Abstract

We reveal that the effective diffraction experienced by light beams launched along the central guiding channel of optical lattice with a quadratic frequency modulation can be tuned in strength and sign. Complete suppression of the linear diffraction in the broad band of spatial frequencies is shown to be possible, thus profoundly affecting properties of nonlinear self-sustained beams as well. In particular, we report on the properties of a new class of stable solitons supported by such lattices in defocusing media.

© 2005 Optical Society of America

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References

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Nature (3)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, �??Discretizing light behavior 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]

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]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. E (1)

E. N. Tsoy and C. M. de Sterke, �??Propagation of nonlinear pulses in chirped fiber gratings,�?? Phys. Rev. E 62, 2882 (2000).
[CrossRef]

Phys. Rev. E. (1)

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]

Phys. Rev. Lett. (5)

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]

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]

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Spatial spectrum of FM lattice at Ω=3. (b) Dispersion curves at Ω=3 and α=0.1. (c) Critical lattice depth versus lattice frequency. (d) Integral factor C on (p,α) plane at Ω=3.

Fig. 2.
Fig. 2.

Beam propagation dynamics in (a) harmonic lattice and (b) lattice with FM rate α=0.11. Lattice depth p=3.4 and frequency Ω=3. Linear medium.

Fig. 3.
Fig. 3.

(a) Profiles of solitons supported by FM lattice at p=2, Ω=2, α=0.3. (b) Soliton width versus energy flow at p=2, Ω=2. (c) Propagation constant cutoff versus lattice depth at α=0.3. (d) Propagation constant cutoff versus frequency modulation rate at p=2, Ω=2. Focusing medium.

Fig. 4.
Fig. 4.

(a) Profiles of solitons supported by FM lattice at α=0.3. (b) Soliton width versus energy flow. (c) Energy flow versus propagation constant. (d) Profiles of solitons supported by harmonic lattice. In all cases p=2, Ω=2. Defocusing medium.

Equations (8)

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

i q ξ = 1 2 2 q η 2 σ q 2 q p R ( η ) q .
U = q 2 d η ,
H = 1 2 ( q η 2 2 p R ( η ) q 2 σ q 2 ) d η
i d q k d ξ = 1 2 k 2 q k p R k ( k k ) q k ( k ) d k ' ,
q k = ( 2 π ) 1 q ( η , ξ ) exp ( i k η ) d η , R k = ( 2 π ) 1 R ( η ) exp ( i k η ) d η .
b ( k ) = k 2 2 + 2 p R k ( 0 ) + 2 p R k ( 2 k ) .
R k ( k ) = ( 12 α Ω ) 1 2 ( Ai [ ( 3 α Ω ) 1 3 ( Ω + k ) ] + Ai [ ( 3 α Ω ) 1 3 ( Ω k ) ] ) ,
C ( α , p , Ω ) = b 2 ( k ) S ( k ) d k .

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