Abstract

We generate experimentally different types of two-dimensional Bloch waves of a square photonic lattice by employing the phase imprinting technique. We probe the local dispersion of the Bloch modes in the photonic lattice by analyzing the linear diffraction of beams associated with the high-symmetry points of the Brillouin zone, and also distinguish the regimes of normal, anomalous, and anisotropic diffraction through observations of nonlinear self-action effects.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  40. G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95,053904 (2005).
    [CrossRef] [PubMed]

2006

R. Fischer, D. Tr¨ager, D. N. Neshev, A. A. Sukhorukov,W. Kr´olikowski, C. Denz, and Yu. S. Kivshar, "Reducedsymmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96,023905 (2006).
[CrossRef] [PubMed]

M. Stepi´c, C. Wirth, C. R¨uter, and D. Kip, "Experimental observation of modulational instability in selfdefocusing nonlinear waveguide arrays," Opt. Lett. 31,247-249 (2006).
[CrossRef] [PubMed]

2005

R. J. P. Engelen, T. J. Karle, H. Gersen, J. P. Korterik, T. F. Krauss, L. Kuipers, and N. F. Hulst, van, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13,4457-4464 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457.
[CrossRef] [PubMed]

B. Freedman, O. Cohen, O. Manela, M. Segev, J. W. Fleischer, and D. N. Christodoulides, "Grating-mediated wave guiding and holographic solitons," J. Opt. Soc. Am. B 22,1349-1355 (2005).
[CrossRef]

R. Iwanow, G. I. Stegeman, R. Schiek, Y. Min, and W. Sohler, "Discrete modulational instability n periodically poled lithium niobate waveguide arrays," Opt. Express 13,7794-7799 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-20-7794.
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95,053904 (2005).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,1239014 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94,1639024 (2005).
[CrossRef] [PubMed]

2004

A. A. Sukhorukov, D. Neshev,W. Kr´olikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92,0939014 (2004).
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92,163902-4 (2004).
[CrossRef] [PubMed]

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, "Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers," Appl. Phys. Lett. 85,4-6 (2004).
[CrossRef]

H. Martin, E. D. Eugenieva, Z. G. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92,123902 (2004).
[CrossRef] [PubMed]

O. Cohen, B. Freedman, J.W. Fleischer, M. Segev, and D. N. Christodoulides, "Grating-mediated waveguiding," Phys. Rev. Lett. 93,103902 (2004).
[CrossRef] [PubMed]

J. Hudock, N. K. Efremidis and D. N. Christodoulides, "Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays," Opt. Lett. 29,268-270 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh and L. Torner, "Soliton trains in photonic lattices," Opt. Express 12,2831 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-2831.
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29,2049-2051 (2004).
[CrossRef] [PubMed]

2003

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90,0539024 (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 422,147-150 (2003).
[CrossRef] [PubMed]

2002

S. I. Bozhevolnyi, V. S. Volkov, T. Sondergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, "Near-field imaging of light propagation in photonic crystal waveguides: explicit role of Bloch harmonics," Phys. Rev. B 66,2352049 (2002).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88,093901-4 (2002).
[CrossRef] [PubMed]

M. Lon¡car, D. Nedeljković, T. P. Pearsall, J. Vu¡cković, A. Scherer, S. Kuchinsky, and D. C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80,1689-1691 (2002).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,0466025 (2002).
[CrossRef]

2001

S. F. Mingaleev and Yu. S. Kivshar, "Self-trapping and stable localized modes in nonlinear photonic crystals," Phys. Rev. Lett. 86,5474-5477 (2001).
[CrossRef] [PubMed]

2000

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

1998

N. Akozbek and S. John, "Optical solitary waves in two- and three-dimensional nonlinear photonic band-gap structures," Phys. Rev. E 57,2287-2319 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, "Modulational instability and tunable multiple soliton generation in apodized fiber gratings," Opt. Commun. 149,267-271 (1998).
[CrossRef]

