Dynamics of a paired optical vortex generated by second-harmonic
generation

doi:10.1364/OE.18.017796

Dynamics of a paired optical vortex generated by second-harmonic generation

Y. Toda, S. Honda, and R. Morita »View Author Affiliations

Optics Express, Vol. 18, Issue 17, pp. 17796-17804 (2010)
http://dx.doi.org/10.1364/OE.18.017796

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Abstract

We study the dynamics of a paired optical vortex (OV) generated by second-harmonic generation (SHG) using sub-picosecond pulses. By changing the position of a thin nonlinear crystal along the propagation direction, we observe a rotation of two vortices with changing separation distance. The dynamics is well explained by SHG with a beam walk-off, which introduces a contamination of zero-order Laguerre-Gaussian beam (LG₀) together with topological charge doubling. The quantitative analysis indicates that the rotation angle of the OVs manifests the Gouy phase while the splitting provides the walk-off angle of the crystal. We also show that the subtraction of LG₀ is realized by the superposition of LG₀ with an anti-balanced phase in the pump.

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.2620) Nonlinear optics : Harmonic generation and mixing
(050.4865) Diffraction and gratings : Optical vortices
(260.6042) Physical optics : Singular optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 15, 2010
Revised Manuscript: July 21, 2010
Manuscript Accepted: July 28, 2010
Published: August 3, 2010

Citation
Y. Toda, S. Honda, and R. Morita, "Dynamics of a paired optical vortex generated by second-harmonic generation," Opt. Express 18, 17796-17804 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-17796

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References

K. T. Gahagan and G. A. Swartzlander, Jr., “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996). [CrossRef] [PubMed]
D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003). [CrossRef] [PubMed]
Y. Tokizane, K. Shimatake, Y. Toda, K. Oka, M. Tsubota, S. Tanda, and R. Morita, “Global evaluation of closed-loop electron dynamics in quasi-one-dimensional conductors using polarization vortices,” Opt. Express 17, 24198–24207 (2009). [CrossRef]
G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004). [CrossRef] [PubMed]
L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef] [PubMed]
M. Berry, “Making waves in physics,” Nature 403, 21–21 (2000). [CrossRef] [PubMed]
M. J. Paz-Alonso and H. Michinel, “Superfluidlike Motion of Vortices in Light Condensates,” Phys. Rev. Lett. 94, 093901-1–4 (2005). [CrossRef] [PubMed]
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]
K. Staliunas, “Dynamics of optical vortices in a laser beam,” Opt. Commun. 90, 123–127 (1992). [CrossRef]
G. Indebetow, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993). [CrossRef]
M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997). [CrossRef]
D. Rozas, C. T. Law, G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997). [CrossRef]
. I. Freund, “Optical vortex trajectories,” Opt. Commun. 181, 19–33 (2000). I. D. Maleev, and G. A. Swartzlander, “Composite optical vortices,” J. Opt. Soc. Am. B 20, 1169–1176 (2003). [CrossRef]
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, R3742–3745 (1996). [CrossRef] [PubMed]
A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150, 372–280 (1998). [CrossRef]
F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901-1–4 (2005). [CrossRef] [PubMed]
A. Dreischuh, D. N. Neshev, V. Z. Kolev, S. Saltiel, M. Samoc, W. Krolikowski, and Y. S. Kivshar, “Nonlinear dynamics of two-color optical vortices in lithium niobate crystals,” Opt. Express 16, 5406–5420 (2008). [CrossRef] [PubMed]
M. W. Beijersbergen, L. Allen, H. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993). [CrossRef]
Y. Yoshikawa and H. Sasada, “Versatile generation of optical vortices based on paraxial mode expansion,” J. Opt. Soc. Am. A 19, 2127–2133 (2002). [CrossRef]
K. Kato, “Second-harmonic generation to 2048 Å in β -BaB2O4,” IEEE J. Quantum Electron., QE-22, 1013–1014 (1986). [CrossRef]
S. M. Baumann, D. M. Kalb, L. H. MacMillan, E. J. Galvez, “Propagation dynamics of optical vortices due to Gouy phase,” Opt. Express 17, 9818–9827 (2009). [CrossRef] [PubMed]
J. H. Chow, G. de Vine, M. B. Gray, and D. E. McClelland, “Measurement of Gouy phase evolution by use of spatial mode interference,” Opt. Lett. 29, 2339–2341 (2004). [CrossRef] [PubMed]
J. Hamazaki, Y. Mineta, K. Oka, and R. Morita, "Direct observation of Gouy phase shift in a propagating optical vortex,” Opt. Express 14, 8382–8392 (2006). [CrossRef] [PubMed]
A. Bahabad and A. Arie, “Generation of optical vortex beams by nonlinear wave mixing,” Opt. Express 15, 17619–17624 (2007). [CrossRef] [PubMed]
Y. Ueno, Y. Toda, S. Adachi, R. Morita and T. Tawara, “Coherent transfer of orbital angular momentum to excitons by optical four-wave mixing,” Opt. Express 17, 20567–20574 (2009). [CrossRef] [PubMed]

