Abstract

We demonstrate experimentally all-optical beam steering in modulated photonic lattices induced optically by three-beam interference in a biased photorefractive crystal. We identify and characterize the key physical parameters governing the beam steering and show that the spatial resolution can be enhanced by the additional effect of nonlinear beam self-localization.

© 2006 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, in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Springer, 1995), p. 585.
    [CrossRef]
  2. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  3. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  4. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  5. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
    [CrossRef]
  6. J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Opt. Lett. 30, 1027 (2005).
    [CrossRef] [PubMed]
  7. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
    [CrossRef]
  8. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902-4 (2003).
    [CrossRef] [PubMed]
  9. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  10. Y. V. Kartashov, L. Torner, and D. N. Christodoulides, Opt. Lett. 30, 1378 (2005).
    [CrossRef] [PubMed]
  11. I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Express 13, 5704 (2005).
    [CrossRef] [PubMed]
  12. S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
    [CrossRef]

2005 (3)

2003 (2)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902-4 (2003).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

2002 (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

1999 (1)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[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 (1)

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

1988 (1)

Agrawal, G. P.

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

Aitchison, J. S.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Opt. Lett. 30, 1027 (2005).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

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

Birks, T. A.

P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Springer, 1995), p. 585.
[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, 023902-4 (2003).
[CrossRef] [PubMed]

Carvalho, M. I.

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

Christodoulides, D. N.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Opt. Lett. 30, 1027 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and D. N. Christodoulides, Opt. Lett. 30, 1378 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902-4 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

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

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902-4 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

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

Fleischer, J. W.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902-4 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Garanovich, I. L.

Joseph, R. I.

Kartashov, Y. V.

Kivshar, Y.

Kivshar, Yu. S.

I. L. Garanovich, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Express 13, 5704 (2005).
[CrossRef] [PubMed]

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

Krolikowski, W.

Lloyd Lucas, F. D.

P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Springer, 1995), p. 585.
[CrossRef]

Meier, J.

Morandotti, R.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Opt. Lett. 30, 1027 (2005).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

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

Neshev, D.

Ostrovskaya, E.

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Springer, 1995), p. 585.
[CrossRef]

Salamo, G.

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Segev, M.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902-4 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Silberberg, Y.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Opt. Lett. 30, 1027 (2005).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

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

Singh, S. R.

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

Sorel, M.

Stegeman, G. I.

Sukhorukov, A. A.

Torner, L.

Yang, H.

Opt. Commun. (1)

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. E (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902-4 (2003).
[CrossRef] [PubMed]

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[CrossRef]

Other (2)

P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Springer, 1995), p. 585.
[CrossRef]

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

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the k-vector configuration in a modulated optical lattice. Beams 1 and 2 define a straight lattice, while the symmetry-breaking control beam 3 introduces transverse and longitudinal lattice modulation, as shown in (b) for the case k 3 x = 1.18 k 12 x and I 3 = 4 I 12 . Bottom, corresponding experimental profiles of modulated lattice at the crystal input ( z = 0 ) , when the maximum of the broad transverse modulation (dashed curve) is (c) aligned with probe beam input ( x = 0 ) or (d) offset by a quarter period.

Fig. 2
Fig. 2

(a), (b) Measured shift and width of a linear probe beam output versus the phase of the modulating lattice beam for three different values of k 3 x k 12 x and I 3 = 4 I 12 . Shading marks the region in which the figure of merit is maximized. (c)–(e) Examples of measured output profiles corresponding to the points c,d,e in the plots (a) and (b).

Fig. 3
Fig. 3

(a) Experimental and theoretical (inset) linear output in a straight lattice ( I 3 = 0 ) . (b) Shift of the nonlinear probe beam output versus the modulating beam power for k 3 x = 1.18 k 12 x and φ 2 π = 0.22 . (c), (d) Experimental and theoretical (inset) nonlinear output in straight and modulated lattice for I 3 = 0 and I 3 = 4 I 12 , respectively, and k 3 x = 1.18 k 12 x . (e), (f) Numerical simulations of the longitudinal propagation.

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