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

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).
[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]

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

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] [PubMed]

2006

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] [PubMed]

2005

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

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

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

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

2004

2003

2002

2001

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

2000

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

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).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

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

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

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]

1998

M. S. Soskin and M. V. Vasnetsov, "Nonlinear singular optics," Pure Appl. Opt. 7, 301-311 (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, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, "Dynamics of optical vortex solitons," Opt. Commun. 152, 198-206 (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]

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]

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]

1997

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).
[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]

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]

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]

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (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, C. T. Law, and G. A. Swartzlander, "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3065 (1997).
[CrossRef]

1996

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

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] [PubMed]

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

1994

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).
[CrossRef] [PubMed]

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).
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Figures (9)

Fig. 1.
Fig. 1.

Experimental arrangement (top) and absorption of the Fe:LiNbO3 crystal (bottom). Solid and dashed lines indicate the FF and SH wavelengths corresponding to the three different cases in the experiment. CHG: computer generated hologram, L: focusing lens.

Fig. 2.
Fig. 2.

(a) Calculated [64] pulse profiles of the FF (solid line) and SH (dashed line) normalized to their maximum intensity at the crystal output. (b) Average power of the ordinary and extraordinary second harmonic [SH(o) and SH(e), respectively] vs. angle of rotation of the FF beam polarization. Focusing by f=50mm lens, l cryst=3 mm. Specific polarization components of interacting waves are marked with vertical lines. Solid lines: spline to the experimental points.

Fig. 3.
Fig. 3.

Far-field FF (upper row) and SH beam patterns (lower row) vs. time: Gaussian input FF beam. Type of interaction: (a) ee-e; (b) oo-e.

Fig. 4.
Fig. 4.

SH far-field (upper row) and near field (lower row) energy density distributions of the OV beam at an initial (a,d), intermediate (b,e), and final evolution stages (c,f). The arrows indicate the position of the two vortices.

Fig. 5.
Fig. 5.

(a) Calculated [64] pulse profiles of the FF (solid line) and SH (dashed line) normalized to their maximum intensity at the crystal output. (b) Average power of the extra-ordinary second harmonic vs. angle of rotation of the FF beam polarization. Focusing by f=38mm lens; l cryst=3 mm). Specific polarization components of interacting waves are marked with vertical lines. Solid line: spline to experimental points.

Fig. 6.
Fig. 6.

Growth of the SH(e) mean power with time. Type of interaction: (oo-e). Gaussian FF beam is focused in (a) the center of the sample (l cryst=15 mm), on its input (b), and output facets (c) with a f=38mm AR-coated lens.

Fig. 7.
Fig. 7.

Rotation of the SH(e) OV pair with time: Input polarisation at 45° with respect to the c-axis. l cryst=15 mm; focusing by f=38mm lens. Inset: initial (left; t=0) and stationary SH pattern (right; t=30 min).

Fig. 8.
Fig. 8.

(a) Normalized spectral width Δλ (z/LD )/ΔλMAX of the SH pulses (diamonds – experimental data, solid curve – sigmoidal fit) and normalized FF beam spectral broadening ω(z/LD )/ω 0 (dashed) vs. crystal position. (b,c) SH spectra of the OV pulses at different positions of the LiNbO3 crystal. ΔλMAX =24 nm (full width at 1/e intensity level) at x=0, whereas Δλ=17.5 and 10.5 nm at crystal positions z=0.7LD and 3LD , respectively.

Fig. 9.
Fig. 9.

(a) Rotation angle of a OV pair vs. crystal position. Squares - experimental data, dashed curve - sigmoidal fit. Solid curve - calculated rotation angle due to linear Guoy phase shift only. (b) Projection of the vortex trajectories onto the CCD camera. Lower row: experimental far-field images corresponding to the points on the graph marked with circles.

Tables (1)

Tables Icon

Table 1. Parameters of the lasers and the Fe3+:LiNbO3 crystal. GVM - group velocity mismatch, SOD - second order dispersion.

Equations (1)

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σ ( λ ) = exp [ ln ( 2 ) ( λ λ b ) 2 λ w 2 ] ,

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