C. M. de Sterke, "Theory of modulational instability in fiber Bragg gratings," J. Opt. Soc. Am. B 15,2660-2667 (1998).
[CrossRef]

1997

1993

1991

P. S. Russell, "Bloch wave analysis of dispersion and pulse-propagation in pure distributed feedback structures," J. Mod. Opt. 38,1599-1619 (1991).
[CrossRef]

1988

1987

W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical-response of superlattices," Phys. Rev. Lett. 58,160-163 (1987).
[CrossRef] [PubMed]

1981

Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, "Stationary waves in non-linear, periodically modulated media with higher group retardation," Zh. Tekh. Fiz. 51,902-907 (1981) (in Russian) [English translation: Tech. Phys. 26, 541-544 (1981)].

Aceves, A. B.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, "Modulational instability and tunable multiple soliton generation in apodized fiber gratings," Opt. Commun. 149,267-271 (1998).
[CrossRef]

Aitchison, J. S.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92,163902-4 (2004).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90,0539024 (2003).
[CrossRef] [PubMed]

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

Akozbek, N.

N. Akozbek and S. John, "Optical solitary waves in two- and three-dimensional nonlinear photonic band-gap structures," Phys. Rev. E 57,2287-2319 (1998).
[CrossRef]

S. John and N. Akozbek, "Nonlinear-optical solitary waves in a photonic band-gap," Phys. Rev. Lett. 71,1168-1171 (1993).
[CrossRef] [PubMed]

Barclay, P. E.

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, "Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers," Appl. Phys. Lett. 85,4-6 (2004).
[CrossRef]

Bartal, G.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94,1639024 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95,053904 (2005).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29,2049-2051 (2004).
[CrossRef] [PubMed]

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,1239014 (2005).
[CrossRef] [PubMed]

Boltasseva, A.

S. I. Bozhevolnyi, V. S. Volkov, T. Sondergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, "Near-field imaging of light propagation in photonic crystal waveguides: explicit role of Bloch harmonics," Phys. Rev. B 66,2352049 (2002).
[CrossRef]

Borel, P. I.

S. I. Bozhevolnyi, V. S. Volkov, T. Sondergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, "Near-field imaging of light propagation in photonic crystal waveguides: explicit role of Bloch harmonics," Phys. Rev. B 66,2352049 (2002).
[CrossRef]

Borselli, M.

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, "Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers," Appl. Phys. Lett. 85,4-6 (2004).
[CrossRef]

Botez, D.

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, T. Sondergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, "Near-field imaging of light propagation in photonic crystal waveguides: explicit role of Bloch harmonics," Phys. Rev. B 66,2352049 (2002).
[CrossRef]

Brauer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88,093901-4 (2002).
[CrossRef] [PubMed]

Buljan, H.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94,1639024 (2005).
[CrossRef] [PubMed]

Chen, W.

W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical-response of superlattices," Phys. Rev. Lett. 58,160-163 (1987).
[CrossRef] [PubMed]

Chen, Z. G.

H. Martin, E. D. Eugenieva, Z. G. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92,123902 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

B. Freedman, O. Cohen, O. Manela, M. Segev, J. W. Fleischer, and D. N. Christodoulides, "Grating-mediated wave guiding and holographic solitons," J. Opt. Soc. Am. B 22,1349-1355 (2005).
[CrossRef]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92,163902-4 (2004).
[CrossRef] [PubMed]

O. Cohen, B. Freedman, J.W. Fleischer, M. Segev, and D. N. Christodoulides, "Grating-mediated waveguiding," Phys. Rev. Lett. 93,103902 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. G. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92,123902 (2004).
[CrossRef] [PubMed]

J. Hudock, N. K. Efremidis and D. N. Christodoulides, "Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays," Opt. Lett. 29,268-270 (2004).
[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 422,147-150 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,0466025 (2002).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled wave-guides," Opt. Lett. 13,794-796 (1988).
[CrossRef] [PubMed]

Cohen, O.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94,1639024 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95,053904 (2005).
[CrossRef] [PubMed]

B. Freedman, O. Cohen, O. Manela, M. Segev, J. W. Fleischer, and D. N. Christodoulides, "Grating-mediated wave guiding and holographic solitons," J. Opt. Soc. Am. B 22,1349-1355 (2005).
[CrossRef]

O. Cohen, B. Freedman, J.W. Fleischer, M. Segev, and D. N. Christodoulides, "Grating-mediated waveguiding," Phys. Rev. Lett. 93,103902 (2004).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29,2049-2051 (2004).
[CrossRef] [PubMed]

de Sterke, C. M.

