Abstract

We study experimentally the nonlinear dynamics of two-color optical vortex beams in the presence of second-harmonic generation combined with the effects of photo- and thermal refraction, as well as self- and induced-phase modulation.We use an iron-doped lithium niobate crystal as a nonlinear medium for the vortex propagation and observe experimentally, depending on the laser wavelength, a decay of a double-charge vortex, splitting and reshaping of background beam, pattern formation, and controllable nonlinear rotation of a vortex pair.

© 2008 Optical Society of America

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2007 (5)

G. Molina Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305-310 (2007).
[CrossRef]

D. Runde, S. Brunken, C. E. Rutter, and D. Kip, "Integrated optical electric field sensor based on a Bragg grating in lithium niobate," Appl. Phys. B 86, 91-95 (2007).

D. N. Neshev et al., "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901-4 (2007).
[CrossRef]

F. Pettazzi, V. Coda, M. Chauvet, and E. Fazio, "Frequency-doubling in self-induced waveguides in lithium niobate," Opt. Commun. 272, 238-241 (2007).
[CrossRef]

I. W. Hsieh, X. G. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. Mcnab, and Y. A. Vlasov, "Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires," Opt. Express 15, 1135-1146 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-3-1135.
[CrossRef]

2006 (2)

K. Bezuhanov, A. Dreischuh, G. G. Paulus, M. G. Schatzel, H. Walther, D. Neshev, W. Krolikowski, and Y. Kivshar, "Spatial phase dislocations in femtosecond laser pulses," J. Opt. Soc. Am. B 23, 26-35 (2006).
[CrossRef]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. Hooft, ’t, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901-4 (2006).
[CrossRef]

2005 (4)

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291-391 (2005).

S. M. Saltiel, A. A. Sukhorukov, and Yu. S. Kivshar, "Multistep parametric processes in nonlinear optics" Prog. Opt. 47, 1-73 (2005).

S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch Marte, "Spiral interferometry," Opt. Lett. 30, 1953-1955 (2005).
[CrossRef]

G. Foo, D. M. Palacios, and G. A. Swartzlander, "Optical vortex coronagraph," Opt. Lett. 30, 3308-3310 (2005).
[CrossRef]

2004 (4)

2003 (3)

2002 (1)

2001 (1)

M. S. Soskin and M. V. Vasnetsov, "Singular optics," Prog. Opt. 42, 219-276 (2001).

2000 (1)

S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, "Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons," Appl. Phys. Lett. 77, 2101-2103 (2000).
[CrossRef]

1999 (6)

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, D. Neshev, and H. Walther, "Modulational instability of multiple-charged optical vortex solitons under saturation of the nonlinearity," Phys. Rev. E 60, 7518-7524 (1999).
[CrossRef]

L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291-372 (1999).

F. Grasbon, A. Dreischuh, G. G. Paulus, F. Zacher, and H. Walther, "Femtosecond interferometric autocorrelations in the presence of pulse front distortions," Proc. SPIE 3571, 164-168 (1999).

S. Lan, M. F. Shih, G. Mizell, J. A. Giordmaine, Z. G. Chen, C. Anastassiou, J. Martin, and M. Segev, "Secondharmonic generation in waveguides induced by photorefractive spatial solitons," Opt. Lett. 24, 1145-1147 (1999).

R. G. Batchko, M. M. Fejer, R. L. Byer, D. Woll, R. Wallenstein, V. Y. Shur, and L. Erman, "Continuous-wave quasi-phase-matched generation of 60 mW at 465 nm by single-pass frequency doubling of a laser diode in backswitch-poled lithium niobate," Opt. Lett. 24, 1293-1295 (1999).

