Abstract

We discuss soliton control in reconfigurable optically-induced photonic lattices created by three interfering beams. We reveal novel dynamical regimes for strongly localized solitons, including binary switching and soliton revivals through resonant wave mixing.

© 2005 Optical Society of America

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References

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  1. P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, �??Photonic Bloch waves and photonic band gaps,�?? in Confined Electrons and Photons, E. Burstein and C. Weisbuch, eds., (Plenum Press, New York, 1995), pp. 585�??633.
  2. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
  3. 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]
  4. 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]
  5. 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 (London) 422, 147�??150 (2003).
    [CrossRef] [PubMed]
  6. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, �??Spatial solitons in optically induced gratings,�?? Opt. Lett. 28, 710�??712 (2003).
    [CrossRef] [PubMed]
  7. D. N. Christodoulides, F. Lederer, and Y. Silberberg, �??Discretizing light behaviour in linear and nonlinear waveguide lattices,�?? Nature (London) 424, 817�??823 (2003).
    [CrossRef] [PubMed]
  8. 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 (2004).
    [CrossRef] [PubMed]
  9. D. Neshev, A. A. Sukhorukov, B. Hanna,W. Krolikowski, and Yu. S. Kivshar, �??Controlled generation and steering of spatial gap solitons,�?? Phys. Rev. Lett. 93, 083905 (2004).
    [CrossRef] [PubMed]
  10. C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, Yu. S. Kivshar, and W. Krolikowski, �??Tunable positive and negative refraction in optically-induced photonic lattices,�?? arXiv physics/0503226 (2005), <a href="http://arxiv.org/abs/physics/0503226">http://arxiv.org/abs/physics/0503226</a>; Optics Letters (2005) in press
  11. Y. V. Kartashov, L. Torner, and D. N. Christodoulides, �??Soliton dragging by dynamic optical lattices,�?? Opt. Lett. 30, 1378�??1380 (2005).
    [CrossRef] [PubMed]
  12. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, �??Diffraction management,�?? Phys. Rev. Lett. 85, 1863�??1866 (2000).
    [CrossRef] [PubMed]
  13. M. J. Ablowitz and Z. H. Musslimani, �??Discrete diffraction managed spatial solitons,�?? Phys. Rev. Lett. 87, 254102 (2001).
    [CrossRef] [PubMed]
  14. U. Peschel and F. Lederer, �??Oscillation and decay of discrete solitons in modulated waveguide arrays,�?? J. Opt. Soc. Am. B 19, 544�??549 (2002).
    [CrossRef]
  15. A. A. Sukhorukov and Yu. S. Kivshar, �??Discrete gap solitons in modulated waveguide arrays,�?? Opt. Lett. 27, 2112�??2114 (2002).
    [CrossRef]
  16. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, �??Dynamics of discrete solitons in optical waveguide arrays,�?? Phys. Rev. Lett. 83, 2726�??2729 (1999).
    [CrossRef]
  17. H. Maritn, E. D. Eugenieva, and Z. Chen, �??Discrete solitons and soliton-Induced dislocations in partially coherent photonic lattices,�?? Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef]
  18. 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]

Confined Electrons and Photons (1)

P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, �??Photonic Bloch waves and photonic band gaps,�?? in Confined Electrons and Photons, E. Burstein and C. Weisbuch, eds., (Plenum Press, New York, 1995), pp. 585�??633.

J. Opt. Soc. Am. B (1)

Nature (London) (2)

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 (London) 422, 147�??150 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, �??Discretizing light behaviour in linear and nonlinear waveguide lattices,�?? Nature (London) 424, 817�??823 (2003).
[CrossRef] [PubMed]

Opt. Lett. (3)

Optics Letters (1)

C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, Yu. S. Kivshar, and W. Krolikowski, �??Tunable positive and negative refraction in optically-induced photonic lattices,�?? arXiv physics/0503226 (2005), <a href="http://arxiv.org/abs/physics/0503226">http://arxiv.org/abs/physics/0503226</a>; Optics Letters (2005) in press

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. (8)

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 Yu. S. Kivshar, �??Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,�?? Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

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

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

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, �??Dynamics of discrete solitons in optical waveguide arrays,�?? Phys. Rev. Lett. 83, 2726�??2729 (1999).
[CrossRef]

H. Maritn, E. D. Eugenieva, and Z. Chen, �??Discrete solitons and soliton-Induced dislocations in partially coherent photonic lattices,�?? Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef]

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]

Other (1)

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

Supplementary Material (1)

» Media 1: GIF (1799 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Examples of one-dimensional photonic lattices modulated by the third beam with the transverse wave number k 3x : (a) k 3x = 0, (b) k 3x = 0.8k 12x , and (c) k 3x = 1.3k 12x . Insets show the wave vectors of two input beams which form the lattice, and the wave vector of the third beam (red, dashed). Parameters are A 12 = 0.25, A 3 = 0.66A 12 and the propagation length is L = 50 mm.

Fig. 2.
Fig. 2.

(1.8MB) All-optical steering of spatial optical solitons controlled by the amplitude of the third lattice beam with inclination k 3x = 1.15k 12x : (a) straight (A 3 = 0.62A 12) and (b) tilted (A 3 = 2.02A 12) propagation. Left: profiles of optically-induced lattices. Middle: evolution of beam intensities along the propagation direction. Right: soliton profiles at the input (dashed) and output (solid). Animation shows the soliton dynamics as the modulation depth increases from zero (A 3 = 0) to a higher value (A 3 = 2.8A 12). Parameters are A 12 = 0.25, A in = 0.5, input beam position x 0 = 0, angle k 0x = 0 and width w = 25μm, and the total propagation length is L = 100 mm.

Fig. 3.
Fig. 3.

Output soliton position vs. the modulating beam amplitude for different positions and angles of the input Gaussian beam. In (a) marked points ‘a’, ‘b’ correspond to the solitons shown in Fig. 2(a) and Fig. 2(b), respectively. Shadings mark stable regions. Parameters are the same as in Fig. 2.

Fig. 4.
Fig. 4.

Output soliton position vs. (a) the amplitude of the input Gaussian beam and (b) the angle between the modulating beam and the lattice-forming beams, defined by the ratio k 3x /k 12x . Dashed line and circles correspond to Fig. 2(a), solid lines and triangles - to Fig. 2(b). Parameters are the same as in Fig. 2.

Fig. 5.
Fig. 5.

Example of the resonant soliton revival in the modulated lattices: (a) linear diffraction at low power (A in = 0.02), (b) revival and periodic transformations of the soliton in the nonlinear regime (A in = 0.2). Variation of the intensity (left) and spatial Fourier spectrum (right) of the input Gaussian beam along the propagation direction are shown (spatial frequency κx is normalized to k 12x /4). Parameters are A 12 = 0.25, A 3 = 0.2A 12, x 0 = 0, k 0x = 0, w = 25μm and the total propagation length is L = 120 mm.

Equations (2)

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i E z + D 2 E x 2 + ( x , E 2 ) E = 0 ,
A L = A 3 exp ( i β 3 z + i k 2 x x ) + 2 A 12 exp ( i β 12 z ) cos ( k 12 x x ) .

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