Abstract

The recent proposal of optical induction for producing nonlinear photonic lattices has revolutionized the study of nonlinear waves in waveguide arrays. In particular, it enabled the first observation of (2+1) dimensional lattice solitons, which were the first 2D solitons observed in any nonlinear periodic system in nature. Since then, progress has been rapid, with many fundamental discoveries made within the past two years. Here, we review our theoretical and experimental contributions to this effort.

© 2005 Optical Society of America

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2005 (1)

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433, 500 (2005).
[CrossRef] [PubMed]

2004 (21)

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

R. Iwanow, R. Schiek, G.I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,” Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

T.J. Alexander, A.A. Sukhorukov, and Y.S. Kivshar, “Asymmetric vortex solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

P.G. Kevrekidis, B.A. Malomed, Z.G. Chen, and D.J. Frantzeskakis, “Stable higher-order vortices and quasivortices in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 70, 056612 (2004).
[CrossRef]

A.A. Sukhorukov, D. Neshev, W. Krolikowski, and Y.S. Kivshar, “Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,” Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

D. Mandelik, R. Morandotti, J.S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

D. Neshev, A.A. Sukhorukov, B. Hanna, W. Krolikowski, and Y.S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

J. Meier, G.I. Stegeman, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Nonlinear optical beam interactions in waveguide arrays,” Phys. Rev. Lett. 93, 093903 (2004).
[CrossRef] [PubMed]

H. Buljan, O. Cohen, J.W. Fleischer, T. Schwartz, M. Segev, Z.H. Musslimani, N.K. Efremidis, and D.N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef] [PubMed]

T. Pertsch, U. Peshchl, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

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

H.J. Shin, “Solutions for solitons in nonlinear optically induced lattices,” Phys. Rev. E 69, 067602 (2004).
[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 (2004).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. App. Math. 113, 389 (2004).
[CrossRef]

J.W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D.N. Christodoulides, “Observation of vortex-ring ‘discrete’ solitons in 2D photonic lattices,” Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

D.N. Neshev, T.J. Alexander, E.A. Ostrovskaya, Y.S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,” Opt. Lett. 29, 468 (2004).
[CrossRef] [PubMed]

A. Fratalocchi, G. Assanto, K.A. Brzdakiewicz, and M.A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett. 29, 1530 (2004).
[CrossRef] [PubMed]

Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29, 1656 (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 (2004).
[CrossRef] [PubMed]

R. Morandotti, D. Mandelik, Y. Silberberg, J.S. Aitchison, M. Sorel, D. Christodoulides, A.A. Sukhorukov, and Y.S. Kivshar, “Observation of discrete gap solitons in binary waveguide arrays,” Opt. Lett. 29, 2890 (2004).
[CrossRef]

2003 (17)

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, 053902 (2003).
[CrossRef] [PubMed]

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays,” Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Kartashov YV, Aleshkevich VA, Vysloukh VA, Egorov AA, and Zelenina AS, “Stability analysis of (1+1)- dimensional cnoidal waves in media with cubic nonlinearity” Phys. Rev. E 67, 036613 (2003).
[CrossRef]

A.S. Desyatnikov, E.A. Ostrovskaya, Y.S. Kivshar, and C. Denz, “Composite Band-Gap Solitons in Nonlinear Optically Induced Lattices,” Phys. Rev. Lett. 91, 153902 (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 (2003).
[CrossRef] [PubMed]

D.N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behavior in linear and nonlinear waveguide lattices,” Nature 424, 817 (2003).
[CrossRef] [PubMed]

P. Russell, “Photonic crystal fibers,” Science 299, 358 (2003).
[CrossRef] [PubMed]

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]

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]

N.K. Efremidis, J. Hudock, D.N. Christodoulides, J.W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

J. Petter, J. Schröder, D. Träger, and C. Denz, “Optical control of arrays of photorefractive screening solitons,” Opt. Lett. 28, 438 (2003).
[CrossRef] [PubMed]

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

R. Morandotti, H.S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C.R. Stanley, and J.S. Aitchison, “Interactions of discrete solitons with structural defects,” Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

E.J. Bochove, P.K. Cheo, and G.G. King, “Self-organization in a multicore fiber laser array,” Opt. Lett. 28, 1200 (2003).
[CrossRef] [PubMed]

J. Yang and Z.H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28, 2094 (2003).
[CrossRef] [PubMed]

D. Mandelik, H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90, 253902 (2003).
[CrossRef] [PubMed]

2002 (2)

