Abstract

We investigate the formation of polarized vortex solitons in nonlocal media with Bessel optical lattices and show the various dynamics of these solitons. Particularly, the stable high-order polarized vortex solitons, which are not found in local media with Bessel optical lattices, are found in nonlocal media. It is found that the nonlocal nonlinearity plays an important role in the stability of these solitons which is similar to that of phase vortex solitons. However, we show that the dynamics of these polarized vortex solitons are quite different from the phase vortex solitons.

© 2015 Optical Society of America

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References

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2013 (1)

Q. Li, Y. H. Zhai, G. Liang, and Q. Guo, “The characteristics of elliptical optical soliton in anisotropic medium,” Wuli Xuebao 62(2), 024202 (2013).

2012 (2)

B. Z. Zhang, H. C. Wang, G. Y. Luo, W. Q. Man, and Y. H. Zheng, “High-order polarization vortex spatial solitons,” Phys. Lett. A 376(45), 3051–3056 (2012).
[Crossref]

B. Gu and Y. Cui, “Nonparaxial and paraxial focusing of azimuthal-variant vector beams,” Opt. Express 20(16), 17684–17694 (2012).
[Crossref] [PubMed]

2011 (2)

L. Ge, Q. Wang, M. Shen, J. L. Shi, and Q. Kong, “Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media,” Optik (Stuttg.) 122(9), 749–753 (2011).
[Crossref]

B. Z. Zhang, “Polarization vortex spatial optical solitons in Bessel optical lattices,” Phys. Lett. A 375(7), 1110–1115 (2011).
[Crossref]

2010 (1)

2009 (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

2008 (2)

D. Deng and Q. Guo, “Propagation of Laguerre–Gaussian beams in nonlocal nonlinear media,” J. Opt. A, Pure Appl. Opt. 10(3), 035101 (2008).
[Crossref]

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33(1), 13–15 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (2)

2005 (5)

C. Conti, M. Peccianti, and G. Assanto, “Spatial solitons and modulational instability in the presence of large birefringence: the case of highly nonlocal liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066614 (2005).
[Crossref] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref] [PubMed]

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(7), 073902 (2005).
[Crossref] [PubMed]

A. Ferrando, M. Zacarés, and M. A. García-March, “Vorticity Cutoff in Nonlinear Photonic Crystals,” Phys. Rev. Lett. 95(4), 043901 (2005).
[Crossref] [PubMed]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13(2), 435–443 (2005).
[Crossref] [PubMed]

2004 (2)

2002 (1)

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066615 (2002).
[Crossref] [PubMed]

2000 (1)

1996 (1)

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, “Spatial solitons and modulational instability in the presence of large birefringence: the case of highly nonlocal liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066614 (2005).
[Crossref] [PubMed]

Bang, O.

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13(2), 435–443 (2005).
[Crossref] [PubMed]

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066615 (2002).
[Crossref] [PubMed]

Briedis, D.

Brown, T.

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref] [PubMed]

Ciattoni, A.

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(7), 073902 (2005).
[Crossref] [PubMed]

Cohen, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref] [PubMed]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, “Spatial solitons and modulational instability in the presence of large birefringence: the case of highly nonlocal liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066614 (2005).
[Crossref] [PubMed]

Crosignani, B.

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(7), 073902 (2005).
[Crossref] [PubMed]

Cui, Y.

Deng, D.

D. Deng and Q. Guo, “Propagation of Laguerre–Gaussian beams in nonlocal nonlinear media,” J. Opt. A, Pure Appl. Opt. 10(3), 035101 (2008).
[Crossref]

Di Porto, P.

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(7), 073902 (2005).
[Crossref] [PubMed]

Edmundson, D.

Ferrando, A.

A. Ferrando, M. Zacarés, and M. A. García-March, “Vorticity Cutoff in Nonlinear Photonic Crystals,” Phys. Rev. Lett. 95(4), 043901 (2005).
[Crossref] [PubMed]

Gaeta, A. L.

García-March, M. A.

A. Ferrando, M. Zacarés, and M. A. García-March, “Vorticity Cutoff in Nonlinear Photonic Crystals,” Phys. Rev. Lett. 95(4), 043901 (2005).
[Crossref] [PubMed]

Ge, L.

L. Ge, Q. Wang, M. Shen, J. L. Shi, and Q. Kong, “Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media,” Optik (Stuttg.) 122(9), 749–753 (2011).
[Crossref]

Grow, T. D.

Gu, B.

Guo, Q.

Q. Li, Y. H. Zhai, G. Liang, and Q. Guo, “The characteristics of elliptical optical soliton in anisotropic medium,” Wuli Xuebao 62(2), 024202 (2013).

