Abstract

We put forward what we believe to be a novel strategy to achieve synthetic nonlinearities where local and nonlocal contributions compete on a similar footing, thus yielding intermediate tunable responses ranging from local to strongly nonlocal. The setting addressed is a semiconductor material with both Kerr and thermal nonlinearities illuminated by a pulse train with suitable pulse width and repetition rate.

© 2009 Optical Society of America

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  1. W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B 6, S288 (2004).
    [CrossRef]
  2. M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
    [CrossRef]
  3. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
    [CrossRef]
  4. X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
    [CrossRef]
  5. Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 30, 3171 (2005).
    [CrossRef] [PubMed]
  6. S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, Opt. Lett. 31, 1100 (2006).
    [CrossRef] [PubMed]
  7. Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
    [CrossRef] [PubMed]
  8. C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
    [CrossRef] [PubMed]
  9. D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
    [CrossRef] [PubMed]
  10. A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
    [CrossRef]
  11. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef] [PubMed]
  12. M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 30, 415 (2005).
    [CrossRef] [PubMed]
  13. D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
    [CrossRef]
  14. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 79, 013803 (2009).
    [CrossRef]
  15. P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
    [CrossRef] [PubMed]
  16. I. Tikhonenkov, B. A. Malomed, and A. Vardi, Phys. Rev. A 78, 043614 (2008).
    [CrossRef]
  17. J. Gomez-Gardenes, B. A. Malomed, L. M. Floria, and A. R. Bishop, Phys. Rev. E 73, 036608 (2006).
    [CrossRef]
  18. P. S. Dobal, H. D. Bist, S. K. Mehta, and R. K. Jain, Appl. Phys. Lett. 65, 2469 (1994).
    [CrossRef]
  19. J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, IEEE J. Quantum Electron. 33, 341 (1997).
    [CrossRef]
  20. J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, Electron. Lett. 28, 1879 (1992).
    [CrossRef]

2009 (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 79, 013803 (2009).
[CrossRef]

2008 (1)

I. Tikhonenkov, B. A. Malomed, and A. Vardi, Phys. Rev. A 78, 043614 (2008).
[CrossRef]

2006 (6)

J. Gomez-Gardenes, B. A. Malomed, L. M. Floria, and A. R. Bishop, Phys. Rev. E 73, 036608 (2006).
[CrossRef]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, Opt. Lett. 31, 1100 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
[CrossRef] [PubMed]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef] [PubMed]

2005 (6)

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 30, 415 (2005).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 30, 3171 (2005).
[CrossRef] [PubMed]

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef] [PubMed]

2004 (2)

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B 6, S288 (2004).
[CrossRef]

2002 (1)

1997 (1)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, IEEE J. Quantum Electron. 33, 341 (1997).
[CrossRef]

1994 (1)

P. S. Dobal, H. D. Bist, S. K. Mehta, and R. K. Jain, Appl. Phys. Lett. 65, 2469 (1994).
[CrossRef]

1992 (1)

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Adamski, A.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Aitchison, J. S.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, IEEE J. Quantum Electron. 33, 341 (1997).
[CrossRef]

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Alfassi, B.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Al-Hemyari, K.

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Assanto, G.

Bang, O.

Bishop, A. R.

J. Gomez-Gardenes, B. A. Malomed, L. M. Floria, and A. R. Bishop, Phys. Rev. E 73, 036608 (2006).
[CrossRef]

Bist, H. D.

P. S. Dobal, H. D. Bist, S. K. Mehta, and R. K. Jain, Appl. Phys. Lett. 65, 2469 (1994).
[CrossRef]

Briedis, D.

Brzdakiewicz, K. A.

Cambournac, C.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Cohen, O.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Conti, C.

Crasovan, L. -C.

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Desyatnikov, A. S.

Dobal, P. S.

P. S. Dobal, H. D. Bist, S. K. Mehta, and R. K. Jain, Appl. Phys. Lett. 65, 2469 (1994).
[CrossRef]

Edmundson, D.

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B 6, S288 (2004).
[CrossRef]

Floria, L. M.

J. Gomez-Gardenes, B. A. Malomed, L. M. Floria, and A. R. Bishop, Phys. Rev. E 73, 036608 (2006).
[CrossRef]

Gomez-Gardenes, J.

J. Gomez-Gardenes, B. A. Malomed, L. M. Floria, and A. R. Bishop, Phys. Rev. E 73, 036608 (2006).
[CrossRef]

Grant, R. S.

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Haelterman, M.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Hutchings, D. C.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, IEEE J. Quantum Electron. 33, 341 (1997).
[CrossRef]

Hutsebaut, X.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Ironside, C. N.

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Jain, R. K.