C. M. de Sterke, "Theory of modulational instability in fiber Bragg gratings," J. Opt. Soc. Am. B 15,2660-2667 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, "Modulational instability and tunable multiple soliton generation in apodized fiber gratings," Opt. Commun. 149,267-271 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, "Nonlinear pulse propagation in Bragg gratings," J. Opt. Soc. Am. B 14,2980-2993 (1997).
[CrossRef]

Denz, C.

R. Fischer, D. Tr¨ager, D. N. Neshev, A. A. Sukhorukov,W. Kr´olikowski, C. Denz, and Yu. S. Kivshar, "Reducedsymmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96,023905 (2006).
[CrossRef] [PubMed]

Efremidis, N. K.

J. Hudock, N. K. Efremidis and D. N. Christodoulides, "Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays," Opt. Lett. 29,268-270 (2004).
[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 422,147-150 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,0466025 (2002).
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, "Modulational instability and tunable multiple soliton generation in apodized fiber gratings," Opt. Commun. 149,267-271 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, "Nonlinear pulse propagation in Bragg gratings," J. Opt. Soc. Am. B 14,2980-2993 (1997).
[CrossRef]

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90,0539024 (2003).
[CrossRef] [PubMed]

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

Engelen, R. J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,1239014 (2005).
[CrossRef] [PubMed]

R. J. P. Engelen, T. J. Karle, H. Gersen, J. P. Korterik, T. F. Krauss, L. Kuipers, and N. F. Hulst, van, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13,4457-4464 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457.
[CrossRef] [PubMed]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. G. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92,123902 (2004).
[CrossRef] [PubMed]

Feng, J.

Fischer, R.

R. Fischer, D. Tr¨ager, D. N. Neshev, A. A. Sukhorukov,W. Kr´olikowski, C. Denz, and Yu. S. Kivshar, "Reducedsymmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96,023905 (2006).
[CrossRef] [PubMed]

Fleischer, J. W.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95,053904 (2005).
[CrossRef] [PubMed]

B. Freedman, O. Cohen, O. Manela, M. Segev, J. W. Fleischer, and D. N. Christodoulides, "Grating-mediated wave guiding and holographic solitons," J. Opt. Soc. Am. B 22,1349-1355 (2005).
[CrossRef]

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94,1639024 (2005).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29,2049-2051 (2004).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,0466025 (2002).
[CrossRef]

Fleischer, J.W.

O. Cohen, B. Freedman, J.W. Fleischer, M. Segev, and D. N. Christodoulides, "Grating-mediated waveguiding," Phys. Rev. Lett. 93,103902 (2004).
[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 422,147-150 (2003).
[CrossRef] [PubMed]

Freedman, B.

B. Freedman, O. Cohen, O. Manela, M. Segev, J. W. Fleischer, and D. N. Christodoulides, "Grating-mediated wave guiding and holographic solitons," J. Opt. Soc. Am. B 22,1349-1355 (2005).
[CrossRef]

O. Cohen, B. Freedman, J.W. Fleischer, M. Segev, and D. N. Christodoulides, "Grating-mediated waveguiding," Phys. Rev. Lett. 93,103902 (2004).
[CrossRef] [PubMed]

Gersen, H.

R. J. P. Engelen, T. J. Karle, H. Gersen, J. P. Korterik, T. F. Krauss, L. Kuipers, and N. F. Hulst, van, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13,4457-4464 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457.
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,1239014 (2005).
[CrossRef] [PubMed]

Hudock, J.

