Abstract

A weakly modulated large-area two-dimensional square photonic lattice slab was fabricated through optical induction technique in a photorefractive photovoltaic LiNbO3:Fe crystal. Bragg-matched diffraction technique was used to characterize the square photonic lattice slab. Interestingly, linear discrete diffraction typical for waveguide arrays was observed in such a square photonic lattice slab, indicating that the lattice slab can be viewed effectively as a one-dimensional waveguide array. Furthermore, discrete soliton was demonstrated in the photonic lattice slab due to a saturable self-defocusing nonlinearity arising from the bulk photorefractive photovoltaic effect of LiNbO3:Fe.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  33. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
  34. X. Qi, S. Liu, R. Guo, Y. Lu, Z. Liua, L. Zhou, and Y. Li, "Defect solitons in optically induced one-dimensional photonic lattices in LiNbO3:Fe crystal," Opt. Commun. 272, 387-390 (2007).
    [CrossRef]

2007

X. Qi, S. Liu, G. Zhang, R. Guo, Z. Liu, L. Zhou, and Y. Li, "Gap solitons in optically induced two-dimensional square photonic lattices in LiNbO3:Fe crystals," Appl. Phys. Lett. 91, 131111 (2007).
[CrossRef]

X. Qi, S. Liu, R. Guo, Y. Lu, Z. Liua, L. Zhou, and Y. Li, "Defect solitons in optically induced one-dimensional photonic lattices in LiNbO3:Fe crystal," Opt. Commun. 272, 387-390 (2007).
[CrossRef]

2006

T. Song, S. Liu, R. Guo, Z. Liu, N. Zhu, and Y. Gao, "Observation of composite gap solitons in optically induced nonlinear lattices in LiNbO3:Fe crystal," Opt. Express 14, 1924-1932 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

E. Smirnov, M. Stepic, C. E. Ruter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31, 2338-2340 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature (London) 5, 93-96 (2006).
[CrossRef]

2005

2004

2003

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147-150 (2003).
[CrossRef]

L. J. Wu, M. Mazilu, and T. F. Krauss, "Beam steering in planar-photonic crystals: from superprism to supercollimator," J. Lightwave Technol. 21, 561-566 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature (London) 424, 817-823 (2003).
[CrossRef]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, "Multigap discrete vector solitons," Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef] [PubMed]

S. Longhi, D. Janner, M. Marano, and P. Laporta, "Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: Dynamic-mode stabilization and radiation-loss suppression," Phys. Rev. E 67, 036601 (2003).
[CrossRef]

2002

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093902 (2002).
[CrossRef]

2000

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

1999

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
[CrossRef]

K. Gallo and G. Assanto, "All-optical diode based on second-harmonic generation in an asymmetric waveguide," J. Opt. Soc. Am. B 16, 267-269 (1999).
[CrossRef]

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, "Vortices in a Bose-Einstein condensate," Phys. Rev. Lett. 83, 2498-2501 (1999).
[CrossRef]

1998

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

S. Darmanyan, A. Kobyakov, and F. Lederer, "Stability of strongly localized excitations in discrete media with cubic nonlinearity," J. Exp. Theor. Phys. 86, 682-686 (1998).
[CrossRef]

1993

Y. S. Kivshar, "Self-localization in arrays of defocusing waveguides," Opt. Lett. 20, 1147-1149 (1993).
[CrossRef]

J. Feng, "Alternative scheme for studying gap solitons in infinite periodic Kerr media," Opt. Lett. 20, 1302-1304 (1993).
[CrossRef]

1992

G. A. Swartzlander, Jr., and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

1988

D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 19, 794-796 (1988).
[CrossRef]

1985

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R78 (1985).
[CrossRef]

1969

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

1961

L. P. Pitaevskii, "Vortex lines in an imperfect Bose gas," J. Exp. Theor. Phys. 13, 451-454 (1961).

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Anderson, B. P.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, "Vortices in a Bose-Einstein condensate," Phys. Rev. Lett. 83, 2498-2501 (1999).
[CrossRef]

Assanto, G.

