Abstract

We show that the nonlinear equation that describes nonparaxial Kerr propagation, together with the already reported bright-soliton solutions, admits of 1+1D dark-soliton solutions. Unlike their paraxial counterparts, dark solitons can be excited only if their asymptotic normalized intensity u2 is below 3/7; their width becomes constant when u2 approaches this value.

© 2005 Optical Society of America

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References

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2004

2003

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, Opt. Commun. 221, 337 (2003).
[CrossRef]

2002

2001

G. Fibich and B. Ilan, Physica D 157, 112 (2001).
[CrossRef]

2000

S. Blair, Chaos 10, 570 (2000).
[CrossRef]

R. de la Fuente, R. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
[CrossRef]

A. Ciattoni, P. Di Porto, B. Crosignani, and A. Yariv, J. Opt. Soc. Am. B 17, 809 (2000).
[CrossRef]

1999

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1999).

1997

1995

1991

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. K. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef]

Andersen, D. R.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. K. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef]

Band, Y. B.

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, Opt. Commun. 221, 337 (2003).
[CrossRef]

Blair, S.

S. Blair, Chaos 10, 570 (2000).
[CrossRef]

Chi, S.

Ciattoni, A.

Conti, C.

Crosignani, B.

de la Fuente, R.

R. de la Fuente, R. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
[CrossRef]

DelRe, E.

Di Porto, P.

Fibich, G.

G. Fibich and B. Ilan, Physica D 157, 112 (2001).
[CrossRef]

Guo, Q.

Ilan, B.

G. Fibich and B. Ilan, Physica D 157, 112 (2001).
[CrossRef]

Kaplan, A. K.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. K. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef]

Marinov, K.

K. Marinov, D. I. Pushkarov, and A. Shivarova, in Soliton-Driven Photonics, A. D. Boardman and A. P. Sukhorukov, eds. (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 293–316.
[CrossRef]

Matuszewski, M.

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, Opt. Commun. 221, 337 (2003).
[CrossRef]

Michinel, H.

R. de la Fuente, R. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
[CrossRef]

Mookherjea, S.

Pushkarov, D. I.

K. Marinov, D. I. Pushkarov, and A. Shivarova, in Soliton-Driven Photonics, A. D. Boardman and A. P. Sukhorukov, eds. (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 293–316.
[CrossRef]

Regan, J. J.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. K. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef]

Segev, M.

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1999).

Shivarova, A.

K. Marinov, D. I. Pushkarov, and A. Shivarova, in Soliton-Driven Photonics, A. D. Boardman and A. P. Sukhorukov, eds. (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 293–316.
[CrossRef]

Stegeman, G. I.

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1999).

Swartzlander, G. A.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. K. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef]

Trippenbach, M.

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, Opt. Commun. 221, 337 (2003).
[CrossRef]

Varela, R.

R. de la Fuente, R. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
[CrossRef]

Wasilewski, W.

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, Opt. Commun. 221, 337 (2003).
[CrossRef]

Yariv, A.

Yin, H.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. K. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef]

Chaos

S. Blair, Chaos 10, 570 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, Opt. Commun. 221, 337 (2003).
[CrossRef]

R. de la Fuente, R. Varela, and H. Michinel, Opt. Commun. 173, 403 (2000).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. K. Kaplan, Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef]

Phys. Today

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1999).

Physica D

G. Fibich and B. Ilan, Physica D 157, 112 (2001).
[CrossRef]

Other

K. Marinov, D. I. Pushkarov, and A. Shivarova, in Soliton-Driven Photonics, A. D. Boardman and A. P. Sukhorukov, eds. (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 293–316.
[CrossRef]

S. Trillo and W. Torruelas, eds. Spatial Solitons (Springer-Verlag, Berlin, 2001).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Soliton envelope uξ and intensity u2ξ for various values of u2<3/7.

Fig. 2
Fig. 2

Normalized soliton half-width Δ as a function of u2 in the paraxial (lower curve) and nonparaxial (upper curve) regimes.

Fig. 3
Fig. 3

Square modulus of field amplitude Uξ,ζ2 for four diffraction lengths obtained by solution of Eq. (2)γ=-1 with boundary condition Uξ,0=uξ for u=0.3.

Fig. 4
Fig. 4

Envelope vξ of the longitudinal field component of the soliton for the same values of u as in Fig. 1.

Equations (11)

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iz+12k2x2A=-kn2n0A2A+13k2A22Ax2+83k2AAx2+56k2A22A*x2,
iζ+122ξ2U=-γU2U+13U22Uξ2+83UUξ2+56U22U*ξ2,
-βu+12u=-γu3+76u2u+83uu2,
dfdu+γ32u3+7γu2f=12β-γu23+7γu2u,
dudξ2=3γ8β+323-623u2+fu0-3γ8×β+323+623u023+7γu023+7γu216/17,
d2udξ=-623u-16γfu0-3γ8β+323+623u02×3+7γu0216/73+7γu2-23/7u.
0=3γ8β+323-623u2+f0-3γ8×β+32333+7γu216/7,  0=-623-16γf0-3γ8×β+32313+7γu233+7γu216/7,
f0=38u2+3γ23-91841+7γ3u223/7,
fu=38u2+3γ23-623u2-3γ1843+7γu23+7γu23+7γu216/7.
fu=38u2-323-623u2+31843-7u23-7u23-7u216/7,
v=1-43u2+32v2uξ-43vu2,

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