Abstract

Considering nonlinear optical propagation through photorefractive crystals in which the bias voltage is periodically modulated along the propagation direction, we are able to identify the conditions in which a beam forms a soliton in a straight line down to micron-sized widths. The effect, which is numerically investigated considering the full (3+1)D spatio-temporal light-matter dynamics, emerges when the period of modulation of the bias is smaller than the beam diffraction length. In conditions in which the two scales are comparable, the soliton follows a characteristic wiggling trajectory, oscillating in response to the oscillating bias. The finding indicates a method to achieve highly miniaturized soliton-based photonic applications that do not require specific off-axis alignment.

© 2008 Optical Society of America

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References

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature (London) 424, 817-823 (2003).
    [CrossRef]
  2. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton control in fading optical lattices," Opt. Lett. 31, 2181-2183 (2006).
    [CrossRef] [PubMed]
  3. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford Press, 1996).
  4. A. Ciattoni, E. DelRe, C. Rizza, and A. Marini, arXiv:0804.3687v1 (2008).
  5. S. Trillo and W. Torruellas, Spatial Solitons (Springer, Berlin, 2001).
  6. E. DelRe, M. Tamburrini, and A. J. Agranat, "Soliton electro-optic effects in paraelectrics," Opt. Lett. 25, 963-965 (2000).
    [CrossRef]
  7. E. DelRe, B. Crosignani, P. Di Porto, E. Palange, and A. J. Agranat, "Electro-optic beam manipulation through photorefractive needles," Opt. Lett. 27, 2188-2190 (2002).
    [CrossRef]
  8. A. DErcole, E. Palange, E. DelRe, A.  Ciattoni, B. Crosignani, and A. J. Agranat, "Miniaturization and embedding of soliton-based electro-optically addressable photonic arrays," Appl. Phys. Lett. 85, 2679-2681 (2004).
    [CrossRef]
  9. E. DelRe, A. Ciattoni, and E. Palange, "Role of charge saturation in photorefractive dynamics of micron-sized beams and departure from soliton behavior," Phys. Rev. E 73, 017601 (2006).
    [CrossRef]
  10. M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals," Opt. Commun. 120, 311-315 (1995).
    [CrossRef]
  11. E. DelRe, G. De Masi, A. Ciattoni, and E. Palange, "Pairing space-charge field conditions with self-guiding for the attainment of circular symmetry in photorefractive solitons," Appl. Phys. Lett. 85, 5499-5501 (2004).
    [CrossRef]

2006 (2)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton control in fading optical lattices," Opt. Lett. 31, 2181-2183 (2006).
[CrossRef] [PubMed]

E. DelRe, A. Ciattoni, and E. Palange, "Role of charge saturation in photorefractive dynamics of micron-sized beams and departure from soliton behavior," Phys. Rev. E 73, 017601 (2006).
[CrossRef]

2004 (2)

A. DErcole, E. Palange, E. DelRe, A.  Ciattoni, B. Crosignani, and A. J. Agranat, "Miniaturization and embedding of soliton-based electro-optically addressable photonic arrays," Appl. Phys. Lett. 85, 2679-2681 (2004).
[CrossRef]

E. DelRe, G. De Masi, A. Ciattoni, and E. Palange, "Pairing space-charge field conditions with self-guiding for the attainment of circular symmetry in photorefractive solitons," Appl. Phys. Lett. 85, 5499-5501 (2004).
[CrossRef]

2003 (1)

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

2002 (1)

E. DelRe, B. Crosignani, P. Di Porto, E. Palange, and A. J. Agranat, "Electro-optic beam manipulation through photorefractive needles," Opt. Lett. 27, 2188-2190 (2002).
[CrossRef]

2000 (1)

E. DelRe, M. Tamburrini, and A. J. Agranat, "Soliton electro-optic effects in paraelectrics," Opt. Lett. 25, 963-965 (2000).
[CrossRef]

1995 (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals," Opt. Commun. 120, 311-315 (1995).
[CrossRef]

Agranat, A. J.

A. DErcole, E. Palange, E. DelRe, A.  Ciattoni, B. Crosignani, and A. J. Agranat, "Miniaturization and embedding of soliton-based electro-optically addressable photonic arrays," Appl. Phys. Lett. 85, 2679-2681 (2004).
[CrossRef]

E. DelRe, B. Crosignani, P. Di Porto, E. Palange, and A. J. Agranat, "Electro-optic beam manipulation through photorefractive needles," Opt. Lett. 27, 2188-2190 (2002).
[CrossRef]

E. DelRe, M. Tamburrini, and A. J. Agranat, "Soliton electro-optic effects in paraelectrics," Opt. Lett. 25, 963-965 (2000).
[CrossRef]

Carvalho, M. I.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals," Opt. Commun. 120, 311-315 (1995).
[CrossRef]

Christodoulides, D. N.