Boyd, R.

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093902 (2002).
[CrossRef]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Chen, C. H.

Chen, F.

Christodoulides, D. N.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-2468 (2005).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147-150 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature (London) 424, 817-823 (2003).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 19, 794-796 (1988).
[CrossRef]

Cohen, O.

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

Cornell, E. A.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, "Vortices in a Bose-Einstein condensate," Phys. Rev. Lett. 83, 2498-2501 (1999).
[CrossRef]

Dahlem, M. S.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature (London) 5, 93-96 (2006).
[CrossRef]

Darmanyan, S.

S. Darmanyan, A. Kobyakov, and F. Lederer, "Stability of strongly localized excitations in discrete media with cubic nonlinearity," J. Exp. Theor. Phys. 86, 682-686 (1998).
[CrossRef]

Draude, A.

A. Draude, H. Franke, and R. A. Lessard, "Two-dimensional refractive index patterns with crystalline symmetry," J. Phys. D: Appl. Phys. 38, 974-980 (2005).
[CrossRef]

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147-150 (2003).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Feng, J.

J. Feng, "Alternative scheme for studying gap solitons in infinite periodic Kerr media," Opt. Lett. 20, 1302-1304 (1993).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Fleischer, J.W.

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147-150 (2003).
[CrossRef]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, "Multiband vector lattice solitons," Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

Franke, H.

A. Draude, H. Franke, and R. A. Lessard, "Two-dimensional refractive index patterns with crystalline symmetry," J. Phys. D: Appl. Phys. 38, 974-980 (2005).
[CrossRef]

Gallo, K.

Gao, Y.

Guo, R.

X. Qi, S. Liu, G. Zhang, R. Guo, Z. Liu, L. Zhou, and Y. Li, "Gap solitons in optically induced two-dimensional square photonic lattices in LiNbO3:Fe crystals," Appl. Phys. Lett. 91, 131111 (2007).
[CrossRef]

X. Qi, S. Liu, R. Guo, Y. Lu, Z. Liua, L. Zhou, and Y. Li, "Defect solitons in optically induced one-dimensional photonic lattices in LiNbO3:Fe crystal," Opt. Commun. 272, 387-390 (2007).
[CrossRef]

T. Song, S. Liu, R. Guo, Z. Liu, N. Zhu, and Y. Gao, "Observation of composite gap solitons in optically induced nonlinear lattices in LiNbO3:Fe crystal," Opt. Express 14, 1924-1932 (2006).
[CrossRef] [PubMed]

Hache, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-2468 (2005).
[CrossRef] [PubMed]

Haljan, P. C.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, "Vortices in a Bose-Einstein condensate," Phys. Rev. Lett. 83, 2498-2501 (1999).
[CrossRef]

Hall, D. S.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, "Vortices in a Bose-Einstein condensate," Phys. Rev. Lett. 83, 2498-2501 (1999).
[CrossRef]

Ibanescu, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature (London) 5, 93-96 (2006).
[CrossRef]

Ippen, E. P.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature (London) 5, 93-96 (2006).
[CrossRef]

Janner, D.

S. Longhi, D. Janner, M. Marano, and P. Laporta, "Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: Dynamic-mode stabilization and radiation-loss suppression," Phys. Rev. E 67, 036601 (2003).
[CrossRef]

Joannopoulos, J. D.