D. Deng and Q. Guo, “Propagation of Laguerre–Gaussian beams in nonlocal nonlinear media,” J. Opt. A, Pure Appl. Opt. 10(3), 035101 (2008).
[Crossref]

Gutiérrez-Vega, J. C.

Haus, J. W.

Ishaaya, A. A.

Kawauchi, H.

Kong, Q.

L. Ge, Q. Wang, M. Shen, J. L. Shi, and Q. Kong, “Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media,” Optik (Stuttg.) 122(9), 749–753 (2011).
[Crossref]

Kozawa, Y.

Krolikowski, W.

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13(2), 435–443 (2005).
[Crossref] [PubMed]

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066615 (2002).
[Crossref] [PubMed]

Li, Q.

Q. Li, Y. H. Zhai, G. Liang, and Q. Guo, “The characteristics of elliptical optical soliton in anisotropic medium,” Wuli Xuebao 62(2), 024202 (2013).

Liang, G.

Q. Li, Y. H. Zhai, G. Liang, and Q. Guo, “The characteristics of elliptical optical soliton in anisotropic medium,” Wuli Xuebao 62(2), 024202 (2013).

Lopez-Aguayo, S.

Luo, G. Y.

B. Z. Zhang, H. C. Wang, G. Y. Luo, W. Q. Man, and Y. H. Zheng, “High-order polarization vortex spatial solitons,” Phys. Lett. A 376(45), 3051–3056 (2012).
[Crossref]

Man, W. Q.

B. Z. Zhang, H. C. Wang, G. Y. Luo, W. Q. Man, and Y. H. Zheng, “High-order polarization vortex spatial solitons,” Phys. Lett. A 376(45), 3051–3056 (2012).
[Crossref]

Manela, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref] [PubMed]

Mozumder, Z.

Musslimani, Z. H.

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, “Spatial solitons and modulational instability in the presence of large birefringence: the case of highly nonlocal liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066614 (2005).
[Crossref] [PubMed]

Petersen, D.

Rasmussen, J. J.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066615 (2002).
[Crossref] [PubMed]

Rotschild, C.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref] [PubMed]

Sato, S.

Schadt, M.

Segev, M.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref] [PubMed]

She, W.

Shen, M.

L. Ge, Q. Wang, M. Shen, J. L. Shi, and Q. Kong, “Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media,” Optik (Stuttg.) 122(9), 749–753 (2011).
[Crossref]

Shi, J. L.

L. Ge, Q. Wang, M. Shen, J. L. Shi, and Q. Kong, “Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media,” Optik (Stuttg.) 122(9), 749–753 (2011).
[Crossref]

Stalder, M.

Vuong, L. T.

Wang, H.

Wang, H. C.

B. Z. Zhang, H. C. Wang, G. Y. Luo, W. Q. Man, and Y. H. Zheng, “High-order polarization vortex spatial solitons,” Phys. Lett. A 376(45), 3051–3056 (2012).
[Crossref]

Wang, Q.

L. Ge, Q. Wang, M. Shen, J. L. Shi, and Q. Kong, “Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media,” Optik (Stuttg.) 122(9), 749–753 (2011).
[Crossref]

Wyller, J.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066615 (2002).
[Crossref] [PubMed]

Yang, J. K.

Yariv, A.

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(7), 073902 (2005).
[Crossref] [PubMed]

Yonezawa, K.

Youngworth, K.

Zacarés, M.

A. Ferrando, M. Zacarés, and M. A. García-March, “Vorticity Cutoff in Nonlinear Photonic Crystals,” Phys. Rev. Lett. 95(4), 043901 (2005).
[Crossref] [PubMed]

Zhai, Y. H.

Q. Li, Y. H. Zhai, G. Liang, and Q. Guo, “The characteristics of elliptical optical soliton in anisotropic medium,” Wuli Xuebao 62(2), 024202 (2013).

Zhan, Q.

Zhang, B. Z.

B. Z. Zhang, H. C. Wang, G. Y. Luo, W. Q. Man, and Y. H. Zheng, “High-order polarization vortex spatial solitons,” Phys. Lett. A 376(45), 3051–3056 (2012).
[Crossref]

B. Z. Zhang, “Polarization vortex spatial optical solitons in Bessel optical lattices,” Phys. Lett. A 375(7), 1110–1115 (2011).
[Crossref]

Zheng, Y. H.

