Abstract

We study the control of modulational instability and pattern formation in a nonlinear dissipative feedback system with a periodic modulation of the material refractive index. We use a one-dimensional photonic lattice in a single-mirror feedback configuration and identify three mechanisms for pattern control: bandgap suppression of instability modes, periodicity induced pattern modes, and orientational pattern control.

© 2008 Optical Society of America

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  1. P. Manneville, Dissipative Structure and Weak Turbulence (Academic, 1990).
  2. C. Denz, Ph. Jander, and M. Schwab, Ann. Phys. 13, 391 (2004).
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    [CrossRef] [PubMed]

2008

C. Cleff, B. Gütlich, and C. Denz, Phys. Rev. Lett. 100, 233902 (2008).
[CrossRef] [PubMed]

2007

2004

U. Peschel, O. Egorov, and F. Lederer, Opt. Lett. 29, 1909 (2004).
[CrossRef] [PubMed]

D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

C. Denz, Ph. Jander, and M. Schwab, Ann. Phys. 13, 391 (2004).
[CrossRef]

2002

R. Neubecker and A. Zimmermann, Phys. Rev. E 65, 035205 (2002).
[CrossRef]

T. Carmon, M. Soljacic, and M. Segev, Phys. Rev. Lett. 89, 183902 (2002).
[CrossRef] [PubMed]

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

2001

M. Schwab, C. Denz, A. V. Mamaev, and M. Saffman, J. Opt. B 3, 318 (2001).
[CrossRef]

2000

G. Montemezzani, Phys. Rev. A 62, 053803 (2000).
[CrossRef]

1997

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

1993

1991

G. D'Alessandro and W. J. Firth, Phys. Rev. Lett. 66, 2597 (1991).
[CrossRef] [PubMed]

Carmon, T.

T. Carmon, M. Soljacic, and M. Segev, Phys. Rev. Lett. 89, 183902 (2002).
[CrossRef] [PubMed]

Chen, M.

Chen, Z.

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Christodoulides, D. N.

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

Cleff, C.

C. Cleff, B. Gütlich, and C. Denz, Phys. Rev. Lett. 100, 233902 (2008).
[CrossRef] [PubMed]

D'Alessandro, G.

G. D'Alessandro and W. J. Firth, Phys. Rev. Lett. 66, 2597 (1991).
[CrossRef] [PubMed]

Denz, C.

C. Cleff, B. Gütlich, and C. Denz, Phys. Rev. Lett. 100, 233902 (2008).
[CrossRef] [PubMed]

S. Koke, D. Träger, P. Jander, M. Chen, D. N. Neshev, W. Krolikowski, Yu. S. Kivshar, and C. Denz, Opt. Express 15, 6279 (2007).
[CrossRef] [PubMed]

C. Denz, Ph. Jander, and M. Schwab, Ann. Phys. 13, 391 (2004).
[CrossRef]

M. Schwab, C. Denz, A. V. Mamaev, and M. Saffman, J. Opt. B 3, 318 (2001).
[CrossRef]

Efremidis, N. K.

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

Egorov, O.

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

Firth, W. J.

G. D'Alessandro and W. J. Firth, Phys. Rev. Lett. 66, 2597 (1991).
[CrossRef] [PubMed]

Fleischer, J. W.

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

Gomila, D.

D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Gütlich, B.

C. Cleff, B. Gütlich, and C. Denz, Phys. Rev. Lett. 100, 233902 (2008).
[CrossRef] [PubMed]

Honda, T.

Jander, P.

Jander, Ph.

C. Denz, Ph. Jander, and M. Schwab, Ann. Phys. 13, 391 (2004).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

Kivshar, Yu. S.

Koke, S.

Krolikowski, W.

Lederer, F.

Lou, C.

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Mamaev, A. V.

M. Schwab, C. Denz, A. V. Mamaev, and M. Saffman, J. Opt. B 3, 318 (2001).
[CrossRef]

Manneville, P.

P. Manneville, Dissipative Structure and Weak Turbulence (Academic, 1990).

Montemezzani, G.

