRef]

A. M. Kamchatnov, A. Gammal, and R. A. Kraenkel, Phys. Rev. A 69, 063604 (2004).
[CrossRef]

Ghofraniha, N.

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

Giacobino, E.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Gladush, Y. G.

A. M. Leszczyszyn, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 79, 063608 (2009).
[CrossRef]

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

Grischkowsky, D.

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

Grosso, G.

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

Heinrich, H. K.

Hivet, R.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Hoefer, M. A.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhardt, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Houdré, R.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Hu, S. X.

I. Carusotto, S. X. Hu, L. A. Collins, and A. Smerzi, Phys. Rev. Lett. 97, 260403 (2006).
[CrossRef]

Jia, S.

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
[CrossRef]

Johnson, A. M.

Kamchatnov, A. M.

Y. V. Kartashov and A. M. Kamchatnov, Opt. Lett. 37, 389 (2012).
[CrossRef]

A. M. Leszczyszyn, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 79, 063608 (2009).
[CrossRef]

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

G. A. El, A. Gammal, and A. M. Kamchatnov, Phys. Rev. Lett. 97, 180405 (2006).
[CrossRef]

A. M. Kamchatnov, A. Gammal, and R. A. Kraenkel, Phys. Rev. A 69, 063604 (2004).
[CrossRef]

Kartashov, Y. V.

Keeling, J.

J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401 (2008).
[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]

Kraenkel, R. A.

A. M. Kamchatnov, A. Gammal, and R. A. Kraenkel, Phys. Rev. A 69, 063604 (2004).
[CrossRef]

Léger, Y.

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

Leménager, G.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Leszczyszyn, A. M.

A. M. Leszczyszyn, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 79, 063608 (2009).
[CrossRef]

Morier-Genoud, F.

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

Nardin, G.

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

Pigeon, S.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Pisanello, F.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Rothenberg, J. E.

J. E. Rothenberg and H. K. Heinrich, Opt. Lett. 17, 261 (1992).
[CrossRef]

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

Ruocco, G.

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

Sala, V. G.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Sanvitto, D.

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

Schweikhardt, V.

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhardt, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

Smerzi, A.

I. Carusotto, S. X. Hu, L. A. Collins, and A. Smerzi, Phys. Rev. Lett. 97, 260403 (2006).
[CrossRef]

Stolen, R. H.

Sun, C.

Tomlinson, W. J.

Trillo, S.

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

Wan, W.

C. Barsi, W. Wan, C. Sun, and J. W. Fleischer, Opt. Lett. 32, 2930 (2007).
[CrossRef]

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
[CrossRef]

Nat. Phys. (1)

W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. 3, 46 (2006).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (4)

A. M. Kamchatnov, A. Gammal, and R. A. Kraenkel, Phys. Rev. A 69, 063604 (2004).
[CrossRef]

M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhardt, Phys. Rev. A 74, 023623 (2006).
[CrossRef]

A. M. Leszczyszyn, G. A. El, Y. G. Gladush, and A. M. Kamchatnov, Phys. Rev. A 79, 063608 (2009).
[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. Lett. (7)

G. Grosso, G. Nardin, F. Morier-Genoud, Y. Léger, and B. Deveaud-Plédran, Phys. Rev. Lett. 107, 245301 (2011).
[CrossRef]

J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401 (2008).
[CrossRef]

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

G. A. El, A. Gammal, and A. M. Kamchatnov, Phys. Rev. Lett. 97, 180405 (2006).
[CrossRef]

I. Carusotto, S. X. Hu, L. A. Collins, and A. Smerzi, Phys. Rev. Lett. 97, 260403 (2006).
[CrossRef]

P. Engels, and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007).
[CrossRef]

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

Science (1)

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet, I. Carusotto, F. Pisanello, G. Leménager, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, Science 332, 1167 (2011).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Maximal wu and minimal wl amplitudes of shock wave versus defect depth at (a) α=0.5, (b) α=1.0, and (c) α=1.5. Vertical dashed lines in (a) and (c) mark the border of existence and stability domains for such waves, respectively. Circles correspond to waves shown in Fig. 2.

Fig. 2.
Fig. 2.

Field modulus distributions in stationary wave structures emerging due to the presence of defect at α=0.5, pr=0.575 (top left panel); α=1.0, pr=0.3 (top right panel); and α=1.5, pr=0.62 (bottom panel). Arrows on the projection plane indicate direction of the energy flow.

Fig. 3.
Fig. 3.

(a) Critical value of defect depth prcr at which stationary disturbances cease to exist for velocities α<1. (b) The defect depth prst at which stationary shock waves become unstable for velocities α>1.

Fig. 4.
Fig. 4.

Unstable evolution of the wave at (a) α=0.5, pr=0.58 and (b) α=1.5, pr=0.90. In (a), the input condition corresponds to the disturbance that propagates stably at α=0.5, pr=0.57, while in (b) the input condition corresponds to shock wave that is stable at α=1.5, pr=0.62. (c) The excitation of a shock wave by tilted plane wave at α=1.5, pr=0.45. The point where dashed lines cross indicates the center of the defect. Arrows in the top row show the direction of the energy flow.

Equations (2)

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iqξ=12(2qη2+2qζ2)+(σriσi)q|q|2+[ipi+prR(η,ζ)]q,
δ=pi±[pi2(|k|2/4)(|k|2+4pi/σi)]1/2.

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