X. An, D. Psaltis, and G.W. Burr, "Thermal fixing of 10,000 holograms in LiNbO3 : Fe," Appl. Opt. 38, 386-393 (1999).

1998 (7)

A. Dreischuh, U. Reiter Domiaty, D. Gruber, L. Windholz, and S. Dinev, "Nonlinear alignment between conical emissions generated in a four-wave parametric mixing process," Appl. Phys. B 66, 175-180 (1998).
[CrossRef]

K. Noguchi, O. Mitomi, and H. Miyazawa, "Millimeter-wave Ti : LiNbO3 optical modulators," J. Lightwave Technol. 16, 615-619 (1998).
[CrossRef]

Yu. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298, 81-197 (1998).
[CrossRef]

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, "Motion control of ensembles of ordered optical vortices generated on finite extent background," Opt. Commun. 151, 413-421 (1998).
[CrossRef]

D. V. Skryabin and W. J. Firth, "Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media," Phys. Rev. E 58, 3916-3930 (1998).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, "Nonlinear singular optics," Pure Appl. Opt. 7, 301-311 (1998).
[CrossRef]

Yu. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, "Dynamics of optical vortex solitons," Opt. Commun. 152, 198-206 (1998).
[CrossRef]

1997 (8)

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, "Self-trapping of an optical vortex by use of the bulk photovoltaic effect," Phys. Rev. Lett. 78, 2948-2951 (1997).
[CrossRef]

L. Torner and D. V. Petrov, "Azimuthal instabilities and self-breaking of beams into sets of solitons in bulk second-harmonic generation," Electron. Lett. 33, 608-610 (1997).
[CrossRef]

A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273-276 (1997).
[CrossRef]

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, "Experimental observation of fluidlike motion of optical vortices," Phys. Rev. Lett. 79, 3399-3402 (1997).
[CrossRef]

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (1997).
[CrossRef]

D. Rozas, C. T. Law, and G. A. Swartzlander, "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3065 (1997).
[CrossRef]

M. F. Shih, Z. G. Chen, M. Mitchell, M. Segev, H. Lee, R. S. Feigelson, and J. P. Wilde, "Waveguides induced by photorefractive screening solitons," J. Opt. Soc. Am. B 14, 3091-3101 (1997).
[CrossRef]

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, "42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate," Opt. Lett. 22, 1834-1836 (1997).

1996 (4)

J. Christou, V. Tikhonenko, Yu. S. Kivshar, and B. Luther-Davies, "Vortex soliton motion and steering," Opt. Lett. 21, 1649-1651 (1996).

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, "Second-harmonic generation and the orbital angular momentum of light," Phys. Rev. A 54, R3742-R3745 (1996).
[CrossRef]

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, "Infrared to ultraviolet measurements of two-photon absorption and n(2) in wide bandgap solids," IEEE J. Quantum Electron. 32, 1324-1333 (1996).
[CrossRef]

S. Orlov, A. Yariv, and M. Segev, "Nonlinear self-phase matching of optical second harmonic generation in lithium niobate," Appl. Phys. Lett. 68, 1610-1612 (1996).
[CrossRef]

1995 (3)

1994 (3)

B. Luther-Davies, R. Powles, and V. Tikhonenko, "Nonlinear rotation of 3-dimensional dark spatial solitons in a gaussian laser-beam," Opt. Lett. 19,1816-1818 (1994).

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50, R4457-R4460 (1994).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50, R4457-R4460 (1994).
[CrossRef]

1993 (3)

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light-beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

G. Indebetouw, "Optical vortices and their propagation," J. Mod. Opt. 40, 73-87 (1993).

B. Crosignani, M. Segev, D. Engin, P. Diporto, A. Yariv, and G. Salamo, "Self-trapping of optical beams in photorefractive media," J. Opt. Soc. Am. B 10, 446-453 (1993).