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, 046602 (2002).
[CrossRef]

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, “Holographic solitons,” Opt. Lett. 27, 2031 (2002).
[CrossRef]

2001 (10)

M.J. Ablowitz and Z.H. Musslimani, “Discrete diffraction managed spatial solitons,” Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

F.S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science 293, 843 (2001).
[CrossRef] [PubMed]

M. Klotz, M. Crosser, A. Guo, M. Henry, G.J. Salamo, M. Segev, and G.L. Wood, “Fixing solitonic Y-junctions in photorefractive strontium barium niobate,” App. Phys. Lett. 79, 1423 (2001).
[CrossRef]

D.N. Christodoulides and E.D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef] [PubMed]

B.A. Malomed and P.G. Kevrekidis, “Discrete vortex solitons,” Phys. Rev. E 64, 026601 (2001).
[CrossRef]

C. Anastassiou, C. Pigier, M. Segev, D. Kip, E.D. Eugenieva, and D.N. Christodoulides, “Self-trapping of bright rings,” Opt. Lett. 26, 911 (2001).
[CrossRef]

A. Guo, M. Henry, G.J. Salamo, M. Segev, and G.L. Wood, “Fixing multiple waveguides induced by photorefractive solitons: directional couplers and beam splitters,” Opt. Lett. 26, 1274 (2001).
[CrossRef]

A. Bramati, W. Chinaglia, S. Minardi, and P. Di Trapani, “Reconstruction of blurred images by controlled formation of spatial solitons,” Opt. Lett. 26, 1409 (2001).
[CrossRef]

E.D. Eugenieva, N.K. Efremidis, and D.N. Christodoulides, “Design of switching junctions in two-dimensional discrete soliton networks,” Opt. Lett. 26, 1978 (2001).
[CrossRef]

2000 (1)

H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

1999 (5)

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J.S. Aitchison, H.S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optics Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

M. Klotz, H. Meng, G. Salamo, M. Segev, and S. R. Montgomery, “Fixing the photorefractive soliton,” Opt. Lett. 24, 77 (1999).
[CrossRef]

S. Lan, E. DelRe, Z. Chen, M. Shih, and M. Segev, “Directional coupler with soliton-induced waveguides,” Opt. Lett. 24, 475 (1999).
[CrossRef]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518 (1999).
[CrossRef] [PubMed]

1998 (4)

S. Darmanyan, A. Kobyakov, and F. Lederer, “Stability of strongly localized excitations in discrete media with cubic nonlinearity,” JETP 86, 682 (1998).
[CrossRef]

Y.S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81 (1998).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Strongly localized vectorial modes in nonlinear waveguide arrays,” Phys. Rev. E 57, 3520 (1998).
[CrossRef]

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

1997 (1)

1996 (2)

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

B.J. Eggleton, R.E. Slusher, C.M. deSterke, P.A. Krug, and J.E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

1995 (1)

D.N. Christodoulides and M.I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am B 12, 1628 (1995).
[CrossRef]

1994 (1)

M. Segev, G.C. Valley, B. Crosignani, P.D. Porto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

1993 (2)

1990 (1)

J.B. Page, “Asymptotic solutions for localized vibrational modes in strongly anharmonic periodic systems,” Phys. Rev. B 41, 7835 (1990).
[CrossRef]

1989 (2)

D.N. Christodoulides and R.I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746 (1989);
[CrossRef] [PubMed]

A.B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37 (1989).
[CrossRef]

1988 (3)

1987 (2)

E. Yablonovich, “Inhibited spontaneous emission in solid-state and electronics,” Phys. Rev. Lett. 58, 2059 (1987).
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W. Chen and D.L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160 (1987);
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1986 (1)

P. St. J. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B 39, 231 (1986).
[CrossRef]

1974 (1)

S.V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248 (1974).

1973 (1)

S. Somekh, E. Garmire, A. Yariv, H.L. Garvin, and R.G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46 (1973).
[CrossRef]

1965 (1)

AA, Egorov

Kartashov YV, Aleshkevich VA, Vysloukh VA, Egorov AA, and Zelenina AS, “Stability analysis of (1+1)- dimensional cnoidal waves in media with cubic nonlinearity” Phys. Rev. E 67, 036613 (2003).
[CrossRef]

Ablowitz, M.J.

M.J. Ablowitz and Z.H. Musslimani, “Discrete diffraction managed spatial solitons,” Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

Aceves, A.B.

A.B. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37 (1989).
[CrossRef]

Aitchison, J.S.