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P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature (London) 5, 93-96 (2006).
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T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093902 (2002).
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X. Qi, S. Liu, R. Guo, Y. Lu, Z. Liua, L. Zhou, and Y. Li, "Defect solitons in optically induced one-dimensional photonic lattices in LiNbO3:Fe crystal," Opt. Commun. 272, 387-390 (2007).
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X. Qi, S. Liu, G. Zhang, R. Guo, Z. Liu, L. Zhou, and Y. Li, "Gap solitons in optically induced two-dimensional square photonic lattices in LiNbO3:Fe crystals," Appl. Phys. Lett. 91, 131111 (2007).
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X. Qi, S. Liu, G. Zhang, R. Guo, Z. Liu, L. Zhou, and Y. Li, "Gap solitons in optically induced two-dimensional square photonic lattices in LiNbO3:Fe crystals," Appl. Phys. Lett. 91, 131111 (2007).
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T. Song, S. Liu, R. Guo, Z. Liu, N. Zhu, and Y. Gao, "Observation of composite gap solitons in optically induced nonlinear lattices in LiNbO3:Fe crystal," Opt. Express 14, 1924-1932 (2006).
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X. Qi, S. Liu, R. Guo, Y. Lu, Z. Liua, L. Zhou, and Y. Li, "Defect solitons in optically induced one-dimensional photonic lattices in LiNbO3:Fe crystal," Opt. Commun. 272, 387-390 (2007).
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S. Longhi, D. Janner, M. Marano, and P. Laporta, "Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: Dynamic-mode stabilization and radiation-loss suppression," Phys. Rev. E 67, 036601 (2003).
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X. Qi, S. Liu, R. Guo, Y. Lu, Z. Liua, L. Zhou, and Y. Li, "Defect solitons in optically induced one-dimensional photonic lattices in LiNbO3:Fe crystal," Opt. Commun. 272, 387-390 (2007).
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S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
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K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-2468 (2005).
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Manela, O.

Marano, M.

S. Longhi, D. Janner, M. Marano, and P. Laporta, "Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: Dynamic-mode stabilization and radiation-loss suppression," Phys. Rev. E 67, 036601 (2003).
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M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, "Vortices in a Bose-Einstein condensate," Phys. Rev. Lett. 83, 2498-2501 (1999).
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Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
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C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
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S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
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H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
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Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
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Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093902 (2002).
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T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093902 (2002).
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P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature (London) 5, 93-96 (2006).
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L. P. Pitaevskii, "Vortex lines in an imperfect Bose gas," J. Exp. Theor. Phys. 13, 451-454 (1961).

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Qi, X.

X. Qi, S. Liu, R. Guo, Y. Lu, Z. Liua, L. Zhou, and Y. Li, "Defect solitons in optically induced one-dimensional photonic lattices in LiNbO3:Fe crystal," Opt. Commun. 272, 387-390 (2007).
[CrossRef]

X. Qi, S. Liu, G. Zhang, R. Guo, Z. Liu, L. Zhou, and Y. Li, "Gap solitons in optically induced two-dimensional square photonic lattices in LiNbO3:Fe crystals," Appl. Phys. Lett. 91, 131111 (2007).
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Rakich, P. T.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature (London) 5, 93-96 (2006).
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C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
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Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
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D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature (London) 424, 817-823 (2003).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, Y. Morandotti, R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

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Soljacic, M.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature (London) 5, 93-96 (2006).
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Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
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S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-2468 (2005).
[CrossRef] [PubMed]

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R78 (1985).
[CrossRef]

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Sukhorukov, A. A.

A. A. Sukhorukov and Y. S. Kivshar, "Multigap discrete vector solitons," Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef] [PubMed]

Suntsov, S.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, "Discrete surface solitons," Opt. Lett. 30, 2466-2468 (2005).
[CrossRef] [PubMed]

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G. A. Swartzlander, Jr., and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
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P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature (London) 5, 93-96 (2006).
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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
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Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
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Wieman, C. E.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, "Vortices in a Bose-Einstein condensate," Phys. Rev. Lett. 83, 2498-2501 (1999).
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Yang, H.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093902 (2002).
[CrossRef]

Zhang, G.

X. Qi, S. Liu, G. Zhang, R. Guo, Z. Liu, L. Zhou, and Y. Li, "Gap solitons in optically induced two-dimensional square photonic lattices in LiNbO3:Fe crystals," Appl. Phys. Lett. 91, 131111 (2007).
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Zhou, L.