1992 (1)

1991 (1)

S. Dinev and A. Dreischuh, "Sum-frequency generation in the xuv," Opt. Quantum Electron. 23, 91-97 (1991).
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1990 (3)

1989 (1)

1987 (1)

E. B. Sonin, "Vortex oscillations and hydrodynamics of rotating superfluids," Rev. Mod. Phys. 59, 87-155 (1987).
[CrossRef]

1986 (2)

1973 (1)

K. H. Yang, J. R. Morris, P. L. Richards, and Y. R. Shen, "Phase-matched far-infrared generation by optical mixing of dye laser beams," Appl. Phys. Lett. 23, 669-671 (1973).
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1968 (1)

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, "Holographic storage in lithium niobate," Appl. Phys. Lett. 13, 223 (1968).
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Appl. Opt. (2)

Appl. Phys. B (2)

A. Dreischuh, U. Reiter Domiaty, D. Gruber, L. Windholz, and S. Dinev, "Nonlinear alignment between conical emissions generated in a four-wave parametric mixing process," Appl. Phys. B 66, 175-180 (1998).
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D. Runde, S. Brunken, C. E. Rutter, and D. Kip, "Integrated optical electric field sensor based on a Bragg grating in lithium niobate," Appl. Phys. B 86, 91-95 (2007).

Appl. Phys. Lett. (4)

F. S. Chen, J. T. LaMacchia, and D. B. Fraser, "Holographic storage in lithium niobate," Appl. Phys. Lett. 13, 223 (1968).
[CrossRef]

K. H. Yang, J. R. Morris, P. L. Richards, and Y. R. Shen, "Phase-matched far-infrared generation by optical mixing of dye laser beams," Appl. Phys. Lett. 23, 669-671 (1973).
[CrossRef]

S. Lan, C. Anastassiou, M. Segev, M. Shih, J. A. Giordmaine, and G. Mizell, "Tuning of second-harmonic generation in waveguides induced by photorefractive spatial solitons," Appl. Phys. Lett. 77, 2101-2103 (2000).
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S. Orlov, A. Yariv, and M. Segev, "Nonlinear self-phase matching of optical second harmonic generation in lithium niobate," Appl. Phys. Lett. 68, 1610-1612 (1996).
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Electron. Lett. (1)

L. Torner and D. V. Petrov, "Azimuthal instabilities and self-breaking of beams into sets of solitons in bulk second-harmonic generation," Electron. Lett. 33, 608-610 (1997).
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IEEE J. Quantum Electron. (2)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, "Infrared to ultraviolet measurements of two-photon absorption and n(2) in wide bandgap solids," IEEE J. Quantum Electron. 32, 1324-1333 (1996).
[CrossRef]

D. H. Jundt, M. M. Fejer, and R. L. Byer, "Optical-properties of lithium-rich lithium-niobate fabricated by vapor transport equilibration," IEEE J. Quantum Electron. 26, 135-138 (1990).
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J. Lightwave Technol. (1)

J. Mod. Opt. (1)

G. Indebetouw, "Optical vortices and their propagation," J. Mod. Opt. 40, 73-87 (1993).

J. Opt. Soc. Am. B (10)

A. D. Boardman,W. Ilecki, and Y. Liu, "Spatial solitons in a photorefractive medium sustaining second-harmonic generation," J. Opt. Soc. Am. B 19, 832-838 (2002).
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G. H. Kim, H. J. Lee, L. U. Kim, and H. Suk, "Propagation dynamics of optical vortices with anisotropic phase profiles," J. Opt. Soc. Am. B 20, 351-359 (2003).
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K. Bezuhanov, A. Dreischuh, G. G. Paulus, M. G. Schatzel, H. Walther, D. Neshev, W. Krolikowski, and Y. Kivshar, "Spatial phase dislocations in femtosecond laser pulses," J. Opt. Soc. Am. B 23, 26-35 (2006).
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R. R. Alfano, P. L. Baldeck, P. P. Ho, and G. P. Agrawal, "Cross-phase modulation and induced focusing due to optical nonlinearities in optical fibers and bulk materials," J. Opt. Soc. Am. B 6, 824-829 (1989).

P. P. Ho, D. Ji, Q. Z. Wang, and R. R. Alfano, "Temporal behavior of cross-phase-modulated second-harmonic generation of ultrashort laser pulses in nonlinear-optical media," J. Opt. Soc. Am. B 7, 276-284 (1990)

B. Crosignani, M. Segev, D. Engin, P. Diporto, A. Yariv, and G. Salamo, "Self-trapping of optical beams in photorefractive media," J. Opt. Soc. Am. B 10, 446-453 (1993).