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[1] K. T. Gahagan and G. A. Swartzlander, Jr., “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996). [CrossRef] [PubMed]

[2] D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003). [CrossRef] [PubMed]

[3] Y. Tokizane, K. Shimatake, Y. Toda, K. Oka, M. Tsubota, S. Tanda, and R. Morita, “Global evaluation of closed-loop electron dynamics in quasi-one-dimensional conductors using polarization vortices,” Opt. Express 17, 24198–24207 (2009). [CrossRef]

[4] G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004). [CrossRef] [PubMed]

[5] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef] [PubMed]

[6] M. Berry, “Making waves in physics,” Nature 403, 21–21 (2000). [CrossRef] [PubMed]

[7] M. J. Paz-Alonso and H. Michinel, “Superfluidlike Motion of Vortices in Light Condensates,” Phys. Rev. Lett. 94, 093901-1–4 (2005). [CrossRef] [PubMed]

[8] 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]

[9] K. Staliunas, “Dynamics of optical vortices in a laser beam,” Opt. Commun. 90, 123–127 (1992). [CrossRef]

[10] G. Indebetow, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993). [CrossRef]

[11] M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997). [CrossRef]

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

[13] . I. Freund, “Optical vortex trajectories,” Opt. Commun. 181, 19–33 (2000). I. D. Maleev, and G. A. Swartzlander, “Composite optical vortices,” J. Opt. Soc. Am. B 20, 1169–1176 (2003). [CrossRef]

[14] 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, R3742–3745 (1996). [CrossRef] [PubMed]

[15] A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, “Sum-frequency mixing of optical vortices in nonlinear crystals,” Opt. Commun. 150, 372–280 (1998). [CrossRef]

[16] F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett. 95, 253901-1–4 (2005). [CrossRef] [PubMed]

[17] A. Dreischuh, D. N. Neshev, V. Z. Kolev, S. Saltiel, M. Samoc, W. Krolikowski, and Y. S. Kivshar, “Nonlinear dynamics of two-color optical vortices in lithium niobate crystals,” Opt. Express 16, 5406–5420 (2008). [CrossRef] [PubMed]

[18] M. W. Beijersbergen, L. Allen, H. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993). [CrossRef]

[19] Y. Yoshikawa and H. Sasada, “Versatile generation of optical vortices based on paraxial mode expansion,” J. Opt. Soc. Am. A 19, 2127–2133 (2002). [CrossRef]

[20] K. Kato, “Second-harmonic generation to 2048 Å in β -BaB2O4,” IEEE J. Quantum Electron., QE-22, 1013–1014 (1986). [CrossRef]

[21] S. M. Baumann, D. M. Kalb, L. H. MacMillan, E. J. Galvez, “Propagation dynamics of optical vortices due to Gouy phase,” Opt. Express 17, 9818–9827 (2009). [CrossRef] [PubMed]

[22] J. H. Chow, G. de Vine, M. B. Gray, and D. E. McClelland, “Measurement of Gouy phase evolution by use of spatial mode interference,” Opt. Lett. 29, 2339–2341 (2004). [CrossRef] [PubMed]

[23] J. Hamazaki, Y. Mineta, K. Oka, and R. Morita, "Direct observation of Gouy phase shift in a propagating optical vortex,” Opt. Express 14, 8382–8392 (2006). [CrossRef] [PubMed]

[24] A. Bahabad and A. Arie, “Generation of optical vortex beams by nonlinear wave mixing,” Opt. Express 15, 17619–17624 (2007). [CrossRef] [PubMed]

[25] Y. Ueno, Y. Toda, S. Adachi, R. Morita and T. Tawara, “Coherent transfer of orbital angular momentum to excitons by optical four-wave mixing,” Opt. Express 17, 20567–20574 (2009). [CrossRef] [PubMed]

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Dynamics of a paired optical vortex generated by second-harmonic generation