Abstract

Optical vortex solitons in a defocusing saturable medium are analyzed in the framework of the (2+1)-dimensional generalized nonlinear Schrödinger equation. Stationary, radially symmetric localized solutions with nonvanishing asymptotics and a phase singularity (vortex solitons) are found numerically for the varying saturation parameter. Relaxation of some localized initial profiles (e.g., vortex-type structures of an elliptic shape) to a vortex soliton is investigated numerically and then compared with the experimentally measured propagation of the vortex solitons created by a laser beam passed through a rubidium vapor, known as a nonlinear medium with strong saturation of the nonlinear refractive index. Reasonably good agreement is found, supporting the validity of the phenomenological model of the saturable nonlinear medium.

© 1998 Optical Society of America

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    [CrossRef] [PubMed]
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  22. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108 (1997).
    [CrossRef]

1997

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108 (1997).
[CrossRef]

1996

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beam in anisotropic nonlinear medium: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Breakup of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25 (1996).
[CrossRef]

1995

D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar ; “Self-focusing of plane dark solitons in defocusing media,” Phys. Rev. E 51, 5016 (1995).
[CrossRef]

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

1994

1993

1992

A. W. Snyder, L. Poladian, and D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281 (1992).
[CrossRef]

1991

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

1988

E. A. Kuznetsov and S. K. Turitsyn, “Instability and collapse of solitons in media with a defocusing nonlinearity,” Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

1981

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pipipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Eksp. Teor. Fiz. 33, 206 (1981) [JETP Lett. 33, 195 (1981)].

1974

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eksp. Teor. Fiz. 65 997 (1973) [Sov. Phys. JETP 38, 494 (1974)].

1961

L. P. Pitaevskii, “Vortex lines in an imperfect Bose gas,” Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].

1958

V. L. Ginzburg and L. P. Pitaevskii, “On the theory of superfluidity,” Zh. Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 34, 858 (1958)].

Andersen, D. R.

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Anderson, D. Z.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Breakup of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beam in anisotropic nonlinear medium: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

Baranova, N. B.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pipipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Eksp. Teor. Fiz. 33, 206 (1981) [JETP Lett. 33, 195 (1981)].

Crosignani, B.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

Di Porto, P.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

Duree, G.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

Firth, W. J.

G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281 (1992).
[CrossRef]

Ginzburg, V. L.

V. L. Ginzburg and L. P. Pitaevskii, “On the theory of superfluidity,” Zh. Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 34, 858 (1958)].

Kaplan, A. E.

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Kivshar, Yu. S.

D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar ; “Self-focusing of plane dark solitons in defocusing media,” Phys. Rev. E 51, 5016 (1995).
[CrossRef]

Kuznetsov, E. A.

E. A. Kuznetsov and S. K. Turitsyn, “Instability and collapse of solitons in media with a defocusing nonlinearity,” Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

Law, C. T.

C. T. Law and G. A. Swartzlander, Jr., “Optical vortex solitons and the stability of dark soliton stripes,” Opt. Lett. 18, 586 (1993).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

Luther-Davies, B.

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Breakup of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beam in anisotropic nonlinear medium: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pipipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Eksp. Teor. Fiz. 33, 206 (1981) [JETP Lett. 33, 195 (1981)].

McDonald, G. S.

G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281 (1992).
[CrossRef]

Mitchell, D. J.

Morin, M.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

Pelinovsky, D. E.

D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar ; “Self-focusing of plane dark solitons in defocusing media,” Phys. Rev. E 51, 5016 (1995).
[CrossRef]

Pipipetskii, N. F.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pipipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Eksp. Teor. Fiz. 33, 206 (1981) [JETP Lett. 33, 195 (1981)].

Pitaevskii, L. P.

L. P. Pitaevskii, “Vortex lines in an imperfect Bose gas,” Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].

V. L. Ginzburg and L. P. Pitaevskii, “On the theory of superfluidity,” Zh. Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 34, 858 (1958)].

Poladian, L.

Powles, R.

Regan, J. J.

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Rubenchik, A. M.

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eksp. Teor. Fiz. 65 997 (1973) [Sov. Phys. JETP 38, 494 (1974)].

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Breakup of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beam in anisotropic nonlinear medium: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

Salamo, G.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

Segev, M.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

Sharp, E.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

Shkunov, V. V.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pipipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Eksp. Teor. Fiz. 33, 206 (1981) [JETP Lett. 33, 195 (1981)].

Snyder, A. W.

Stepanyants, Yu. A.

D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar ; “Self-focusing of plane dark solitons in defocusing media,” Phys. Rev. E 51, 5016 (1995).
[CrossRef]

Swartzlander , Jr., G. A.

C. T. Law and G. A. Swartzlander, Jr., “Optical vortex solitons and the stability of dark soliton stripes,” Opt. Lett. 18, 586 (1993).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Syed, K. S.

G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281 (1992).
[CrossRef]

Tikhonenko, V.

Turitsyn, S. K.

E. A. Kuznetsov and S. K. Turitsyn, “Instability and collapse of solitons in media with a defocusing nonlinearity,” Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

Yariv, A.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

Yin, H.

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eksp. Teor. Fiz. 65 997 (1973) [Sov. Phys. JETP 38, 494 (1974)].

Zel’dovich, B. Ya.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pipipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Eksp. Teor. Fiz. 33, 206 (1981) [JETP Lett. 33, 195 (1981)].

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Breakup of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beam in anisotropic nonlinear medium: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

Europhys. Lett.

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Breakup of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25 (1996).
[CrossRef]

JETP Lett.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pipipetskii, and V. V. Shkunov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Eksp. Teor. Fiz. 33, 206 (1981) [JETP Lett. 33, 195 (1981)].

Opt. Commun.

