Abstract

We propose a common criterion for the effect of Gouy phase on the distinct polarization transition of focused vector vortex beams (VVBs). Such polarization transition is strongly dependent on the parity of the smaller modulus between VVB’s polarization order and topological charge. Significantly, the cross polarization transitions are observed at areas where the two spin components with equi-intensity are exactly overlapping and the Gouy phase difference (GPD) between them equals to (2k + 1)π, k is an integer. As a whole, the focal field shows radially variant polarization distributions resulting from the unequal intensity proportion of the two spin components. This polarization transition holds potential in modifying the patterns of periodic surface structure induced by femtosecond vector beams.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (3)

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Y. Zhang, P. Li, C. Ma, S. Liu, H. Cheng, L. Han, and J. Zhao, “Efficient generation of vector beams by calibrating the phase response of a spatial light modulator,” Appl. Opt. 56(17), 4956–4960 (2017).

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photonics Res. 5(1), 15–21 (2017).

2016 (8)

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[PubMed]

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).

S. Liu, P. Li, Y. Zhang, X. Gan, M. Wang, and J. Zhao, “Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift,” Sci. Rep. 6, 20774 (2016).
[PubMed]

J. Zhou, W. Zhang, Y. Liu, Y. Ke, Y. Liu, H. Luo, and S. Wen, “Spin-dependent manipulating of vector beams by tailoring polarization,” Sci. Rep. 6, 34276 (2016).
[PubMed]

K. J. Kaltenecker, J. C. Konig-Otto, M. Mittendorff, S. Winnerl, H. Schneider, M. Helm, H. Helm, M. Walther, and B. M. Fischer, “Gouy phase shift of a tightly focused, radially polarized beam,” Optica 3(1), 35–41 (2016).

A. P. Porfirev, A. V. Ustinov, and S. N. Khonina, “Polarization conversion when focusing cylindrically polarized vortex beams,” Sci. Rep. 6(1), 6 (2016).
[PubMed]

Y. Zhang, P. Li, S. Liu, L. Han, H. Cheng, and J. Zhao, “Optimized weak measurement for spatial spin-dependent shifts at Brewster angle,” Appl. Phys. B 122, 184 (2016).

M. Neugebauer, S. Grosche, S. Rothau, G. Leuchs, and P. Banzer, “Lateral spin transport in paraxial beams of light,” Opt. Lett. 41(15), 3499–3502 (2016).
[PubMed]

2015 (3)

2013 (6)

2012 (2)

H. Cui, X. Wang, B. Gu, Y. Li, J. Chen, and H. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14(5), 055707 (2012).

G. M. Philip, V. Kumar, G. Milione, and N. K. Viswanathan, “Manifestation of the Gouy phase in vector-vortex beams,” Opt. Lett. 37(13), 2667–2669 (2012).
[PubMed]

2011 (1)

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[PubMed]

2010 (1)

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283(18), 3371–3375 (2010).

2009 (3)

2008 (1)

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101(5), 050501 (2008).
[PubMed]

2007 (4)

R. J. Gordon and V. J. Barge, “Effect of the Gouy phase on the coherent phase control of chemical reactions,” J. Chem. Phys. 127(20), 204302 (2007).
[PubMed]

R. Zambrini and S. M. Barnett, “Angular momentum of multimode and polarization patterns,” Opt. Express 15(23), 15214–15227 (2007).
[PubMed]

H. Chen, Q. Zhan, Y. Zhang, and Y. Li, “The Gouy phase shift of the highly focused radially polarized beam,” Phys. Lett. A 371(3), 259–261 (2007).

X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
[PubMed]

2006 (3)

2004 (3)

2003 (2)

2001 (2)

S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26(8), 485–487 (2001).
[PubMed]

T. Ackermann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189(1), 5–14 (2001).

1996 (2)

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt. 43(2), 219–221 (1996).

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21(23), 1948–1950 (1996).
[PubMed]

1995 (1)

1994 (1)

M. W. Beijerbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

1992 (1)

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(11), 8185–8189 (1992).
[PubMed]

1966 (1)

1890 (2)

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” C. R. Acad. Sci. 110, 1251–1253 (1890).

L. G. Gouy, “Sur la propagation anormale des ondes,” Compt. Rendue Acad. Sci. 111, 33–35 (1890).

Abeysinghe, D. C.

Abouraddy, A.

Ackermann, T.

T. Ackermann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189(1), 5–14 (2001).

Aiello, A.

Allen, L.

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(11), 8185–8189 (1992).
[PubMed]

Alpmann, C.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Andrews, D. L.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Arlt, J.

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50(10), 1573–1580 (2003).

Baker, M.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Baltuška, A.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy Phase Shift for Few-Cycle Laser Pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Banzer, P.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

M. Neugebauer, S. Grosche, S. Rothau, G. Leuchs, and P. Banzer, “Lateral spin transport in paraxial beams of light,” Opt. Lett. 41(15), 3499–3502 (2016).
[PubMed]

Barge, V. J.

R. J. Gordon and V. J. Barge, “Effect of the Gouy phase on the coherent phase control of chemical reactions,” J. Chem. Phys. 127(20), 204302 (2007).
[PubMed]

Barnett, S. M.

Bauer, T.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Baumann, S. M.

Beijerbergen, M. W.

M. W. Beijerbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

Beijersbergen, M. W.