Hulst, N. F.

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,1239014 (2005).
[CrossRef] [PubMed]

R. J. P. Engelen, T. J. Karle, H. Gersen, J. P. Korterik, T. F. Krauss, L. Kuipers, and N. F. Hulst, van, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13,4457-4464 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457.
[CrossRef] [PubMed]

Iwanow, R.

John, S.

N. Akozbek and S. John, "Optical solitary waves in two- and three-dimensional nonlinear photonic band-gap structures," Phys. Rev. E 57,2287-2319 (1998).
[CrossRef]

S. John and N. Akozbek, "Nonlinear-optical solitary waves in a photonic band-gap," Phys. Rev. Lett. 71,1168-1171 (1993).
[CrossRef] [PubMed]

Joseph, R. I.

Karle, T. J.

R. J. P. Engelen, T. J. Karle, H. Gersen, J. P. Korterik, T. F. Krauss, L. Kuipers, and N. F. Hulst, van, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13,4457-4464 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457.
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,1239014 (2005).
[CrossRef] [PubMed]

Kartashov, Y. V.

Kip, D.

Kivshar, Yu. S.

R. Fischer, D. Tr¨ager, D. N. Neshev, A. A. Sukhorukov,W. Kr´olikowski, C. Denz, and Yu. S. Kivshar, "Reducedsymmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96,023905 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. Neshev,W. Kr´olikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92,0939014 (2004).
[CrossRef] [PubMed]

S. F. Mingaleev and Yu. S. Kivshar, "Self-trapping and stable localized modes in nonlinear photonic crystals," Phys. Rev. Lett. 86,5474-5477 (2001).
[CrossRef] [PubMed]

Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen,W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94,1239014 (2005).
[CrossRef] [PubMed]

R. J. P. Engelen, T. J. Karle, H. Gersen, J. P. Korterik, T. F. Krauss, L. Kuipers, and N. F. Hulst, van, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13,4457-4464 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457.
[CrossRef] [PubMed]

Kr´olikowski, W.

R. Fischer, D. Tr¨ager, D. N. Neshev, A. A. Sukhorukov,W. Kr´olikowski, C. Denz, and Yu. S. Kivshar, "Reducedsymmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96,023905 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. Neshev,W. Kr´olikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92,0939014 (2004).
[CrossRef] [PubMed]

Krauss, T. F.

Kristensen, M.

S. I. Bozhevolnyi, V. S. Volkov, T. Sondergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, "Near-field imaging of light propagation in photonic crystal waveguides: explicit role of Bloch harmonics," Phys. Rev. B 66,2352049 (2002).
[CrossRef]

Kuipers, L.

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88,093901-4 (2002).
[CrossRef] [PubMed]

Mandelik, D.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90,0539024 (2003).
[CrossRef] [PubMed]

Manela, O.

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95,053904 (2005).
[CrossRef] [PubMed]

B. Freedman, O. Cohen, O. Manela, M. Segev, J. W. Fleischer, and D. N. Christodoulides, "Grating-mediated wave guiding and holographic solitons," J. Opt. Soc. Am. B 22,1349-1355 (2005).
[CrossRef]

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94,1639024 (2005).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29,2049-2051 (2004).
[CrossRef] [PubMed]

Martin, H.

H. Martin, E. D. Eugenieva, Z. G. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92,123902 (2004).
[CrossRef] [PubMed]

Meier, J.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92,163902-4 (2004).
[CrossRef] [PubMed]

Mills, D. L.

W. Chen and D. L. Mills, "Gap solitons and the nonlinear optical-response of superlattices," Phys. Rev. Lett. 58,160-163 (1987).
[CrossRef] [PubMed]

Min, Y.

Mingaleev, S. F.

S. F. Mingaleev and Yu. S. Kivshar, "Self-trapping and stable localized modes in nonlinear photonic crystals," Phys. Rev. Lett. 86,5474-5477 (2001).
[CrossRef] [PubMed]

Morandotti, R.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92,163902-4 (2004).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90,0539024 (2003).
[CrossRef] [PubMed]

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

Nabiev, R. F.

