Abstract

We study experimentally nonlinear localization effects in optically induced gratings created by interfering plane waves in a photorefractive crystal. We demonstrate the generation of spatial bright solitons similar to those observed in arrays of coupled optical waveguides. We also create pairs of out-of-phase solitons, which resemble twisted localized states in nonlinear lattices.

© 2003 Optical Society of America

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  1. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  2. Yu. S. Kivshar, Opt. Lett. 18, 1147 (1993).
    [CrossRef]
  3. W. Krolikowski and Yu. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
    [CrossRef]
  4. A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
    [CrossRef]
  5. F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, Berlin, 2001), p. 269.
    [CrossRef]
  6. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  7. Y. Silberberg and G. I. Stegeman, in Spatial Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, Berlin, 2001), p. 37.
    [CrossRef]
  8. A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. E 65, 036609 (2002).
    [CrossRef]
  9. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. Fleischer, and M. Segev, Phys. Rev. E 66, 046601 (2002).
    [CrossRef]
  10. P. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
    [CrossRef]
  11. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef]

2003 (2)

P. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

2002 (2)

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. E 65, 036609 (2002).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. Fleischer, and M. Segev, Phys. Rev. E 66, 046601 (2002).
[CrossRef]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1996 (2)

W. Krolikowski and Yu. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
[CrossRef]

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

1993 (1)

1988 (1)

Aceves, A. B.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

Christodoulides, D. N.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. Fleischer, and M. Segev, Phys. Rev. E 66, 046601 (2002).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
[CrossRef] [PubMed]

Darmanyan, S.

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, Berlin, 2001), p. 269.
[CrossRef]

De Angelis, C.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. Fleischer, and M. Segev, Phys. Rev. E 66, 046601 (2002).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Fleischer, J.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. Fleischer, and M. Segev, Phys. Rev. E 66, 046601 (2002).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

Joseph, R. I.

Kivshar, Yu. S.

P. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. E 65, 036609 (2002).
[CrossRef]

W. Krolikowski and Yu. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
[CrossRef]

Yu. S. Kivshar, Opt. Lett. 18, 1147 (1993).
[CrossRef]

Kobyakov, A.

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, Berlin, 2001), p. 269.
[CrossRef]

Krolikowski, W.

Lederer, F.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, Berlin, 2001), p. 269.
[CrossRef]

Louis, P. Y.

P. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Muschall, R.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Ostrovskaya, E. A.

P. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Peschel, T.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Savage, C. M.

P. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. Fleischer, and M. Segev, Phys. Rev. E 66, 046601 (2002).
[CrossRef]

Segev, M.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. Fleischer, and M. Segev, Phys. Rev. E 66, 046601 (2002).
[CrossRef]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Y. Silberberg and G. I. Stegeman, in Spatial Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, Berlin, 2001), p. 37.
[CrossRef]

Stegeman, G. I.

Y. Silberberg and G. I. Stegeman, in Spatial Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, Berlin, 2001), p. 37.
[CrossRef]

Sukhorukov, A. A.

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. E 65, 036609 (2002).
[CrossRef]

Trillo, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

Wabnitz, S.

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

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

Opt. Lett. (2)

Phys. Rev. A (1)

P. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Yu. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Phys. Rev. E (3)

A. B. Aceves, C. De Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, Phys. Rev. E 53, 1172 (1996).
[CrossRef]

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. E 65, 036609 (2002).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. Fleischer, and M. Segev, Phys. Rev. E 66, 046601 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

Other (2)

Y. Silberberg and G. I. Stegeman, in Spatial Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, Berlin, 2001), p. 37.
[CrossRef]

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, Berlin, 2001), p. 269.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Band structure of the energy spectrum, β, in the linear grating potential Vglin=1+I0 cos2Kx-1 (for γnl=1): Bloch bands are numbered; bandgaps are indicated by hash marks. Inset, effective potential Vglin, shown for two values of grating intensity I0.

Fig. 2
Fig. 2

Experimental setup: M’s, mirrors; PZTM, piezoelectric translational mirror; PBS’s, polarizing beam splitters; BS’s, plane beam splitters; P’s, polarizers; SBN, photorefractive crystal; O, microscope objective; λ/2’s, half-wave plates; L, antireflection-coated lens; F’s, filters; CCD’s, cameras.

Fig. 3
Fig. 3

Experimental demonstration of odd and even spatial solitons: (a) Input beam and optical lattice (power, 23 µW); (b) output probe beam at low power 2×10-3 µW; (c) localized states 87×10-3 µW. Left, vibrating piezoelectric translational mirror; middle, even excitation; right, odd excitation. Electric field, 3600 V/cm.

Fig. 4
Fig. 4

Experimental demonstration of the soliton bound states’ twisted modes: (a) input, (b)–(e) outputs; (b) linear diffraction, (c) dipole beam, (d) even-symmetry twisted mode, (e) odd-symmetry twisted mode. Powers: grating, 23 µW; dipole beam, 0.12 µW. Intensity ratio I0/E2, 1.3; electric field, 3600 V/cm; grating period, 16 µm.

Equations (1)

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2ik1Ez+2Ex2-k02ne4r33EscE=0,

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