Abstract

Transverse instabilities are shown to accompany counterpropagation of optical beams through reflection gratings in Kerr media. The instability threshold of continuous waves is analytically derived, and it is shown that the presence of the grating broadens and narrows the stability region of plane waves in focusing and defocusing media, respectively. Furthermore, counterpropagating soliton stability is numerically investigated and compared with the transverse modulation instability analysis, revealing an underlying physical link.

© 2006 Optical Society of America

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References

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2006 (2)

2005 (1)

2003 (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

2002 (2)

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 15, 2031 (2002).
[CrossRef]

O. Cohen, R. Uzdin, T. Carmon, J. W. Flescher, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 1339001 (2002).

1993 (1)

1990 (1)

Belic, M.

Carmon, T.

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 15, 2031 (2002).
[CrossRef]

O. Cohen, R. Uzdin, T. Carmon, J. W. Flescher, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 1339001 (2002).

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Ciattoni, A.

Cohen, O.

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 15, 2031 (2002).
[CrossRef]

O. Cohen, R. Uzdin, T. Carmon, J. W. Flescher, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 1339001 (2002).

DelRe, E.

Denz, C.

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Feng, J.

Firth, W. J.

Fischer, R. A.

R. A. Fischer, Optical Phase Conjugation (Academic, 1983).

Fitzgerlad, A.

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Flescher, J. W.

O. Cohen, R. Uzdin, T. Carmon, J. W. Flescher, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 1339001 (2002).

Jander, Ph.

Jovic, D.

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Odoulov, S.

O. Cohen, R. Uzdin, T. Carmon, J. W. Flescher, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 1339001 (2002).

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 15, 2031 (2002).
[CrossRef]

Palange, E.

Paré, C.

Petrovic, M.

Rizza, C.

Schröeder, J.

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 15, 2031 (2002).
[CrossRef]

O. Cohen, R. Uzdin, T. Carmon, J. W. Flescher, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 1339001 (2002).

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Uzdin, R.

O. Cohen, R. Uzdin, T. Carmon, J. W. Flescher, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 1339001 (2002).

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

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

O. Cohen, R. Uzdin, T. Carmon, J. W. Flescher, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 1339001 (2002).

Other (1)

R. A. Fischer, Optical Phase Conjugation (Academic, 1983).

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Figures (3)

Fig. 1
Fig. 1

Static curves (solid curves) at which perturbations are stationary ( λ = 0 ) and an oblique asymptote (dashed line) limiting from above the region where instabilities can occur. The plotted curves are obtained from Eq. (5) at exact Bragg matching of background plane waves ( η = 0 ) , and they are the closest to the stability region. In the gray zone perturbations are stable, being characterized by R e λ < 0 .

Fig. 2
Fig. 2

Stationary profile of U + obtained by solving Eqs. (1) numerically for the soliton dimensionless intensity I = 8 ( 3 L ) and η = 0 . The deviation from the exact soliton profile is associated with the transverse perturbations that arise during the transient.

Fig. 3
Fig. 3

Soliton intensity I versus transverse wave vector K (solid straight segments), in the plane ( K 2 L 2 , L I ) , of the perturbations arising during soliton formation. The gray zone is the plane-wave stability region.

Equations (6)

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( i ζ + i τ + 1 2 2 ξ 2 ) U + = g 2 exp ( i η ζ + i L + i θ ) U γ 2 [ U + 2 + 2 U 2 ] U + ,
( i ζ i τ 1 2 2 ξ 2 ) U = g 2 exp ( i η ζ i L i θ ) U + + γ 2 [ 2 U + 2 + U 2 ] U ,
g = σ ( η 3 γ I )
f = f + ( ζ ) exp ( i K ξ + λ τ ) + f * ( ζ ) exp ( i K ξ + λ * τ ) = b + ( ζ ) exp ( i K ξ + λ τ ) + b * ( ζ ) exp ( i K ξ + λ * τ ) ,
[ i d d ζ + i λ + 1 2 ( γ I σ g K 2 ) ] f + + γ I 2 f + ( g 2 + γ I ) b + + γ I b = 0 ,
2 + 2 cos Q + cos Q + L 2 ( g + γ I ) ( g + 3 γ I ) + 4 ρ + ρ 2 Q + Q sin Q + sin Q = 0 ,

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