D. Mandelik, R. Morandotti, J.S. Aitchison, and Y. Silberberg, “Gap solitons in waveguide arrays,” Phys. Rev. Lett. 92, 093904 (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 (2004).
[CrossRef] [PubMed]

J. Meier, G.I. Stegeman, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Nonlinear optical beam interactions in waveguide arrays,” Phys. Rev. Lett. 93, 093903 (2004).
[CrossRef] [PubMed]

R. Morandotti, D. Mandelik, Y. Silberberg, J.S. Aitchison, M. Sorel, D. Christodoulides, A.A. Sukhorukov, and Y.S. Kivshar, “Observation of discrete gap solitons in binary waveguide arrays,” Opt. Lett. 29, 2890 (2004).
[CrossRef]

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, 053902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H.S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C.R. Stanley, and J.S. Aitchison, “Interactions of discrete solitons with structural defects,” Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays,” Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

D. Mandelik, H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Observation of mutually trapped multiband optical breathers in waveguide arrays,” Phys. Rev. Lett. 90, 253902 (2003).
[CrossRef] [PubMed]

R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Diffraction Management,” Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J.S. Aitchison, H.S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optics Bloch oscillations,” Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

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

P. Millar, J.S. Aitchison, J.U. Kang, G.I. Stegeman, A. Villeneuve, G.T. Kennedy, and W. Sibbett, “Nonlinear waveguide arrays in AlGaAs,” J. Opt. Soc. Am. B 14, 3224 (1997).
[CrossRef]

Alexander, T.J.

T.J. Alexander, A.A. Sukhorukov, and Y.S. Kivshar, “Asymmetric vortex solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

D.N. Neshev, T.J. Alexander, E.A. Ostrovskaya, Y.S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Anastassiou, C.

AS, Zelenina

Kartashov YV, Aleshkevich VA, Vysloukh VA, Egorov AA, and Zelenina AS, “Stability analysis of (1+1)- dimensional cnoidal waves in media with cubic nonlinearity” Phys. Rev. E 67, 036613 (2003).
[CrossRef]

Assanto, G.

Bartal, G.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433, 500 (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 (2004).
[CrossRef] [PubMed]

J.W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D.N. Christodoulides, “Observation of vortex-ring ‘discrete’ solitons in 2D photonic lattices,” Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J.W. Fleischer, and M. Segev, “Observation of 2nd-band vortex solitons in 2D photonic lattices,” submitted to Phys. Rev. Lett..

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” submitted to Phys. Rev. Lett.

Bartelt, H.

T. Pertsch, U. Peshchl, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Bezryadina, A.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. App. Math. 113, 389 (2004).
[CrossRef]

Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29, 1656 (2004).
[CrossRef] [PubMed]

Bochove, E.J.

Boyd, A.R.

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

Bramati, A.

Brauer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Brzdakiewicz, K.A.

Buljan, H.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433, 500 (2005).
[CrossRef] [PubMed]

H. Buljan, O. Cohen, J.W. Fleischer, T. Schwartz, M. Segev, Z.H. Musslimani, N.K. Efremidis, and D.N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef] [PubMed]

H. Buljan, M. Segev, and A. Vardi, “Incoherent matter wave solitons: mutual self-trapping of a Bose-Einstein condensate and its surrounding thermal cloud,” submitted to Phys. Rev. Lett.

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” submitted to Phys. Rev. Lett.

Burger, S.

F.S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science 293, 843 (2001).
[CrossRef] [PubMed]

Burghoff, J.

Carmon, T.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433, 500 (2005).
[CrossRef] [PubMed]

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]

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, “Holographic solitons,” Opt. Lett. 27, 2031 (2002).
[CrossRef]

Carvalho, M.I.

D.N. Christodoulides and M.I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am B 12, 1628 (1995).
[CrossRef]

Cataliotti, F.S.

F.S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science 293, 843 (2001).
[CrossRef] [PubMed]

Chen, W.

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

Chen, Z.

Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29, 1656 (2004).
[CrossRef] [PubMed]

H. Martin, E.D. Eugenieva, Z. 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. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, “Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,” Stud. App. Math. 113, 389 (2004).
[CrossRef]

D.N. Neshev, T.J. Alexander, E.A. Ostrovskaya, Y.S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of discrete vortex solitons in optically induced photonic lattices,” Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

S. Lan, E. DelRe, Z. Chen, M. Shih, and M. Segev, “Directional coupler with soliton-induced waveguides,” Opt. Lett. 24, 475 (1999).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

Chen, Z.G.