Neshev, D.

A. A. Sukhorukov, D. Neshev,W. Kr´olikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92,0939014 (2004).
[CrossRef] [PubMed]

Neshev, D. N.

R. Fischer, D. Tr¨ager, D. N. Neshev, A. A. Sukhorukov,W. Kr´olikowski, C. Denz, and Yu. S. Kivshar, "Reducedsymmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96,023905 (2006).
[CrossRef] [PubMed]

Painter, O.

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, "Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers," Appl. Phys. Lett. 85,4-6 (2004).
[CrossRef]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88,093901-4 (2002).
[CrossRef] [PubMed]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88,093901-4 (2002).
[CrossRef] [PubMed]

R¨uter, C.

Russell, P. S.

P. S. Russell, "Bloch wave analysis of dispersion and pulse-propagation in pure distributed feedback structures," J. Mod. Opt. 38,1599-1619 (1991).
[CrossRef]

Ryzhov, Yu. N.

Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, "Stationary waves in non-linear, periodically modulated media with higher group retardation," Zh. Tekh. Fiz. 51,902-907 (1981) (in Russian) [English translation: Tech. Phys. 26, 541-544 (1981)].

Salamo, G.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92,163902-4 (2004).
[CrossRef] [PubMed]

Schiek, R.

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,0466025 (2002).
[CrossRef]

Segev, M.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94,1639024 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95,053904 (2005).
[CrossRef] [PubMed]

B. Freedman, O. Cohen, O. Manela, M. Segev, J. W. Fleischer, and D. N. Christodoulides, "Grating-mediated wave guiding and holographic solitons," J. Opt. Soc. Am. B 22,1349-1355 (2005).
[CrossRef]

O. Cohen, B. Freedman, J.W. Fleischer, M. Segev, and D. N. Christodoulides, "Grating-mediated waveguiding," Phys. Rev. Lett. 93,103902 (2004).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29,2049-2051 (2004).
[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 422,147-150 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66,0466025 (2002).
[CrossRef]

Silberberg, Y.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92,163902-4 (2004).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90,0539024 (2003).
[CrossRef] [PubMed]

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

Sipe, J. E.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, "Modulational instability and tunable multiple soliton generation in apodized fiber gratings," Opt. Commun. 149,267-271 (1998).
[CrossRef]

Slusher, R. E.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, "Modulational instability and tunable multiple soliton generation in apodized fiber gratings," Opt. Commun. 149,267-271 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, "Nonlinear pulse propagation in Bragg gratings," J. Opt. Soc. Am. B 14,2980-2993 (1997).
[CrossRef]

Sohler, W.

Sondergaard, T.

S. I. Bozhevolnyi, V. S. Volkov, T. Sondergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, "Near-field imaging of light propagation in photonic crystal waveguides: explicit role of Bloch harmonics," Phys. Rev. B 66,2352049 (2002).
[CrossRef]

Sorel, M.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92,163902-4 (2004).
[CrossRef] [PubMed]

Sotin, V. E.

Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, "Stationary waves in non-linear, periodically modulated media with higher group retardation," Zh. Tekh. Fiz. 51,902-907 (1981) (in Russian) [English translation: Tech. Phys. 26, 541-544 (1981)].

Srinivasan, K.

P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, "Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers," Appl. Phys. Lett. 85,4-6 (2004).
[CrossRef]

Stegeman, G. I.

R. Iwanow, G. I. Stegeman, R. Schiek, Y. Min, and W. Sohler, "Discrete modulational instability n periodically poled lithium niobate waveguide arrays," Opt. Express 13,7794-7799 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-20-7794.
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92,163902-4 (2004).
[CrossRef] [PubMed]

Stepi´c, M.

Strasser, T. A.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, "Modulational instability and tunable multiple soliton generation in apodized fiber gratings," Opt. Commun. 149,267-271 (1998).
[CrossRef]

Sukhorukov, A. A.

