Abstract

Radially polarized, circularly symmetric optical vortex solitons are shown to be able to exist in Kerr media beyond paraxial approximation. Unlike those of the paraxial linearly polarized counterparts, the topological charges of these solitons should not be less than 2. The properties associated with these solitons, such as their spatial width, and longitudinal and transverse field profiles, are characterized to depend on their normalized asymptotic intensity u2 and nonparaxial degree. It is found that the asymptotic intensity u2 of these solitons cannot exceed a threshold value in correspondence of which their width reaches a minimum value.

© 2006 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  15. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, "Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings," Opt. Lett. 27, 285 (2002).
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2005 (6)

2004 (1)

2003 (1)

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, "Self-consistent treatment of the full vectorial nonlinear optical pulse propagation equation in an isotropic medium," Opt. Commun. 221, 337 (2003).
[CrossRef]

2002 (1)

2000 (2)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Asman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

A. Ciattoni, P. Di. Porto, B. Crosignani, and A. Yariv, "Vectorial non-paraxial propagation equation in the presence of a tensorial refractive-index perturbation," J. Opt. Soc. Am. B 17, 809 (2000).
[CrossRef]

1995 (1)

1994 (1)

1990 (1)

1982 (1)

1965 (1)

P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Asman, E.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Asman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Band, Y. B.

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, "Self-consistent treatment of the full vectorial nonlinear optical pulse propagation equation in an isotropic medium," Opt. Commun. 221, 337 (2003).
[CrossRef]

Biener, G.

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Asman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Bomzon, Z.

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, "Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings," Opt. Lett. 27, 285 (2002).
[CrossRef]

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Asman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Chen, Y.

Chi, S.

Ciattoni, A.

Crosignani, B.

Cutolo, A.

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Asman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Di, P.

Di Porto, P.

Ford, D. H.

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Asman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Guo, Q.

Hasman, E.

Kelley, P. L.

P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Kimura, W. D.

Kleiner, V.

Kozawa, Y.

Matuszewski, M.

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, "Self-consistent treatment of the full vectorial nonlinear optical pulse propagation equation in an isotropic medium," Opt. Commun. 221, 337 (2003).
[CrossRef]

Mitchell, D. J.

Mookherjea, S.

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Asman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

Sato, S.

She, W.

Snyder, A. W.

Tidwell, S. C.

Trippenbach, M.

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, "Self-consistent treatment of the full vectorial nonlinear optical pulse propagation equation in an isotropic medium," Opt. Commun. 221, 337 (2003).
[CrossRef]

Wang, H.

Wasilewski, W.

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, "Self-consistent treatment of the full vectorial nonlinear optical pulse propagation equation in an isotropic medium," Opt. Commun. 221, 337 (2003).
[CrossRef]

Yariv, A.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon and E. Asman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

M. Matuszewski, W. Wasilewski, M. Trippenbach, and Y. B. Band, "Self-consistent treatment of the full vectorial nonlinear optical pulse propagation equation in an isotropic medium," Opt. Commun. 221, 337 (2003).
[CrossRef]

H. Wang and W. She, "Modulation instability and interaction of non-paraxial beams in self-focusing Kerr Media," Opt. Commun. 254, 145 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. Lett. (2)

P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

A. Ciattoni, B. Crosignani, P. Di. Porto, and A. Yariv, "Azimuthally polarized spatial dark solitons: exact solutions of Maxwell's equations in a Kerr medium," Phys. Rev. Lett. 94, 073902 (2005).
[CrossRef] [PubMed]

Other (1)

Yu. S. Kivshar and G. P. Agrawal, Optical solitons: From Fiber to Photonic Crystals (Academic Press, San Diego, 2003) and references therein.

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Figures (2)

Fig. 1.
Fig. 1.

Plots of (a) transverse component u(ρ) and (b) longitudinal component u 3(ρ) of nonparaxial double-charged vortex solitons for various values of u ; (c) and (d): the analogous plots of triple-charged vortex solitons.

Fig. 2.
Fig. 2.

Existence curves of non-paraxial double-(solid curve) and triple-charged (dashed curve) vortex solitons when f 2=0.015.

Equations (18)

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× E = i ω B , × B = i ω c 2 n 0 2 E i ω μ 0 P nl .
P n l = 4 3 ε 0 n 0 n 2 [ E 2 E + 1 2 ( E E ) E * ] ,
× × E = k 2 E + 4 3 k 2 n 2 n 0 [ E 2 E + 1 2 ( E E ) E * ] ,
E = 4 3 n 2 n 0 [ E 2 E + 1 2 ( E E ) E * ] .
E 1 = E r cos θ , E 2 = E r sin θ ,
E = E 1 e x + E 2 e y = E r e r .
s = x r 0 , t = y r 0 , ρ = s 2 + t 2 , ξ = z ( k r 0 2 ) , U = k r 0 n 2 n 0 exp ( ik z ) E ,
f 2 2 U ρ ξ 2 + 2 i U ρ ξ + 1 ρ ρ ( ρ U ρ ρ ) + 1 ρ 2 ( 2 U ρ θ 2 U ρ ) 2 U ρ 2 U ρ 2 3 f 2 U ρ ρ + U ρ ρ 2 U ρ
2 f 2 ρ [ 1 ρ ρ ( ρ U ρ 2 U ρ ) ] = 0 ,
U 3 = if ( U ρ ρ + U ρ ρ ) + O ( f 3 ) .
U ρ ( ρ , θ , ξ ) = u ( ρ ) exp ( imθ ) exp ( i β ξ ) ,
U 3 ( ρ , θ , ξ ) = u 3 ( ρ ) exp ( imθ ) exp ( i β ξ ) ,
( β f 2 + 2 β ) u + 1 ρ u ρ + 2 u ρ 2 m 2 + 1 ρ 2 u 2 u 3 2 3 f 2 ( u ρ + u ρ ) 2 u 2 f 2 ρ [ 1 ρ ρ ( ρ u 3 ) ] = 0 ,
u 3 ( ρ ) = if ( u ρ + u ρ ) .
u ( 0 ) = 0 , u ( ) = u , u ' ( ) = 0 , u ' ' ( ) = 0 ,
u ( ρ ) = δ ρ m 2 + 1 + O ( ρ 2 + m 2 + 1 ) ,
β = f 2 ( 1 ± 1 2 f 2 u 2 ) ,
u < 1 ( 2 f ) .

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