G. Montemezzani, Phys. Rev. A 62, 053803 (2000).
[CrossRef]

Neshev, D. N.

Neubecker, R.

R. Neubecker and A. Zimmermann, Phys. Rev. E 65, 035205 (2002).
[CrossRef]

Oppo, G.-L.

D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Peschel, U.

Saffman, M.

M. Schwab, C. Denz, A. V. Mamaev, and M. Saffman, J. Opt. B 3, 318 (2001).
[CrossRef]

Schwab, M.

C. Denz, Ph. Jander, and M. Schwab, Ann. Phys. 13, 391 (2004).
[CrossRef]

M. Schwab, C. Denz, A. V. Mamaev, and M. Saffman, J. Opt. B 3, 318 (2001).
[CrossRef]

Sears, S.

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

Segev, M.

T. Carmon, M. Soljacic, and M. Segev, Phys. Rev. Lett. 89, 183902 (2002).
[CrossRef] [PubMed]

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

Soljacic, M.

T. Carmon, M. Soljacic, and M. Segev, Phys. Rev. Lett. 89, 183902 (2002).
[CrossRef] [PubMed]

Träger, D.

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

Wang, X.

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Xu, J.

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Zambrini, R.

D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

Zimmermann, A.

R. Neubecker and A. Zimmermann, Phys. Rev. E 65, 035205 (2002).
[CrossRef]

Ann. Phys.

C. Denz, Ph. Jander, and M. Schwab, Ann. Phys. 13, 391 (2004).
[CrossRef]

J. Opt. B

M. Schwab, C. Denz, A. V. Mamaev, and M. Saffman, J. Opt. B 3, 318 (2001).
[CrossRef]

Nature

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, Nature 386, 143 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

G. Montemezzani, Phys. Rev. A 62, 053803 (2000).
[CrossRef]

Phys. Rev. E

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

R. Neubecker and A. Zimmermann, Phys. Rev. E 65, 035205 (2002).
[CrossRef]

Phys. Rev. Lett.

T. Carmon, M. Soljacic, and M. Segev, Phys. Rev. Lett. 89, 183902 (2002).
[CrossRef] [PubMed]

D. Gomila, R. Zambrini, and G.-L. Oppo, Phys. Rev. Lett. 92, 253904 (2004).
[CrossRef] [PubMed]

C. Cleff, B. Gütlich, and C. Denz, Phys. Rev. Lett. 100, 233902 (2008).
[CrossRef] [PubMed]

G. D'Alessandro and W. J. Firth, Phys. Rev. Lett. 66, 2597 (1991).
[CrossRef] [PubMed]

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Other

P. Manneville, Dissipative Structure and Weak Turbulence (Academic, 1990).

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Figures (4)

Fig. 1
Fig. 1

Top, experimental setup. L, lenses; PBS, polarizing beam splitter; SF, spatial filter; Lat, 1D transmission grating; λ 2 , half-wave plate; M, mirror; VM, virtual mirror; PC, Ba Ti O 3 photorefractive crystal. Inset, typical far- and near-field patterns. Bottom, far-field patterns (a) hexagonal pattern without optical lattice, (b) linear diffraction on the optical lattice, and (c) coexistence between nonlinear optical pattern and linear diffraction for k L 2.2 k P . Dashed lines denote the position of the lattice bandgap.

Fig. 2
Fig. 2

Bandgap inhibition of instability modes for two different lattice beam intensities. (a) and (b) Suppression of instability modes for k L 3 k P . (c) and (d) Suppression of instability modes when k L 2 k P in perpendicular direction. Dashed lines indicate the edges of the Brillouin zone.

Fig. 3
Fig. 3

Seeding of instability modes. Diagonal pattern obtained at intensity below the hexagon formation threshold with (a) k L 1.3 k P ( hexagons ) and (b) k L 2.2 k P ( hexagons ) . k P is the new wave vector associated with the new diagonal pattern.

Fig. 4
Fig. 4

Pattern orientation control. From left to right, pattern orientation following the lattice rotation. Dotted lines indicate the optical lattice position; the arrows indicate the rotation of the lattice.

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