Abstract

We predict a sharp crossover from nonlinear self-defocusing to discrete self-trapping of a narrow Gaussian beam with the increase of the refractive index contrast in a periodic photonic lattice. We demonstrate experimentally nonlinear discrete localization of light with defocusing nonlinearity by single site excitation in LiNbO3 waveguide arrays.

© 2006 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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Nature

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817-823 (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]

Opt. Express

Opt. Lett.

Phys. Rev. A

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50, R4457-R4460 (1994).
[CrossRef] [PubMed]

Phys. Rev. E

G. L. Alfimov, P. G. Kevrekidis, V. V. Konotop, and M. Salerno, "Wannier functions analysis of the nonlinear Schrodinger equation with a periodic potential," Phys. Rev. E 66, 46608-6 (2002).
[CrossRef]

Phys. Rev. Lett.

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92, 093901-4 (2004).
[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, 023902-4 (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]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296-3299 (2001).
[CrossRef] [PubMed]

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, 3383-3386 (1998).
[CrossRef]

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, 113902-4 (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, 123902-4 (2004).
[CrossRef] [PubMed]

Other

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart And Winston, New York, 1976).

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic of a discrete lattice with nearest-neighbor coupling. (b) Refractive index profile of coupled LiNbO3 waveguides.

Fig. 2.
Fig. 2.

(a,b) Bandgap spectrum of linear waves for index contrasts of 1.1 × 10-4 and 2.8×10-4, respectively. (c,d) Profiles of staggered gap solitons having the minimum width for cases (a,b), respectively. Shading marks index maxima. (e) Minimum width of the gap soliton vs. the refractive index contrast; (f) Efficiency of beam self-trapping calculated as the power fraction remaining in the 20 central waveguides at the output for an optimized input power (solid) compared with linear diffraction (dashed) vs. the refractive index contrast.

Fig. 3.
Fig. 3.

(a) Intensity distribution at the output facet of the array for linear propagation at low laser power (10 nW). (b) Corresponding intensity profiles: Solid - experimental measurement; shading - numerical solution of the full model [Eq. (2)]; crosses - lattice site amplitudes calculated from the discrete model [Eq. (1)]. (c) Evolution of the beam intensity along the sample for a low input power simulated with Eq. (2). (d-f) Same as (a-c) for nonlinear propagation at high laser power (1 mW).

Fig. 4.
Fig. 4.

(a) Saturated camera image of the single channel localized state at the output of the array, zoomed at the dashed rectangle in Fig. 3(d). (b) Interferogram confirming the staggered phase structure of the output beam.

Equations (2)

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i d a n dz + β a n + C ( a n 1 + a n + 1 ) + γ a n 2 a n = 0 ,
i E z + D 2 E x 2 + ( E 2 ) E + ρ Δ n ( x ) E = 0 ,

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