P.G. Kevrekidis, B.A. Malomed, Z.G. Chen, and D.J. Frantzeskakis, “Stable higher-order vortices and quasivortices in the discrete nonlinear Schrödinger equation,” Phys. Rev. E 70, 056612 (2004).
[CrossRef]

Cheo, P.K.

Chinaglia, W.

Christodoulides, D.

R. Morandotti, D. Mandelik, Y. Silberberg, J.S. Aitchison, M. Sorel, D. Christodoulides, A.A. Sukhorukov, and Y.S. Kivshar, “Observation of discrete gap solitons in binary waveguide arrays,” Opt. Lett. 29, 2890 (2004).
[CrossRef]

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J.S. Aitchison, “Discrete vector solitons in Kerr nonlinear waveguide arrays,” Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef] [PubMed]

Christodoulides, D.N.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433, 500 (2005).
[CrossRef] [PubMed]

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

H. Buljan, O. Cohen, J.W. Fleischer, T. Schwartz, M. Segev, Z.H. Musslimani, N.K. Efremidis, and D.N. Christodoulides, “Random-phase solitons in nonlinear periodic lattices,” Phys. Rev. Lett. 92, 223901 (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 (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.W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D.N. Christodoulides, “Observation of vortex-ring ‘discrete’ solitons in 2D photonic lattices,” Phys. Rev. Lett. 92, 123904 (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 (2003).
[CrossRef] [PubMed]

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 424, 817 (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]

N.K. Efremidis, J. Hudock, D.N. Christodoulides, J.W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (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, 046602 (2002).
[CrossRef]

C. Anastassiou, C. Pigier, M. Segev, D. Kip, E.D. Eugenieva, and D.N. Christodoulides, “Self-trapping of bright rings,” Opt. Lett. 26, 911 (2001).
[CrossRef]

D.N. Christodoulides and E.D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef] [PubMed]

E.D. Eugenieva, N.K. Efremidis, and D.N. Christodoulides, “Design of switching junctions in two-dimensional discrete soliton networks,” Opt. Lett. 26, 1978 (2001).
[CrossRef]

D.N. Christodoulides and M.I. Carvalho, “Bright, dark, and gray spatial soliton states in photorefractive media,” J. Opt. Soc. Am B 12, 1628 (1995).
[CrossRef]

D.N. Christodoulides and R.I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746 (1989);
[CrossRef] [PubMed]

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

B. Freedman, O. Cohen, O. Manela, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Grating-mediated waveguiding and holographic solitons,” J. Opt. Soc. Am. B (to be published).

Cohen, O.

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Observation of random-phase lattice solitons,” Nature 433, 500 (2005).
[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]

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

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D. Neshev, A.A. Sukhorukov, B. Hanna, W. Krolikowski, and Y.S. Kivshar, “Controlled generation and steering of spatial gap solitons,” Phys. Rev. Lett. 93, 083905 (2004).
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Other (6)

G. Bartal, O. Manela, O. Cohen, J.W. Fleischer, and M. Segev, “Observation of 2nd-band vortex solitons in 2D photonic lattices,” submitted to Phys. Rev. Lett..

B. Freedman, O. Cohen, O. Manela, J.W. Fleischer, M. Segev, and D.N. Christodoulides, “Grating-mediated waveguiding and holographic solitons,” J. Opt. Soc. Am. B (to be published).

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, and M. Segev, “Brillouin zone spectroscopy of nonlinear photonic lattices,” submitted to Phys. Rev. Lett.

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Figures (9)

Fig. 1.
Fig. 1.

Linear band structure and diffraction properties of a 1D waveguide array. (a) Transmission spectrum consisting of bands of allowed propagation constants separated by forbidden gaps. (b) Modes in convex regions experience normal diffraction. (c) Modes in concave regions experience anomalous diffraction.

Fig. 2.
Fig. 2.

1D discrete or lattice solitons from the first band (a) 1D transmission spectrum showing the nonlinear propagation constants for the fundamental LS (base of the BZ zone) and spatial gap soliton (edge of BZ zone). (b) The fundamental LS has an in-phase structure that requires a self-focusing nonlinearity (positive defect). (c) The first-band gap soliton has a staggered phase structure that requires a defocusing nonlinearity (negative defect).

Fig. 3.
Fig. 3.

Band structure and optical induction of a square waveguide array. (a,b) Band structure of a 2D square lattice, with high-symmetry points labeled in (b). (c) Interference of four plane waves to optically induce a 2D square array of 2D waveguides. (d) Photograph of a typical output face, showing a lattice with an 11µm period.

