Abstract

We present both experimental and theoretical results on discrete solitons in two-dimensional optically-induced photonic lattices in a variety of settings, including fundamental discrete solitons, vector-like discrete solitons, discrete dipole solitons, and discrete soliton trains. In each case, a clear transition from two-dimensional discrete diffraction to discrete trapping is demonstrated with a waveguide lattice induced by partially coherent light in a bulk photorefractive crystal. Our experimental results are in good agreement with the theoretical analysis of these effects.

© 2005 Optical Society of America

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References

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J. Opt. Soc. Am. B

Z, Chen, H. Martin, A. Bezryadina, D.N. Neshev, Y.S. Kivshar, and D.N. Christodoulides, "Experiments on Gaussian beams and vortices in optically-induced photonic lattices,�?? J. Opt. Soc. Am. B, to appear 2005.
[CrossRef]

J. Phys. A

P.G. Kevrekidis, B.A. Malomed, A.R. Bishop, �??Bound states of two-dimensional solitons in the discrete nonlinear Schrodinger equation.�?? J. Phys. A 34, 9615 (2001).
[CrossRef]

Nature

D.N. Christodoulides, F. Lederer and Y. Siberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices,�?? Nature 424, 817 (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]

Opt. Commun.

S.R. Singh and D.N. Christodoulides, �??Evolution of spatial optical solitons in biased photorefractive media under steady state conditions,�?? Opt. Commun. 118, 569 (1995).
[CrossRef]

Opt. Lett.

Phys. Rev. E

A.A. Sukhorukov and Y.S. Kivshar, "Spatial optical solitons in nonlinear photonic crystals,�?? Phys. Rev. E 65, 036609 (2002).
[CrossRef]

M.J. Ablowitz and Z.H. Musslimani, "Discrete vector spatial solitons in a nonlinear waveguide array,�?? Phys. Rev. E 65, 056618 (2002).
[CrossRef]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics,�?? Phys. Rev. E 67, 056618 (2003).
[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, 046602 (2002).
[CrossRef]

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

Phys. Rev. E.

P. G. Kevrekidis, A.R. Bishop, and K. Rasmussen, "Twisted localized modes,�?? Phys. Rev. E 63, 036603 (2001).
[CrossRef]

Phys. Rev. Lett.

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. Meier, J. Hudock, D.N. 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]

J. Yang, I. Makasyuk, H. Martin, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, and Z. Chen, "Necklace-like solitons in optically induced photonic lattices,�?? Phys. Rev. Lett, submitted.

A. Smerzi, A. Trombettoni, P. G. Kevrekidis and A. R. Bishop, Dynamical superfluid-insulator transition in a chain of weakly coupled Bose-Einstein condensates,�?? Phys. Rev. Lett. 89, 170402 (2002).
[CrossRef] [PubMed]

D. N. Christodoulides, T. Coskun, M. Mitchell and M. Segev, "Theory of incoherent self-focusing in biased photorefractive media,�?? Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

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

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

M. Soljacic, M, Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, "Modulation instability of incoherent beams in noninstantaneous nonlinear media,�?? Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

H.S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays,�?? Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

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. 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]

Z. Chen, H. Martin, E.D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains,�?? Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Phys. Today

D. Campbell, S. Flach and Y.S. Kivshar, 'Localizing energy through nonlinearity and discreteness,�?? Phys. Today, 57, 43 (2004).
[CrossRef]

Stud. Appl. Math.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole and Quadrupole Solitons in Optically-induced Two-dimensional Photonic Lattices: Theory and Experiment,�?? Stud. Appl. Math. 113, 389 (2004).
[CrossRef]

Supplementary Material (3)

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Figures (9)

Fig. 1.
Fig. 1.

Experimental setup. PBS: polarizing beam splitter; PZT: piezo-transducer; SBN: strantium barium niobate. The right insert shows a photonic lattice created by optical induction.

Fig. 2.
Fig. 2.

Experimental demonstration of a discrete soliton in a partially coherent lattice. (a) Input, (b) diffraction output without the lattice, (c) discrete diffraction at 900 V/cm, and (d) discrete soliton at 3000 V/cm. Top: 3D intensity plots; Bottom: 2D transverse patterns. Animation of the experimentally observed process can be viewed in the multimedia file. [Media 1]

Fig. 3.
Fig. 3.

Numerical results corresponding to Fig. 1(c–d). Inserts are 2D transverse patterns.

Fig. 4.
Fig. 4.

Output intensity patterns of a soliton-forming beam as a function of the intensity ratio at a fixed bias field (top) and as a function of the bias field at an intensity ratio (bottom).

Fig. 5.
Fig. 5.

Experimental and numerical results of a 2D discrete vector soliton. (a) input, (b) discrete diffraction at low bias field, (c, d) mutual trapping and decoupled output at high bias field, respectively. Row 1&2 show the two components of the vector soliton from experiment. Since the two components from simulations are the same, only one of the components from simulation is shown (Row 3).

Fig. 6.
Fig. 6.

Experimental results on dipole-like solitons in a 2D photonic lattice. Top panel: two beams are out-of-phase; Bottom panel: two beams are in-phase. (a) input; (b) output at a low bias field of 100V/mm; (c) and (d) output at a high bias field of 320V/mm with and without the lattice, respectively.

Fig. 7.
Fig. 7.

Numerical results corresponding to Fig. 6. For simplicity, numerical model does not include self-bending and anisotropic effects associated with the photorefractive nonlinearity.

Fig. 8.
Fig. 8.

Experimental demonstration of 2D discrete soliton trains. Shown are the transverse intensity patterns of a stripe beam taken from crystal input (a) and output (b-d) faces. (b) Normal diffraction, (c) discrete diffraction, and (d) discrete soliton trains. Arrows indicate initial location of the stripe. (e) and (f) are 3D intensity plots corresponding to (c) and (d), respectively.

Fig. 9.
Fig. 9.

Numerical results showing discrete diffraction (left) and discrete trapping (right) of a stripe beam in the lattice. Animations of the observed process as obtained from numerical simulations can be viewed in the media files. [Media 2] [Media 3]

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