G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beam in anisotropic nonlinear medium: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870 (1996).
[CrossRef] [PubMed]

Phys. Rev. E

D. E. Pelinovsky, Yu. A. Stepanyants, and Yu. S. Kivshar ; “Self-focusing of plane dark solitons in defocusing media,” Phys. Rev. E 51, 5016 (1995).
[CrossRef]

Phys. Rev. Lett.

G. A. Swartzlander, Jr., D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583 (1991).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262 (1996).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978 (1995).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108 (1997).
[CrossRef]

Sov. Phys. JETP

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eksp. Teor. Fiz. 65 997 (1973) [Sov. Phys. JETP 38, 494 (1974)].

E. A. Kuznetsov and S. K. Turitsyn, “Instability and collapse of solitons in media with a defocusing nonlinearity,” Zh. Eksp. Teor. Fiz. 94, 119 (1988) [Sov. Phys. JETP 67, 1583 (1988)].

V. L. Ginzburg and L. P. Pitaevskii, “On the theory of superfluidity,” Zh. Eksp. Teor. Fiz. 34, 1240 (1958) [Sov. Phys. JETP 34, 858 (1958)].

L. P. Pitaevskii, “Vortex lines in an imperfect Bose gas,” Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].

Other

V. Tikhonenko, J. Christou, B. Luther-Davies, and Y. S. Kivshar, “Creation of vortex pairs via transverse instability of dark solitons,” in Proceedings of the 20th Australian Conference on Optical Fibre Technology ACOFT’95 (Institution of Radio and Electronics Engineers Australia Society, Milsons Point, NSW, Australia, 1995), pp. 51–54; V. Tikhonenko, J. Christou, B. Luther-Davies, and Y. S. Kivshar, “Observation of vortex solitons created by the instability of dark soliton stripes,” Opt. Lett. 21, 1129 (1996).
[CrossRef] [PubMed]

S. Baluschev, A. Dreischuh, I. Velchev, S. Dinev, and O. Marazov “Generation and evolution of two-dimensional dark spatial solitons,” Phys. Rev. E 52, 5517 (1995); S. Baluchev, A. Dreischuh, I. Velchev, S. Dinev, and O. Marazov, “Odd and even two-dimensional dark spatial solitons,” Appl. Phys. B 61, 121 (1995).
[CrossRef]

V. E. Zakharov and A. B. Shabat, “Interactions between solitons in a stable medium,” Zh. Eksp. Teor. Fiz. 64 1623 (1973) [Sov. Phys. JETP 37, 823 (1973)]; see also Yu. S. Kivshar, “Dark solitons in nonlinear optics,” IEEE J. Quantum Electron. 28, 250 (1993); Yu. S. Kivshar and B. Luther-Davies, “Optical dark solitons: physics and applications,” Phys. Rep. (to be published).
[CrossRef]

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037 (1990) [JETP Lett. 52, 429 (1990)]; I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604 (1995).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Profiles A(r) of the vortex soliton amplitude defined by Eq. (7) for (a) the single-charged vortex soliton and (b) the double-charged vortex soliton for several values of the dimensionless saturation parameter, s=0, 1, 5.

Fig. 2
Fig. 2

Diameters of the vortex soliton de2 and d05 as functions of the dimensionless saturation parameter s. The dashed curve is the analytical prediction that follows from Eq. (9).

Fig. 3
Fig. 3

Spatial evolution of a radially symmetric input vortex structure [Eq. (10)] with s=1 when its initial diameter d is approximately two times smaller than that of the corresponding vortex diameter: (a) diameters d05 and de2 as functions of the propagation distance z; (b) intensity profiles |u|2 for the values of the propagation distance z equal to 1, 5, 10, and 15.  

Fig. 4
Fig. 4

Same as in Fig. 3 but for the case when the input beam diameter d is approximately two times larger than the diameter of the corresponding vortex soliton.

Fig. 5
Fig. 5

Spatial evolution of the single-charged (|m|=1) elliptical vortex-type input beam [Eq. (11)] for s=1, d05, x=3, and d05, y=6. (a)–(f) Correspond to the values of the propagation distance z changing from 0 through 5 in increments of 1.

Fig. 6
Fig. 6

Schematic presentation of the experimental setup for the measurement of the vortex parameters.

Fig. 7
Fig. 7

Experimentally observed evolution of the output vortex soliton profile (binary images). The experimental parameters in (a) correspond to row 1 of Table 1; those in (b) to row 4; and those in (c) to row 6.

Fig. 8
Fig. 8

Comparison between theory and experiment for the diameters of the vortex soliton versus saturation. Shown are the experimentally measured beam diameter deff (solid curve) as a function of the dimensionless saturation s. The similar value d05 obtained from theory is shown as a long-dashed curve. The short-dashed curve displays the variation of the dimensionless propagation distance.

Tables (1)

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Table 1 Experimental Data

Equations (11)

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nNL(I)=n2I1+I/Isat,
E(R, Z; t)=E(R, Z)exp(iβ0Z-iωt)+c.c.,
2ikn0 EZ+2EX2+2EY2+2n0k2nNL(I)E=0.
βNL=k|n2|I01+I0/Isat
i uz+12 2ux2+2uy2=1s(1+s) 1-1+s1+s|u|2u,
u(r)=A(r)exp(imφ),
d2Adr2+1r dAdr-m2r2 A=2s(1+s) 1-1+s1+sA2A,
A(r)ar|m|+O(r|m|+2)asr0.
A(r)=1-m24r2 (1+s)2+O(r-4)asr.
u(r, z=0)=[1-exp(-r2/d2)]1/2 exp(iφ).
u(r, z=0)=1-exp-x2dx2-y2dy21/2 exp(imφ),

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