Abstract

We consider optical propagation through a centrosymmetric photorefractive crystal with the externally applied bias voltage modulated along the optical propagation direction. We analytically prove that, if the modulation scale is smaller than the optical diffraction length, the resulting effective nonlinearity has an even parity in the transverse plane for an even-symmetric intensity profile and supports bending-free solitons down to few-micrometer beam widths. Numerical integration of the full photorefractive model for light–matter interaction allows us to confirm the feasibility of these miniaturized solitons and, for longer modulation periods, to investigate the excitation of self-trapped wiggling optical beams.

© 2008 Optical Society of America

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References

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  1. M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
    [CrossRef]
  2. M. Segev, M. F. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
    [CrossRef]
  3. E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
    [CrossRef]
  4. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 70, 066613 (2004).
    [CrossRef]
  5. M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).
    [CrossRef] [PubMed]
  6. A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
    [CrossRef] [PubMed]
  7. D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
    [CrossRef] [PubMed]
  8. A. Ciattoni, C. Rizza, E. DelRe, and E. Palange, Phys. Rev. Lett. 98, 043901 (2007).
    [CrossRef] [PubMed]
  9. Substituting the field A=A0+δA into the parabolic equation we derive an approximate equation for δA whose solution is substituted back into the remaining equation for A0, thus yielding Eq. .
  10. M. Segev and A. J. Agranat, Opt. Lett. 22, 1299 (1997).
    [CrossRef]
  11. B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
    [CrossRef]
  12. L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford Press, 1996).
  13. The extension of these results to the (2+1)D situation is reported in A. Ciattoni, E. DelRe, A. Marini, and C. Rizza, Opt. Express 12, 12002 (2008).

2008 (1)

The extension of these results to the (2+1)D situation is reported in A. Ciattoni, E. DelRe, A. Marini, and C. Rizza, Opt. Express 12, 12002 (2008).

2007 (1)

A. Ciattoni, C. Rizza, E. DelRe, and E. Palange, Phys. Rev. Lett. 98, 043901 (2007).
[CrossRef] [PubMed]

2006 (2)

E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
[CrossRef]

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef] [PubMed]

2004 (2)

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 70, 066613 (2004).
[CrossRef]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

1999 (1)

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

1997 (1)

1996 (1)

1995 (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

1991 (1)

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

Agranat, A. J.

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

M. Segev and A. J. Agranat, Opt. Lett. 22, 1299 (1997).
[CrossRef]

Carvalho, M. I.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

Centurion, M.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef] [PubMed]

Christodoulides, D. N.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

Ciattoni, A.

The extension of these results to the (2+1)D situation is reported in A. Ciattoni, E. DelRe, A. Marini, and C. Rizza, Opt. Express 12, 12002 (2008).

A. Ciattoni, C. Rizza, E. DelRe, and E. Palange, Phys. Rev. Lett. 98, 043901 (2007).
[CrossRef] [PubMed]

E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
[CrossRef]

Crosignani, B.

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

Degasperis, A.

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

DelRe, E.

The extension of these results to the (2+1)D situation is reported in A. Ciattoni, E. DelRe, A. Marini, and C. Rizza, Opt. Express 12, 12002 (2008).

A. Ciattoni, C. Rizza, E. DelRe, and E. Palange, Phys. Rev. Lett. 98, 043901 (2007).
[CrossRef] [PubMed]

E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
[CrossRef]

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

Di Porto, P.

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

Grunnet-Jepsen, A.

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

Hanna, B.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Hasegawa, A.

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

Kevrekidis, P. G.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef] [PubMed]

Kivshar, Y. S.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Kodama, Y.

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

Krolikowski, W.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Malomed, B. A.

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 70, 066613 (2004).
[CrossRef]

Marini, A.

The extension of these results to the (2+1)D situation is reported in A. Ciattoni, E. DelRe, A. Marini, and C. Rizza, Opt. Express 12, 12002 (2008).

Neshev, D.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Palange, E.

A. Ciattoni, C. Rizza, E. DelRe, and E. Palange, Phys. Rev. Lett. 98, 043901 (2007).
[CrossRef] [PubMed]

E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
[CrossRef]

Porter, M. A.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef] [PubMed]

Psaltis, D.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef] [PubMed]

Rizza, C.

The extension of these results to the (2+1)D situation is reported in A. Ciattoni, E. DelRe, A. Marini, and C. Rizza, Opt. Express 12, 12002 (2008).

A. Ciattoni, C. Rizza, E. DelRe, and E. Palange, Phys. Rev. Lett. 98, 043901 (2007).
[CrossRef] [PubMed]

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 70, 066613 (2004).
[CrossRef]

Segev, M.

Shih, M. F.

Singh, S. R.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

Solymar, L.

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

Sukhorukov, A. A.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Valley, G. C.

Webb, D. J.

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

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

Opt. Commun. (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

Opt. Express (1)

The extension of these results to the (2+1)D situation is reported in A. Ciattoni, E. DelRe, A. Marini, and C. Rizza, Opt. Express 12, 12002 (2008).

Opt. Lett. (1)

Phys. Rev. E (2)

E. DelRe, A. Ciattoni, and E. Palange, Phys. Rev. E 73, 017601 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 70, 066613 (2004).
[CrossRef]

Phys. Rev. Lett. (5)

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef] [PubMed]

A. Hasegawa and Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

A. Ciattoni, C. Rizza, E. DelRe, and E. Palange, Phys. Rev. Lett. 98, 043901 (2007).
[CrossRef] [PubMed]

B. Crosignani, A. Degasperis, E. DelRe, P. Di Porto, and A. J. Agranat, Phys. Rev. Lett. 82, 1664 (1999).
[CrossRef]

Other (2)

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

Substituting the field A=A0+δA into the parabolic equation we derive an approximate equation for δA whose solution is substituted back into the remaining equation for A0, thus yielding Eq. .

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Figures (2)

Fig. 1
Fig. 1

Devising a bending-free self-trapping nonlinearity in photorefractives. (1a)–(3a), Crystal layers, electrode geometries (gray and black stripes) and optical beam configurations. (1b)–(3b), Steady-state optical intensity profiles. (1c)–(3c), Nonlinear refractive index profiles supporting the corresponding optical propagations. Note the transition into the longitudinally averaged regime in case (3).

Fig. 2
Fig. 2

Soliton existence curves σ = σ ( u 0 ) relating soliton FWHM σ and u 0 for different values of γ.

Equations (5)

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Φ = χ log Q + V 0 cosh ( κ v x ) cosh ( κ v L x ) [ 1 L x 0 x d x Q ( x , z ) ] cos ( κ v z ) ,
δ n = α ( I + I d ) 2 [ ψ cos ( κ v z ) + χ I x ] 2 ,
( i z + 1 2 k 2 x 2 ) A 0 = k n 0 α [ 1 2 ψ 2 + ( χ I x ) 2 ] ( I + I d ) 2 A 0 .
d 2 u d ξ 2 = β u + 1 2 + γ ( d u 2 d ξ ) 2 ( 1 + u 2 ) 2 u .
Γ ( u , d u d ξ ) = 1 2 exp [ 4 γ ( 1 + u 2 ) ] ( 1 + u 2 ) 4 γ ( d u d ξ ) 2 d u exp [ 4 γ ( 1 + u 2 ) ] ( 1 + u 2 ) 4 γ u [ β + 1 2 ( 1 + u 2 ) 2 ]

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