F. S. Roux, "Dynamical behavior of optical vortices," J. Opt. Soc. Am. B 12, 1215-1221 (1995).

V. Tikhonenko, J. Christou, and B. Luther-Davies, "Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium," J. Opt. Soc. Am. B 12, 2046-2052 (1995).

D. Rozas, C. T. Law, and G. A. Swartzlander, "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3065 (1997).
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M. F. Shih, Z. G. Chen, M. Mitchell, M. Segev, H. Lee, R. S. Feigelson, and J. P. Wilde, "Waveguides induced by photorefractive screening solitons," J. Opt. Soc. Am. B 14, 3091-3101 (1997).
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Nat. Phys. (1)

G. Molina Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305-310 (2007).
[CrossRef]

Nature (1)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef]

Opt. Commun. (5)

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, "Motion control of ensembles of ordered optical vortices generated on finite extent background," Opt. Commun. 151, 413-421 (1998).
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Yu. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, "Dynamics of optical vortex solitons," Opt. Commun. 152, 198-206 (1998).
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F. Pettazzi, V. Coda, M. Chauvet, and E. Fazio, "Frequency-doubling in self-induced waveguides in lithium niobate," Opt. Commun. 272, 238-241 (2007).
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A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, "Conversion of topological charge of optical vortices in a parametric frequency converter," Opt. Commun. 140, 273-276 (1997).
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I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light-beams with screw dislocations," Opt. Commun. 103, 422-428 (1993).
[CrossRef]

Opt. Express (1)

Opt. Lett. (13)

V. Z. Kolev, M. J. Lederer, B. Luther-Davies, and A. V. Rode, "Passive mode locking of a Nd:YVO4 laser with an extra-long optical resonator," Opt. Lett. 28, 1275-1277 (2003).
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C. Lou, J. Xu, H. Qiao, X. Zhang, Y. Chen, and Z. Chen, "Enhanced second-harmonic generation by means of high-power confinement in a photovoltaic soliton-induced waveguide," Opt. Lett. 29, 953-955 (2004).
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K. Bezuhanov, A. Dreischuh, G. G. Paulus, M. G. Schatzel, and H. Walther, "Vortices in femtosecond laser fields," Opt. Lett. 29, 1942-1944 (2004).
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S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch Marte, "Spiral interferometry," Opt. Lett. 30, 1953-1955 (2005).
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G. Foo, D. M. Palacios, and G. A. Swartzlander, "Optical vortex coronagraph," Opt. Lett. 30, 3308-3310 (2005).
[CrossRef]

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, "42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate," Opt. Lett. 22, 1834-1836 (1997).

S. Lan, M. F. Shih, G. Mizell, J. A. Giordmaine, Z. G. Chen, C. Anastassiou, J. Martin, and M. Segev, "Secondharmonic generation in waveguides induced by photorefractive spatial solitons," Opt. Lett. 24, 1145-1147 (1999).

R. G. Batchko, M. M. Fejer, R. L. Byer, D. Woll, R. Wallenstein, V. Y. Shur, and L. Erman, "Continuous-wave quasi-phase-matched generation of 60 mW at 465 nm by single-pass frequency doubling of a laser diode in backswitch-poled lithium niobate," Opt. Lett. 24, 1293-1295 (1999).

J. Christou, V. Tikhonenko, Yu. S. Kivshar, and B. Luther-Davies, "Vortex soliton motion and steering," Opt. Lett. 21, 1649-1651 (1996).

F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11,659-661 (1986).

J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1986).

M. Horowitz, R. Daisy, O. Werner, and B. Fischer, "Large thermal nonlinearities and spatial self-phase modulation in SrxBa1−xNb2O6 and BaTiO3 crystals," Opt. Lett. 17, 475-477 (1992).