B. Z. Zhang, H. C. Wang, G. Y. Luo, W. Q. Man, and Y. H. Zheng, “High-order polarization vortex spatial solitons,” Phys. Lett. A 376(45), 3051–3056 (2012).
[Crossref]

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

D. Deng and Q. Guo, “Propagation of Laguerre–Gaussian beams in nonlocal nonlinear media,” J. Opt. A, Pure Appl. Opt. 10(3), 035101 (2008).
[Crossref]

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

Opt. Express (8)

Opt. Lett. (3)

Optik (Stuttg.) (1)

L. Ge, Q. Wang, M. Shen, J. L. Shi, and Q. Kong, “Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media,” Optik (Stuttg.) 122(9), 749–753 (2011).
[Crossref]

Phys. Lett. A (2)

B. Z. Zhang, “Polarization vortex spatial optical solitons in Bessel optical lattices,” Phys. Lett. A 375(7), 1110–1115 (2011).
[Crossref]

B. Z. Zhang, H. C. Wang, G. Y. Luo, W. Q. Man, and Y. H. Zheng, “High-order polarization vortex spatial solitons,” Phys. Lett. A 376(45), 3051–3056 (2012).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, “Generic features of modulational instability in nonlocal Kerr media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066615 (2002).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Spatial solitons and modulational instability in the presence of large birefringence: the case of highly nonlocal liquid crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(6), 066614 (2005).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref] [PubMed]

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(7), 073902 (2005).
[Crossref] [PubMed]

A. Ferrando, M. Zacarés, and M. A. García-March, “Vorticity Cutoff in Nonlinear Photonic Crystals,” Phys. Rev. Lett. 95(4), 043901 (2005).
[Crossref] [PubMed]

Wuli Xuebao (1)

Q. Li, Y. H. Zhai, G. Liang, and Q. Guo, “The characteristics of elliptical optical soliton in anisotropic medium,” Wuli Xuebao 62(2), 024202 (2013).

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Figures (9)

Fig. 1
Fig. 1 The intensity (left) and phase (right) distribution of soliton solutions of Eq. (5) with Γ = 3 . (a)   σ 0 = 0.5 , P = 1 ;(b) σ 0 = 2 , P = 2 .
Fig. 2
Fig. 2 The power curve of PV solitons with Γ = 3 , P = 1 .
Fig. 3
Fig. 3 The evolution of the intensity | E | 2 distribution of polarized vortex solitons with σ 0 = 0.3 , P = 1 .
Fig. 4
Fig. 4 The dynamics of polarized vortex solitons (a) σ 0 = 0.5 , P = 1 ;(b) σ 0 = 1 , P = 1 .
Fig. 5
Fig. 5 The dynamics of polarized vortex solitons with σ 0 = 2 , P = 2 .
Fig. 6
Fig. 6 The dynamics of polarized vortex solitons with σ 0 = 2 , P = 2 .
Fig. 7
Fig. 7 (a) The zeroth-order optical Bessel lattice potential with p = 6 ; (b) the first-order optical Bessel lattice potential with p = 6 .
Fig. 8
Fig. 8 The dynamics of polarized vortex solitons with σ 0 = 0.2 , P = 1 in zeroth-order Bessel optical lattices.
Fig. 9
Fig. 9 The dynamics of polarized vortex solitons in first-order Bessel optical lattices: (a) σ 0 = 0.1 , P = 1 ; (b) σ 0 = 0.5 , P = 1 .

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

i E z + T 2 E + E R ( r r ) | E ( r ) | 2 d r V ( x , y ) E = 0 ,
E x ( ρ , θ , z ) = U ( ρ ) cos ( P θ + φ 0 ) exp ( i Γ z ) , E y ( ρ , θ , z ) = U ( ρ ) sin ( P θ + φ 0 ) exp ( i Γ z ) ,
2 U x ρ 2 + 1 ρ U x ρ P 2 U x ρ 2 Γ U x + U x R ( r r ) U 2 d r V ( x , y ) U x = 0 ,
2 U y ρ 2 + 1 ρ U y ρ P 2 U y ρ 2 Γ U y + U y R ( r r ) U 2 d r V ( x , y ) U y = 0 ,
d 2 U d ρ 2 + 1 ρ d U d ρ P 2 ρ 2 U Γ U + U R ( r r ) U 2 d r V ( x , y ) U = 0 ,
T 2 Ψ Γ Ψ + Ψ R ( r r ) | Ψ | 2 d r V ( x , y ) Ψ = 0 ,
F ( Ψ m + 1 ) = 1 | k | 2 + c [ P ( η L ) P ( η N ) ] 1 / 2 [ ( c Γ ) F ( Ψ m ) F ( V Ψ m ) ]                                     + 1 | k | 2 + c [ P ( η L ) P ( η N ) ] 3 / 2 F ( Ψ m R ( r r ) | Ψ ( r ) m | 2 d r )
P ( η L ) = [ ( | k | 2 + Γ ) F ( Ψ m ) + F ( V Ψ m ) ] F ( Ψ m ) * d k ,
P ( η N ) = [ F ( Ψ m R ( r r ) | Ψ ( r ) m | 2 d r ) ] F ( Ψ m ) * d k ,

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