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(11), 8185–8189 (1992).
[PubMed]

Belmonte, A.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Berry, M. V.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Biener, G.

Bigelow, N. P.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Bliokh, K. Y.

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

Burge, R. E.

Cardano, F.

Chen, H.

H. Chen, Q. Zhan, Y. Zhang, and Y. Li, “The Gouy phase shift of the highly focused radially polarized beam,” Phys. Lett. A 371(3), 259–261 (2007).

Chen, J.

H. Cui, X. Wang, B. Gu, Y. Li, J. Chen, and H. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14(5), 055707 (2012).

Cheng, H.

Coerwinkel, R. P. C.

M. W. Beijerbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

Cui, H.

H. Cui, X. Wang, B. Gu, Y. Li, J. Chen, and H. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14(5), 055707 (2012).

Cui, Y.

B. Gu, J. Wu, Y. Pan, and Y. Cui, “Controllable vector bottle-shaped fields generated by focused spatial-variant linearly polarized vector beams,” Appl. Phys. B 113, 165–170 (2013).

B. Gu, J. L. Wu, Y. Pan, and Y. Cui, “Achievement of needle-like focus by engineering radial-variant vector fields,” Opt. Express 21(25), 30444–30452 (2013).
[PubMed]

de Lisio, C.

Dennis, M. R.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Denz, C.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Ding, J.

Feng, S.

Fickler, R.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Fischer, B. M.

Forbes, A.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Fourkas, J.

Galvez, E. J.

Gan, X.

S. Liu, P. Li, Y. Zhang, X. Gan, M. Wang, and J. Zhao, “Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift,” Sci. Rep. 6, 20774 (2016).
[PubMed]

Gordon, R.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Gordon, R. J.

R. J. Gordon and V. J. Barge, “Effect of the Gouy phase on the coherent phase control of chemical reactions,” J. Chem. Phys. 127(20), 204302 (2007).
[PubMed]

Goulielmakis, E.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy Phase Shift for Few-Cycle Laser Pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Gouy, L. G.

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” C. R. Acad. Sci. 110, 1251–1253 (1890).

L. G. Gouy, “Sur la propagation anormale des ondes,” Compt. Rendue Acad. Sci. 111, 33–35 (1890).

Grosche, S.

Grosse-Nobis, W.

T. Ackermann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189(1), 5–14 (2001).

Gu, B.

B. Gu, J. Wu, Y. Pan, and Y. Cui, “Controllable vector bottle-shaped fields generated by focused spatial-variant linearly polarized vector beams,” Appl. Phys. B 113, 165–170 (2013).

B. Gu, J. L. Wu, Y. Pan, and Y. Cui, “Achievement of needle-like focus by engineering radial-variant vector fields,” Opt. Express 21(25), 30444–30452 (2013).
[PubMed]

H. Cui, X. Wang, B. Gu, Y. Li, J. Chen, and H. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14(5), 055707 (2012).

Guo, C. S.

Guzzinati, G.

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

Hamazaki, J.

Han, L.

Hariharan, P.

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt. 43(2), 219–221 (1996).

Hasman, E.

Helm, H.

Helm, M.

Hnatovsky, C.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[PubMed]

Jiao, X.

Kalb, D. M.

Kaltenecker, K. J.

Karimi, E.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21(7), 8815–8820 (2013).
[PubMed]

Kawase, D.

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101(5), 050501 (2008).
[PubMed]

Ke, Y.

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photonics Res. 5(1), 15–21 (2017).

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).

J. Zhou, W. Zhang, Y. Liu, Y. Ke, Y. Liu, H. Luo, and S. Wen, “Spin-dependent manipulating of vector beams by tailoring polarization,” Sci. Rep. 6, 34276 (2016).
[PubMed]

J. Zhou, Y. Liu, Y. Ke, H. Luo, and S. Wen, “Generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases,” Opt. Lett. 40(13), 3193–3196 (2015).
[PubMed]

Khonina, S. N.

A. P. Porfirev, A. V. Ustinov, and S. N. Khonina, “Polarization conversion when focusing cylindrically polarized vortex beams,” Sci. Rep. 6(1), 6 (2016).
[PubMed]

Kleiner, V.

Kogelnik, H.

Konig-Otto, J. C.

Krausz, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy Phase Shift for Few-Cycle Laser Pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Kristensen, M.

M. W. Beijerbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

Krolikowski, W.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[PubMed]

Kumar, V.

Leuchs, G.

Lezius, M.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy Phase Shift for Few-Cycle Laser Pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Li, P.

Li, T.

Li, Y.

H. Cui, X. Wang, B. Gu, Y. Li, J. Chen, and H. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14(5), 055707 (2012).

H. Chen, Q. Zhan, Y. Zhang, and Y. Li, “The Gouy phase shift of the highly focused radially polarized beam,” Phys. Lett. A 371(3), 259–261 (2007).

Lin, J.

Lindner, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy Phase Shift for Few-Cycle Laser Pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Ling, X.

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).

Lippi, G. L.

T. Ackermann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189(1), 5–14 (2001).

Litchinitser, N. M.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Liu, S.

Liu, Y.

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photonics Res. 5(1), 15–21 (2017).

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photonics Res. 5(1), 15–21 (2017).

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).

J. Zhou, W. Zhang, Y. Liu, Y. Ke, Y. Liu, H. