Abstract

A new achromatic method to generate the optical vortex was proposed and supercontinuum optical vortex generation ranging ~500 to ~800 nm was experimentally demonstrated without spatial nor topological-charge dispersions. In addition, polarization evolution in our system using Jones vectors and matrices was discussed and the condition of the polarizer to transfer polarizations was elucidated. This method is useful for the application to time-resolved nonlinear spectroscopy utilizing ultrabroadband optical vortex pulses in topological materials such as ring-shaped crystals or annular materials.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]

2008

2007

I. Zeylikovich, H. I. Sztul, V. Kartazaev, T. Le, and R. R. Alfano, "Ultrashort Laguerre-Gaussian pulses with angular and group velocity dispersion compensation", Opt. Lett. 32, 2025-2027 (2007).
[CrossRef] [PubMed]

Y. Iketaki, T. Watanabe, N. Bokor, T. Omatsu, T. Hiraga, K. Yamamoto, and M. Fujii, "Measurement of contrast transfer function in super-resolution microscopy using Two-color Fluorescence Dip Spectroscopyh, Appl. Spectroscopy 616-10 (2007).
[CrossRef]

2006

M. Yamashita, K. Yamane, and R. Morita, "Quasi-automatic phase-control technique for chirp compensation of pulses with over-one-octave bandwidth—generation of few- to mono-cycle optical pulses", IEEE J. Sel. Top. Quantum Electron. 12, 213-222 (2006).
[CrossRef]

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

G. A. Swartzlander, Jr. "Achromatic optical vortex lens", Opt. Lett. 31, 2042-2044 (2006).
[CrossRef] [PubMed]

J. Hamazaki, Y. Mineta, K. Oka, and R. Morita, "Direct observation of Gouy phase shift in a propagating optical vortex", Opt. Express 148382-8392 (2006).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. t’Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices", Phys. Rev. Lett. 96133901 (2006).
[CrossRef]

K. Shimatake, Y. Toda, and S. Tanda, "Quenching of phase coherence in quasi-one-dimensional ring crystals", Phys. Rev. B 73, 153403 (2006).
[CrossRef]

K. J. Moh, X.-C. Yuan, D. Y. Tang, W. C. Cheong, L. S. Zhang, D. K. Y. Low, X. Peng, H. B. Niu, and Z. Y. Lin, "Generation of femtosecond optical vortices using a single refractive optical element", Appl. Phys. Lett. 88, 091103 (2006).
[CrossRef]

K. I. Willig, S. O. Rizzoli, V. Westphal, S. W. Hell, and R. Jahn, "STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis", Nature 440, 935-939 (2006).
[CrossRef] [PubMed]

2005

A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, "Stable vortex soliton in nonlocal self-focusing nonlinear media", Phys. Rev. E 71065603 (2005).
[CrossRef]

I. G. Mariyenko, J. Strohaber, and C. J. G. J. Uiterwaal, "Creation of optical vortices in femtosecond pulses", Opt. Express 13, 7599-7608 (2005).
[CrossRef] [PubMed]

2004

2003

K. Yamane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, "Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation", Opt. Lett. 28, 2258-2260 (2003).
[CrossRef] [PubMed]

V. Garcés-Chávez, D. M. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

J. Leach and M. J. Padgett, "Observation of chromatic effects near a white-light vortex", New J. Phys. 5, 15417 (2003).
[CrossRef]

2002

A. Vaziri, G. Weihs, and A. Zeilinger, "Experimental two-photon, three-dimensional entanglement for quantum communication," Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, "Polychromatic vectorial vortex formed by geometric phase elements", Opt. Lett. 32, 847-849 (2002).
[CrossRef]

S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, and N. Hatakenaka, "AM¨obius strip of single crystals", Nature 417, 397-398 (2002).
[CrossRef] [PubMed]

2001

E. M. Wright, J. Arlt, K. Dholakia, K. T. Gahagan, and G. A. Swartzlander, Jr., "Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams," Phys. Rev. A 63, 013608 (2001).

J. Tempere, J. T. Devreese, E. R. I. Abraham, K. T. Gahagan, and G. A. Swartzlander, Jr., "Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap," Phys. Rev. A 64, 023603 (2001).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, "Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum," Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt,W. Sibbet, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

1999

A. D. Mehta, M. Rief, J. A. Spudich, D. A. Smith, and R. M. Simmons, "Single-molecule biomechanics with optical methods," Science 283, 1689-1695 (1999).
[CrossRef] [PubMed]

1997

T. Kuga, Y. Torii, N. Shiokawa, T. Hirano, Y. Shimizu, and H. Sasada, "Novel optical trap of atoms with a doughnut beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner," Opt. Lett. 22, 52-54 (1997).
[CrossRef] [PubMed]

1996

1995

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity", Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

1994

M. W. Beijersbergen, R. P. C. Coeerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate", Opt. Commun. 112, 321-327 (1994).
[CrossRef]

S. W. Hell and J. Wichmann, "Breaking the diffraction resolution limit by stimulated emission: stimulate demission-depletion fluorescence microscopy", Opt. Lett. 19, 780-782 (1994).
[CrossRef] [PubMed]

1992

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]

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1990

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocations in their wavefronts", JETP Lett. 52, 1037-1039 (1990).

1959

Y. Aharonov and D. Bohm, "Significance of electromagnetic potentials in the quantum theory", Phys. Rev. 115, 485-491 (1959).
[CrossRef]

1942

Abraham, E. R. I.

J. Tempere, J. T. Devreese, E. R. I. Abraham, K. T. Gahagan, and G. A. Swartzlander, Jr., "Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap," Phys. Rev. A 64, 023603 (2001).
[CrossRef]

Aharonov, Y.

Y. Aharonov and D. Bohm, "Significance of electromagnetic potentials in the quantum theory", Phys. Rev. 115, 485-491 (1959).
[CrossRef]

Alfano, R. R.

Allen, L.

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner," Opt. Lett. 22, 52-54 (1997).
[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]

Arlt, J.

E. M. Wright, J. Arlt, K. Dholakia, K. T. Gahagan, and G. A. Swartzlander, Jr., "Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams," Phys. Rev. A 63, 013608 (2001).

L. Paterson, M. P. MacDonald, J. Arlt,W. Sibbet, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Bazhenov, V. Y.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocations in their wavefronts", JETP Lett. 52, 1037-1039 (1990).

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coeerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate", Opt. Commun. 112, 321-327 (1994).
[CrossRef]

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]

Bezuhanov, K.

Biener, G.

Bohm, D.

Y. Aharonov and D. Bohm, "Significance of electromagnetic potentials in the quantum theory", Phys. Rev. 115, 485-491 (1959).
[CrossRef]

Bokor, N.

Y. Iketaki, T. Watanabe, N. Bokor, T. Omatsu, T. Hiraga, K. Yamamoto, and M. Fujii, "Measurement of contrast transfer function in super-resolution microscopy using Two-color Fluorescence Dip Spectroscopyh, Appl. Spectroscopy 616-10 (2007).
[CrossRef]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt,W. Sibbet, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Cheong, W. C.

K. J. Moh, X.-C. Yuan, D. Y. Tang, W. C. Cheong, L. S. Zhang, D. K. Y. Low, X. Peng, H. B. Niu, and Z. Y. Lin, "Generation of femtosecond optical vortices using a single refractive optical element", Appl. Phys. Lett. 88, 091103 (2006).
[CrossRef]

Coeerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coeerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wavefront laser beams produced with a spiral phaseplate", Opt. Commun. 112, 321-327 (1994).
[CrossRef]

Devreese, J. T.

J. Tempere, J. T. Devreese, E. R. I. Abraham, K. T. Gahagan, and G. A. Swartzlander, Jr., "Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap," Phys. Rev. A 64, 023603 (2001).
[CrossRef]

Dholakia, K.

V. Garcés-Chávez, D. M. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

E. M. Wright, J. Arlt, K. Dholakia, K. T. Gahagan, and G. A. Swartzlander, Jr., "Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams," Phys. Rev. A 63, 013608 (2001).

L. Paterson, M. P. MacDonald, J. Arlt,W. Sibbet, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner," Opt. Lett. 22, 52-54 (1997).
[CrossRef] [PubMed]

Dreischuh, A.

Dultz, W.

V. Garcés-Chávez, D. M. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity", Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Fujii, M.

Y. Iketaki, T. Watanabe, N. Bokor, T. Omatsu, T. Hiraga, K. Yamamoto, and M. Fujii, "Measurement of contrast transfer function in super-resolution microscopy using Two-color Fluorescence Dip Spectroscopyh, Appl. Spectroscopy 616-10 (2007).
[CrossRef]

Gaeta, A. L.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. t’Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices", Phys. Rev. Lett. 96133901 (2006).
[CrossRef]

Gahagan, K. T.

E. M. Wright, J. Arlt, K. Dholakia, K. T. Gahagan, and G. A. Swartzlander, Jr., "Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams," Phys. Rev. A 63, 013608 (2001).

J. Tempere, J. T. Devreese, E. R. I. Abraham, K. T. Gahagan, and G. A. Swartzlander, Jr., "Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap," Phys. Rev. A 64, 023603 (2001).
[CrossRef]

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

Garcés-Chávez, V.

V. Garcés-Chávez, D. M. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle," Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Gibson, G. M.

Girkin, J. M.

Grow, T. D.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. t’Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices", Phys. Rev. Lett. 96133901 (2006).
[CrossRef]

Hamazaki, J.

Hasman, E.

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K. I. Willig, S. O. Rizzoli, V. Westphal, S. W. Hell, and R. Jahn, "STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis", Nature 440, 935-939 (2006).
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K. J. Moh, X.-C. Yuan, D. Y. Tang, W. C. Cheong, L. S. Zhang, D. K. Y. Low, X. Peng, H. B. Niu, and Z. Y. Lin, "Generation of femtosecond optical vortices using a single refractive optical element", Appl. Phys. Lett. 88, 091103 (2006).
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K. J. Moh, X.-C. Yuan, D. Y. Tang, W. C. Cheong, L. S. Zhang, D. K. Y. Low, X. Peng, H. B. Niu, and Z. Y. Lin, "Generation of femtosecond optical vortices using a single refractive optical element", Appl. Phys. Lett. 88, 091103 (2006).
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Figures (6)

Fig. 1.
Fig. 1.

Schematic drawing of ultrabroadband optical vortex generation system without spatial or topological-charge dispersions. Polarization distribution of the beam are shown after passing through optical components.

Fig. 2.
Fig. 2.

Experimental setup for ultrabroadband optical vortex generation without spatial or topological-charge dispersions.

Fig. 3.
Fig. 3.

Spectral intensity of a generated supercontinuum, normalized by the maximum intensity at 799 nm. The spectrum ranges from ~450 to ~900 nm and its full-width at one-thousandth maximum is ~450 nm.

Fig. 4.
Fig. 4.

Spectrally-resolved vortex pulses with (a) a center wavelength λ0=800 nm and a bandwidth Δλ=11 nm, (b) λ0=680 nm and Δλ=11 nm, and (c) λ0=500 nm and Δλ=65 nm from a generated supercontinuum. Line profiles show horizontal (x-direction) and vertical (y-direction) intensity along the lines including the beam center. (d) superposition of intensity profiles and line profiles of (a)–(c).

Fig. 5.
Fig. 5.

Observed interference patterns for (a) λ0=800 nm and Δλ=11 nm, (b) λ0=680 nm and Δλ=11 nm, and (c) λ0=500 nm and Δλ=65 nm, which are spectrally-resolved from a generated supercontinuum. They all yield clear four-pronged fork patterns, indicating that spectrally-resolved vortex pulses before entering the interferometer definitely possess the same topological charge of ℓ=2as designed.

Fig. 6.
Fig. 6.

Radial polarization Ẽrad can be decomposed into the superposition of constant amplitude left circular polarization ẼL and right polarization ẼR. Only the right polarization component has azimuthal angle φ-dependent phase, while the left circular polarization component has the uniform phase. In this case, a linear polarized optical vortex with topological charge =2 can be generated.

Tables (1)

Tables Icon

Table 1. Top row: Optical components used in our technique, second row: Jones matrix of each component, and bottom row: Jones vector after passing through the component in the experimental setup.

Equations (5)

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

E˜=(E˜L,E˜)E˜L+(E˜R,E˜)E˜R.
F2E˜=i(E˜R,E˜)[01],
E˜rad=12eiϕ[cosϕsinϕ]=12E˜L+12ei2ϕE˜R.
P=[P11P12P21P22]
E˜out=F2R(θ)PR(θ)F1E˜in=12ei2θ[0{P12+P21i(P11P22)}Ein,1],

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