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

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals," Opt. Commun. 120, 311-315 (1995).
[CrossRef]

Ciattoni, A.

E. DelRe, A. Ciattoni, and E. Palange, "Role of charge saturation in photorefractive dynamics of micron-sized beams and departure from soliton behavior," Phys. Rev. E 73, 017601 (2006).
[CrossRef]

Ciattoni, A.

A. DErcole, E. Palange, E. DelRe, A.  Ciattoni, B. Crosignani, and A. J. Agranat, "Miniaturization and embedding of soliton-based electro-optically addressable photonic arrays," Appl. Phys. Lett. 85, 2679-2681 (2004).
[CrossRef]

Ciattoni, A.

E. DelRe, G. De Masi, A. Ciattoni, and E. Palange, "Pairing space-charge field conditions with self-guiding for the attainment of circular symmetry in photorefractive solitons," Appl. Phys. Lett. 85, 5499-5501 (2004).
[CrossRef]

Crosignani, B.

A. DErcole, E. Palange, E. DelRe, A.  Ciattoni, B. Crosignani, and A. J. Agranat, "Miniaturization and embedding of soliton-based electro-optically addressable photonic arrays," Appl. Phys. Lett. 85, 2679-2681 (2004).
[CrossRef]

E. DelRe, B. Crosignani, P. Di Porto, E. Palange, and A. J. Agranat, "Electro-optic beam manipulation through photorefractive needles," Opt. Lett. 27, 2188-2190 (2002).
[CrossRef]

De Masi, G.

E. DelRe, G. De Masi, A. Ciattoni, and E. Palange, "Pairing space-charge field conditions with self-guiding for the attainment of circular symmetry in photorefractive solitons," Appl. Phys. Lett. 85, 5499-5501 (2004).
[CrossRef]

DelRe, E.

E. DelRe, A. Ciattoni, and E. Palange, "Role of charge saturation in photorefractive dynamics of micron-sized beams and departure from soliton behavior," Phys. Rev. E 73, 017601 (2006).
[CrossRef]

E. DelRe, G. De Masi, A. Ciattoni, and E. Palange, "Pairing space-charge field conditions with self-guiding for the attainment of circular symmetry in photorefractive solitons," Appl. Phys. Lett. 85, 5499-5501 (2004).
[CrossRef]

A. DErcole, E. Palange, E. DelRe, A.  Ciattoni, B. Crosignani, and A. J. Agranat, "Miniaturization and embedding of soliton-based electro-optically addressable photonic arrays," Appl. Phys. Lett. 85, 2679-2681 (2004).
[CrossRef]

E. DelRe, B. Crosignani, P. Di Porto, E. Palange, and A. J. Agranat, "Electro-optic beam manipulation through photorefractive needles," Opt. Lett. 27, 2188-2190 (2002).
[CrossRef]

E. DelRe, M. Tamburrini, and A. J. Agranat, "Soliton electro-optic effects in paraelectrics," Opt. Lett. 25, 963-965 (2000).
[CrossRef]

DErcole, A.

A. DErcole, E. Palange, E. DelRe, A.  Ciattoni, B. Crosignani, and A. J. Agranat, "Miniaturization and embedding of soliton-based electro-optically addressable photonic arrays," Appl. Phys. Lett. 85, 2679-2681 (2004).
[CrossRef]

Di Porto, P.

E. DelRe, B. Crosignani, P. Di Porto, E. Palange, and A. J. Agranat, "Electro-optic beam manipulation through photorefractive needles," Opt. Lett. 27, 2188-2190 (2002).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton control in fading optical lattices," Opt. Lett. 31, 2181-2183 (2006).
[CrossRef] [PubMed]

Lederer, F.

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

Palange, E.

E. DelRe, A. Ciattoni, and E. Palange, "Role of charge saturation in photorefractive dynamics of micron-sized beams and departure from soliton behavior," Phys. Rev. E 73, 017601 (2006).
[CrossRef]

A. DErcole, E. Palange, E. DelRe, A.  Ciattoni, B. Crosignani, and A. J. Agranat, "Miniaturization and embedding of soliton-based electro-optically addressable photonic arrays," Appl. Phys. Lett. 85, 2679-2681 (2004).
[CrossRef]

E. DelRe, G. De Masi, A. Ciattoni, and E. Palange, "Pairing space-charge field conditions with self-guiding for the attainment of circular symmetry in photorefractive solitons," Appl. Phys. Lett. 85, 5499-5501 (2004).
[CrossRef]

E. DelRe, B. Crosignani, P. Di Porto, E. Palange, and A. J. Agranat, "Electro-optic beam manipulation through photorefractive needles," Opt. Lett. 27, 2188-2190 (2002).
[CrossRef]

Silberberg, Y.