P. S. Dobal, H. D. Bist, S. K. Mehta, and R. K. Jain, Appl. Phys. Lett. 65, 2469 (1994).
[CrossRef]

Kang, J. U.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, IEEE J. Quantum Electron. 33, 341 (1997).
[CrossRef]

Kartashov, Y. V.

Kivshar, Y.

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Kivshar, Y. S.

Krolikowski, W.

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Lopez-Aguayo, S.

Malomed, B. A.

I. Tikhonenkov, B. A. Malomed, and A. Vardi, Phys. Rev. A 78, 043614 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

J. Gomez-Gardenes, B. A. Malomed, L. M. Floria, and A. R. Bishop, Phys. Rev. E 73, 036608 (2006).
[CrossRef]

Manela, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Mehta, S. K.

P. S. Dobal, H. D. Bist, S. K. Mehta, and R. K. Jain, Appl. Phys. Lett. 65, 2469 (1994).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
[CrossRef] [PubMed]

Neshev, D.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B 6, S288 (2004).
[CrossRef]

Neyts, K.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Nikolov, N. I.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B 6, S288 (2004).
[CrossRef]

Peccianti, M.

Pedri, P.

P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef] [PubMed]

Petersen, D.

Rasmussen, J. J.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B 6, S288 (2004).
[CrossRef]

Rotschild, C.

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef] [PubMed]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Santos, L.

P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef] [PubMed]

Segev, M.

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef] [PubMed]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Sibbett, W.

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

Skupin, S.

Stegeman, G. I.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, IEEE J. Quantum Electron. 33, 341 (1997).
[CrossRef]

Tikhonenkov, I.

I. Tikhonenkov, B. A. Malomed, and A. Vardi, Phys. Rev. A 78, 043614 (2008).
[CrossRef]

Torner, L.

Vardi, A.

I. Tikhonenkov, B. A. Malomed, and A. Vardi, Phys. Rev. A 78, 043614 (2008).
[CrossRef]

Villeneuve, A.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, IEEE J. Quantum Electron. 33, 341 (1997).
[CrossRef]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 79, 013803 (2009).
[CrossRef]

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
[CrossRef] [PubMed]

Wyller, J.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B 6, S288 (2004).
[CrossRef]

Xu, Z.

Yakimenko, A. I.

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Zaliznyak, Y. A.

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Appl. Phys. Lett. (1)

P. S. Dobal, H. D. Bist, S. K. Mehta, and R. K. Jain, Appl. Phys. Lett. 65, 2469 (1994).
[CrossRef]

Electron. Lett. (1)

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, Electron. Lett. 28, 1879 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, IEEE J. Quantum Electron. 33, 341 (1997).
[CrossRef]

J. Opt. B (1)

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B 6, S288 (2004).
[CrossRef]

Nat. Phys. (1)

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Opt. Commun. (1)

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (2)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 79, 013803 (2009).
[CrossRef]

I. Tikhonenkov, B. A. Malomed, and A. Vardi, Phys. Rev. A 78, 043614 (2008).
[CrossRef]

Phys. Rev. E (3)

J. Gomez-Gardenes, B. A. Malomed, L. M. Floria, and A. R. Bishop, Phys. Rev. E 73, 036608 (2006).
[CrossRef]

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Typical spatiotemporal temperature distributions upon heating of the sample with pulse sequence when transverse intensity distribution features (a) one or (b) two humps. In both cases τ rep = 50 and τ dur = 0.5 .

Fig. 2
Fig. 2

(a),(c) Temporal and (b),(d) spatial distributions at τ = 0 of intensity ϕ I (black curves) and temperature γ θ [gray (red online) curves] for fundamental (top) and dipole (bottom) solitons at τ rep = 5 and τ dur = 0.004 . Upper curves in each panel correspond to b = 2 ; lower curves correspond to b = 1 . For fundamental solitons temporal distributions are shown at η = 0 , while for dipoles they are shown at the point corresponding to the intensity maximum.

Fig. 3
Fig. 3

(a) U versus b for the fundamental soliton at τ rep = 5 for (a) τ dur 0 , (2) τ dur = 0.004 , and (3) τ dur = 0.009 . Circles correspond to the solitons in Figs. 2a, 2b. Temperature γ θ 0 at η = τ = 0 and maximal temperature difference γ θ d at η = 0 versus (b) τ rep at τ dur = 0.002 and versus (c) τ dur at τ rep = 5 . In (b) and (c) b = 1 .

Fig. 4
Fig. 4

Stable propagation of perturbed (a) dipole and (b) five-hump solitons with b = 4 , τ rep = 5 , and τ dur = 0.004 .

Equations (2)

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

i q ξ = 1 2 2 q η 2 | q | 2 q γ θ q ,
θ τ 2 θ η 2 = ϕ ( τ ) | q | 2 .

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