B. Luther-Davies, R. Powles, and V. Tikhonenko, "Nonlinear rotation of 3-dimensional dark spatial solitons in a gaussian laser-beam," Opt. Lett. 19,1816-1818 (1994).

Opt. Quantum Electron. (1)

S. Dinev and A. Dreischuh, "Sum-frequency generation in the xuv," Opt. Quantum Electron. 23, 91-97 (1991).
[CrossRef]

Phys. Rep. (1)

Yu. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298, 81-197 (1998).
[CrossRef]

Phys. Rev. A (4)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, "Second-harmonic generation and the orbital angular momentum of light," Phys. Rev. A 54, R3742-R3745 (1996).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50, R4457-R4460 (1994).
[CrossRef]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, "Dark and bright photovoltaic spatial solitons," Phys. Rev. A 50, R4457-R4460 (1994).
[CrossRef]

M. Taya, M. C. Bashaw, M. M. Fejer, M. Segev, and G. C. Valley, "Observation of dark photovoltaic spatial solitons," Phys. Rev. A 52, 3095-3100 (1995).
[CrossRef]

Phys. Rev. E (2)

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, D. Neshev, and H. Walther, "Modulational instability of multiple-charged optical vortex solitons under saturation of the nonlinearity," Phys. Rev. E 60, 7518-7524 (1999).
[CrossRef]

D. V. Skryabin and W. J. Firth, "Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media," Phys. Rev. E 58, 3916-3930 (1998).
[CrossRef]

Phys. Rev. Lett. (6)

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (1997).
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L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. Hooft, ’t, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901-4 (2006).
[CrossRef]

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, "Experimental observation of fluidlike motion of optical vortices," Phys. Rev. Lett. 79, 3399-3402 (1997).
[CrossRef]

D. N. Neshev et al., "Nonlinear spectral-spatial control and localization of supercontinuum radiation," Phys. Rev. Lett. 99, 123901-4 (2007).
[CrossRef]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Maker, "Self-trapping of an optical vortex by use of the bulk photovoltaic effect," Phys. Rev. Lett. 78, 2948-2951 (1997).
[CrossRef]

G. A. Swartzlander and J. Schmit, "Temporal correlation vortices and topological dispersion," Phys. Rev. Lett. 93, 093901-4 (2004).
[CrossRef]

Phys. Status Solidi A (1)

L. Arizmendi, "Photonic applications of lithium niobate crystals," Phys. Status Solidi A 201, 253-283 (2004).

Proc. SPIE (1)

F. Grasbon, A. Dreischuh, G. G. Paulus, F. Zacher, and H. Walther, "Femtosecond interferometric autocorrelations in the presence of pulse front distortions," Proc. SPIE 3571, 164-168 (1999).

Prog. Opt. (4)

S. M. Saltiel, A. A. Sukhorukov, and Yu. S. Kivshar, "Multistep parametric processes in nonlinear optics" Prog. Opt. 47, 1-73 (2005).

L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291-372 (1999).

M. S. Soskin and M. V. Vasnetsov, "Singular optics," Prog. Opt. 42, 219-276 (2001).

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Prog. Opt. 47, 291-391 (2005).

Pure Appl. Opt. (1)

M. S. Soskin and M. V. Vasnetsov, "Nonlinear singular optics," Pure Appl. Opt. 7, 301-311 (1998).
[CrossRef]

Rev. Mod. Phys. (1)

E. B. Sonin, "Vortex oscillations and hydrodynamics of rotating superfluids," Rev. Mod. Phys. 59, 87-155 (1987).
[CrossRef]

Other (5)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gasses (Academic Press, New York, 1984).

D. N. Nikogosyan, Properties of Optical and Laser-Related Materials: A Handbook (Wiley, Chichester, UK, 1997).

SNLO nonlinear optics code available from A.V. Smith, Sandia National Laboratories, Albuquerque, NM87185-1423.

A. E. Siegman, Lasers (University Science Books, Sausalito, Calif., 1986), p. 1283.

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