X. Qi, S. Liu, G. Zhang, R. Guo, Z. Liu, L. Zhou, and Y. Li, "Gap solitons in optically induced two-dimensional square photonic lattices in LiNbO3:Fe crystals," Appl. Phys. Lett. 91, 131111 (2007).
[CrossRef]

X. Qi, S. Liu, R. Guo, Y. Lu, Z. Liua, L. Zhou, and Y. Li, "Defect solitons in optically induced one-dimensional photonic lattices in LiNbO3:Fe crystal," Opt. Commun. 272, 387-390 (2007).
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Appl. Phys. Lett.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett. 74, 1212-1214 (1999).
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X. Qi, S. Liu, G. Zhang, R. Guo, Z. Liu, L. Zhou, and Y. Li, "Gap solitons in optically induced two-dimensional square photonic lattices in LiNbO3:Fe crystals," Appl. Phys. Lett. 91, 131111 (2007).
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Bell Syst. Tech. J.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).

J. Appl. Phys.

G. I. Stegeman and C. T. Seaton, "Nonlinear integrated optics," J. Appl. Phys. 58, R57-R78 (1985).
[CrossRef]

J. Exp. Theor. Phys.

S. Darmanyan, A. Kobyakov, and F. Lederer, "Stability of strongly localized excitations in discrete media with cubic nonlinearity," J. Exp. Theor. Phys. 86, 682-686 (1998).
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J. Lightwave Technol.

J. Opt. Soc. Am. B

J. Phys. D: Appl. Phys.

A. Draude, H. Franke, and R. A. Lessard, "Two-dimensional refractive index patterns with crystalline symmetry," J. Phys. D: Appl. Phys. 38, 974-980 (2005).
[CrossRef]

Nature (London)

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature (London) 422, 147-150 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature (London) 424, 817-823 (2003).
[CrossRef]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, "Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal," Nature (London) 5, 93-96 (2006).
[CrossRef]

Opt. Commun.

X. Qi, S. Liu, R. Guo, Y. Lu, Z. Liua, L. Zhou, and Y. Li, "Defect solitons in optically induced one-dimensional photonic lattices in LiNbO3:Fe crystal," Opt. Commun. 272, 387-390 (2007).
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Opt. Express

Opt. Lett.

Phys. Rev. E

S. Longhi, D. Janner, M. Marano, and P. Laporta, "Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: Dynamic-mode stabilization and radiation-loss suppression," Phys. Rev. E 67, 036601 (2003).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup. S. F., spatial filter; L1 and L2, lens; M, mirror; λ/2, half-wavelength plate; A. T., attenuator; CCD, charge coupled device camera. The inset shows the mask on the X-Z plane of the LiNbO3:Fe crystal, each pinhole has a diameter of 10 µm and the spacing between the two nearest pinholes is 20 µm; C denotes the crystalline C-axis.

Fig. 2.
Fig. 2.

Bragg-matched diffraction of a collimated He-Ne laser beam from the 2D PLS. The red spots in (a)–(e) correspond to output positions of the incident beam and the diffracted beam at the incident angles of 0°, 0.92°, 1.87°, 2.86° and 3.75° in air, respectively. The Bragg-matched diffractions in (b)–(e) are associated with lattice faces with Miller indices (1, 0), (2, 1), (3, 1) and (4, 1), respectively.

Fig. 3.
Fig. 3.

The fine intensity distribution structure (the bottom image) on the X-Y output surface of an optically induced 2D PLS when one launches a collimated He-Ne laser beam onto the 2D PLS along the Z-coordinate, which indicates the effective waveguide array property of the photonic structure. The top image shows the profile of the amplitude mask on the X-Z plane.

Fig. 4.
Fig. 4.

The intensity distribution images (left column) and the corresponding intensity distribution profiles (right column) on the output X-Y surface of the 2D PLS at different exposure time t when a probe He-Ne laser beam was coupled into one backbone waveguide. The exposure time of the probe beam was t=0 minutes for (a) and (d), t=200 minutes for (b) and (e), and t=530 minutes for (c) and (f), respectively.

Fig. 5.
Fig. 5.

Numerical simulation of the light propagation dynamics in the 2D PLS. Output intensity profiles (top row) and the corresponding beam propagation(bottom row) for different values of the normalized input intensity 0 (a), 0.69 (b) and 1.69 (c), respectively.

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