Fig. 4.
Fig. 4.

Principles of grating-mediated waveguiding. (a) Type-I guide, with a bell-shaped y-profile. (b) Type-II guide, with a trough-shaped y-profile. (c) Index grating with three different amplitudes, corresponding to three different y-planes. (d) The dispersion/diffraction curves near the edge of the first Brillouin zone for gratings with index profile n(x,y)=n 0[1+εA(y)cos(πx/D)]. (e,f) Typical index amplitudes A(y) of (e) Type-I gratings and (f) Type-II gratings. (g) The effective waveguide structure in y: Type-I beams need a cos(πx/D) dependence and Type-II beams need a sin(πx/D) dependence to experience grating-mediated waveguiding. Taken from [60].

Fig. 5.
Fig. 5.

Experimental scheme and resutls of a Type-II (trough-shaped) grating-mediated waveguide. (a) Schematic of optical induction of waveguide. (b) Photograph of input beam. (c) Waveguiding when position and phase of (b) match with grating structure. (d–f) Diffraction in unguided conditions: (d) Free-space diffraction of (b) in absence of waveguide. (e) Diffraction when the input is not Bragg-matched with the grating. (f) Diffraction when the input (b) is Bragg-matched but has the “wrong” phase relative to the grating. In (b–f), the intensity in each figure is normalized to its own peak intensity. Taken from [60].

Fig. 6.
Fig. 6.

Experimental observation of discrete diffraction and solitons in 1D optically-induced waveguide arrays. (a–c) Propagation for an on-axis input probe. Discrete diffraction (a) in the linear regime. Soliton intensity (b) and relative phase (c) in the nonlinear regime (+1.6kV/cm). The phase information (c) is obtained by interfering the output signal (b) with a plane wave. (d–f) Propagation at the Bragg angle, corresponding to the edge of the first Brillouin zone. Discrete diffraction (d) in the linear regime. Soliton intensity (e) and relative phase (f) in the nonlinear regime (-2.0kV/cm). Note that the central peak experiences destructive interference, while the surrounding lobes experience constructive interference. Note also the need for defocusing nonlinearity (negative voltage) to create the 1D gap soliton (e). Taken from [14].

Fig. 7.
Fig. 7.

Experimental observation of discrete diffraction and solitons in 2D optically-induced waveguide arrays. (a–c) Propagation for an on-axis input probe. Discrete diffraction (a) in the linear regime. Soliton intensity (b) and relative phase (c) in the nonlinear regime (+1.6kV/cm). The phase information (c) is obtained by interfering the output signal (b) with a plane wave. (d–f) Propagation at the Bragg angle, corresponding to the corner of the first Brillouin zone (M-point in Fig. 4c). Discrete diffraction (d) in the linear regime. Soliton intensity (e) and relative phase (f) in the nonlinear regime (-1.6kV/cm). Note that the central peak experiences destructive interference, while the surrounding lobes experience constructive interference. Note also the need for defocusing nonlinearity (negative voltage) to create the 2D gap soliton (e). Taken from [26].

Fig. 8.
Fig. 8.

Experimental observation of discrete vortex solitons in 2D optically-induced waveguide arrays. (a) Discrete diffraction and (b) spiral phase structure (formed by interfering the output (a) with a plane wave) in the linear regime. (b) Soliton intensity and (c) relative phase in the nonlinear regime (+1.6kV/cm) for a vortex with its singularity centered on-site. (d) Soliton intensity and (e) relative phase in the nonlinear regime (+1.6kV/cm) for a vortex with its singularity centered in-between sites. The vortex solitons keep their relative phase, despite the fact that the conservation of angular momentum (topological charge) is not guaranteed in a lattice. Taken from [56].

Fig. 9.
Fig. 9.

Theoretical characterization of random-phase lattice soliton (RPLS). (a) Modes are taken statistically from regions of the transmission spectrum with the same band curvature. (b,c) Power spectrum in the (b) Fouier basis and (c) Floquet-Bloch basis. Note the sharp cut-offs in (c), implying that the F-B representation is more appropriate for lattice modes. (d,e) Statistical properties of RPLS. The blue lines indicate the centers of each waveguide in the 1D array. (d) Mutual coherence/correlation function centered on the central waveguide. (e) Soliton profile in black and correlation length in red. (f) Modal structure as given by waveguide theory. See text for its relation to the correlation behavior in (e). Taken from [82].

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