R. Fischer, D. Tr¨ager, D. N. Neshev, A. A. Sukhorukov,W. Kr´olikowski, C. Denz, and Yu. S. Kivshar, "Reducedsymmetry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96,023905 (2006).
[CrossRef] [PubMed]

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S. I. Bozhevolnyi, V. S. Volkov, T. Sondergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, "Near-field imaging of light propagation in photonic crystal waveguides: explicit role of Bloch harmonics," Phys. Rev. B 66,2352049 (2002).
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[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92,163902-4 (2004).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1.
Fig. 1.

(a) Experimental image of a two-dimensional optically-induced photonic lattice, that is spatially periodic in the transverse directions (x,y) and stationary along the longitudinal direction z. (b) Calculated bandgap dispersion β(K). Dots indicate the main symmetry points. Inset in (b) depicts the corresponding first Brillouin zone.

Fig. 2.
Fig. 2.

Intensity (top) and phase (bottom) of different Bloch modes from the high symmetry points of the first and second band of a square lattice. The blue color for the phase distribution corresponds to the zero phase, while the red color corresponds to the π phase.

Fig. 3.
Fig. 3.

Experimental setup for the excitation of two-dimensional Bloch modes: HV: High voltage, CCD: camera, FF: Fourier filter mask, λ/2: half wave plate; PPM: Programmable phase modulator, DOE: Diffractive optical element to produce four coherent beams, PBS: Polarizing beam splitter. Left inset: Geometry of the two-dimensional optical lattice. Right inset: Example of a phase and amplitude engineered wave in the optical lattice.

Fig. 4.
Fig. 4.

Experimental data (top row) and numerical results (bottom) for the excitation of the two-dimensional Bloch waves from the Γ point of the first spectral band (Γ1). (a) Input beam; (b-e) outputs for input powers of 25nW, 125 nW, 250 nW, and 375 nW, respectively.

Fig. 5.
Fig. 5.

Experimental data (top row) and numerical results (bottom) for the excitation of the two-dimensional Bloch waves from the X point of the first spectral band (X1). (a) Input beam; (b,c) outputs for input powers of 25nW and 375 nW, respectively.

Fig. 6.
Fig. 6.

Experimental data (top row) and numerical results (bottom) for the excitation of the two-dimensional Bloch waves from the M point of the first spectral band (M1). (a) Input beam; (b-e) outputs for input powers of 40nW, 125nW, 300nW, and 850nW, respectively.

Fig. 7.
Fig. 7.

Experimental data (top row) and numerical results (bottom) for the excitation of the two-dimensional Bloch waves from the X point of the second spectral band (X2). (a) Input beam; (b-e) outputs for input powers of 20nW, 50nW, 100nW, and 200nW, respectively.

Fig. 8.
Fig. 8.

Experimental data (top row) and numerical results (bottom) for the excitation of the two-dimensional Bloch waves from the M point of the second spectral band (M2). (a) Input beam; (b-e) outputs for input powers of 25nW, 90nW, 270nW, and 660nW, respectively.

Equations (9)

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

I p x y = I g { cos [ π ( x + y ) d ] + cos [ π ( x y ) d ] } 2 ,
i E z + D ( 2 E x 2 + 2 E y 2 ) + x y E 2 E = 0 ,
x y E 2 = γ I b + I p x y + E 2
E x y z = ψ x y exp ( iβz + i K x x + i K y y ) ,
E x y = A exp ( x 2 w x 2 y 2 w y 2 ) ,
E x y = A cos ( Kx ) exp ( x 2 w x 2 y 2 w y 2 ) ,
E x y = A cos ( Kx ) cos ( Ky ) exp ( x 2 w x 2 y 2 w y 2 ) ,
E x y = A cos [ K ( x d 2 ) ] exp ( x 2 w x 2 y 2 w y 2 ) ,
E x y = A cos ( Kx + Ky ) exp ( x 2 w x 2 y 2 w y 2 ) ,

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