Abstract

We demonstrate, both theoretically and experimentally, the existence of nonlocal gap solitons in two-dimensional periodic photonic structures with defocusing thermal nonlinearity. We employ liquid-infiltrated photonic crystal fibers and show how the system geometry can modify the effective response of a nonlocal medium and the properties of two-dimensional gap solitons.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]

2008 (2)

Y.-Y. Lin, I.-H. Chen, and R.-K. Lee, J. Opt. A 10, 044017 (2008).
[CrossRef]

N. K. Efremidis, Phys. Rev. A 77, 063824 (2008).
[CrossRef]

2007 (3)

2006 (2)

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

Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 31, 2027 (2006).
[CrossRef] [PubMed]

2005 (1)

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

2004 (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]

2003 (2)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

2000 (1)

S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, Phys. Rev. E 62, 5777 (2000).
[CrossRef]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1993 (1)

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Alfassi, B.

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

Bang, O.

C. R. Rosberg, F. H. Bennet, D. N. Neshev, W. Krolikowski, Yu. S. Kivshar, P. D. Rasmussen, O. Bang, and A. Bjarklev, Opt. Express 15, 12145 (2007).
[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]

Bennet, F. H.

Bjarklev, A.

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Chen, I.-H.

Y.-Y. Lin, I.-H. Chen, and R.-K. Lee, J. Opt. A 10, 044017 (2008).
[CrossRef]

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Cohen, O.

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

Dreischuh, A.

Edmundson, 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]

Efremidis, N. K.

N. K. Efremidis, Phys. Rev. A 77, 063824 (2008).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Kartashov, Y. V.

Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 31, 2027 (2006).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

Kivshar, Yu. S.

Krolikowski, W.

Lee, R.-K.

Y.-Y. Lin, I.-H. Chen, and R.-K. Lee, J. Opt. A 10, 044017 (2008).
[CrossRef]

Lin, Y.-Y.

Y.-Y. Lin, I.-H. Chen, and R.-K. Lee, J. Opt. A 10, 044017 (2008).
[CrossRef]

Louis, P. J. Y.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Mingaleev, S. F.

S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, Phys. Rev. E 62, 5777 (2000).
[CrossRef]

Minovich, A.

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

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]

Neshev, D. N.

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]

Ostrovskaya, E. A.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

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]

Rasmussen, P. D.

Rosberg, C. R.

Rotschild, C.

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

Sammut, R. A.

S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, Phys. Rev. E 62, 5777 (2000).
[CrossRef]

Savage, C. M.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Segev, M.

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

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Sukhorukov, A. A.

Torner, L.

Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 31, 2027 (2006).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[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.

Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 31, 2027 (2006).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

J. Opt. A (1)

Y.-Y. Lin, I.-H. Chen, and R.-K. Lee, J. Opt. A 10, 044017 (2008).
[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]

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (2)

N. K. Efremidis, Phys. Rev. A 77, 063824 (2008).
[CrossRef]

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Phys. Rev. E (1)

S. F. Mingaleev, Yu. S. Kivshar, and R. A. Sammut, Phys. Rev. E 62, 5777 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) System geometry. (b) Bandgap structure for n S = 1.46 , n L = 1.4605 , and d Λ = 0.5 . Shaded regions correspond to the bands of the finite structure in (a), while the solid curves show the edges of the first bandgap of an infinite lattice. The dashed line indicates the index of the solid material n S .

Fig. 2
Fig. 2

Families of nonlocal gap solitons. (a), (b) Power P = E 2 d r and soliton width versus effective index for different values of s. The normalized wave number is q = 200 . The dots correspond to the example in Fig. 3.

Fig. 3
Fig. 3

Numerically calculated nonlocal gap soliton for power P = 4 × 10 5 and s = 10 , marked with a dot in Fig. 2. (a) Intensity and (b) corresponding phase distribution. (c) Soliton profile and (d) induced temperature change along the symmetry line shown as the white dashed line in (a).

Fig. 4
Fig. 4

(a), (b) Experimentally observed output diffraction pattern and soliton localization in a liquid-infiltrated PCF at low and high input power, respectively. (c) Fraction of light in the input hole versus input power. (d) Measured interference pattern of the output beam with an inclined reference beam.

Equations (2)

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i a z ( x , y , z ) + 2 a ( x , y , z ) p 2 a ( x , y , z ) = [ n 0 ( x , y ) τ ( x , y , z ) f ( x , y ) ] 2 q 2 a ( x , y , z ) ,
2 τ ( x , y , z ) = a ( x , y , z ) 2 ,

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