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

Singh, S. R.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals," Opt. Commun. 120, 311-315 (1995).
[CrossRef]

Tamburrini, M.

E. DelRe, M. Tamburrini, and A. J. Agranat, "Soliton electro-optic effects in paraelectrics," Opt. Lett. 25, 963-965 (2000).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton control in fading optical lattices," Opt. Lett. 31, 2181-2183 (2006).
[CrossRef] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton control in fading optical lattices," Opt. Lett. 31, 2181-2183 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

A. DErcole, E. Palange, E. DelRe, A.  Ciattoni, B. Crosignani, and A. J. Agranat, "Miniaturization and embedding of soliton-based electro-optically addressable photonic arrays," Appl. Phys. Lett. 85, 2679-2681 (2004).
[CrossRef]

E. DelRe, G. De Masi, A. Ciattoni, and E. Palange, "Pairing space-charge field conditions with self-guiding for the attainment of circular symmetry in photorefractive solitons," Appl. Phys. Lett. 85, 5499-5501 (2004).
[CrossRef]

Nature (London) (1)

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

Opt. Commun. (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, "Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals," Opt. Commun. 120, 311-315 (1995).
[CrossRef]

Opt. Lett. (3)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton control in fading optical lattices," Opt. Lett. 31, 2181-2183 (2006).
[CrossRef] [PubMed]

E. DelRe, M. Tamburrini, and A. J. Agranat, "Soliton electro-optic effects in paraelectrics," Opt. Lett. 25, 963-965 (2000).
[CrossRef]

E. DelRe, B. Crosignani, P. Di Porto, E. Palange, and A. J. Agranat, "Electro-optic beam manipulation through photorefractive needles," Opt. Lett. 27, 2188-2190 (2002).
[CrossRef]

Phys. Rev. E (1)

E. DelRe, A. Ciattoni, and E. Palange, "Role of charge saturation in photorefractive dynamics of micron-sized beams and departure from soliton behavior," Phys. Rev. E 73, 017601 (2006).
[CrossRef]

Other (3)

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford Press, 1996).

A. Ciattoni, E. DelRe, C. Rizza, and A. Marini, arXiv:0804.3687v1 (2008).

S. Trillo and W. Torruellas, Spatial Solitons (Springer, Berlin, 2001).

Supplementary Material (3)

» Media 1: AVI (1371 KB)     
» Media 2: AVI (1658 KB)     
» Media 3: AVI (1618 KB)     

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Figures (2)

Fig. 1.
Fig. 1.

Top-sided electrode settings in the standard (a) and in periodically biased (b) configuration. Electrodes are positioned on the x = Lx facet, their transverse spacing is dy and their voltages are -V 0 and V 0 for black and red electrodes, respectively. In configuration (b) longitudinal periodicity is dz whereas electrodes longitudinal length is dz /4.

Fig. 2.
Fig. 2.

Optical beam photorefractive time dynamics (equal intensity surfaces) (a1) (movie:Fig2a1-Mov.avi, 1371 Kb) [Media 1], (b1) (movie:Fig2b1-Mov.avi, 1658 Kb) [Media 2] and (c1) (movie:Fig2c1-Mov.avi, 1618 Kb)[Media 3] and refractive index patterns supporting the corresponding steady state optical propagation (a2) (b2) (c2) . Configuration (a) corresponds to the well-known setting of a longitudinally uniform biased top-sided electrode geometry of Fig. 1(a) whose steady state is a bent optical beam. Configurations (b) and (c) correspond to a periodically biased top-sided electrode geometry as in Fig. 1(b) with electrode periodicity greater (b) and smaller (c) than the optical diffraction length, respectively. Note the wiggling and straight steady state optical beam of settings (b) and (c), respectively. The Half Width at Half Maximum (HWHM) of the input Gaussian beam is, in all the simulations, w 0 = 3.3μm.

Equations (3)

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E = K B T q log Q Φ
ρ t = μ q [ · ( N e E ) + K B T q 2 N e ] ,
i A z + 1 2 k ( 2 A x 2 + 2 A y 2 ) = k n 0 [ 1 2 n 0 3 g ε 0 2 ( ε r 1 ) 2 E y 2 ] A

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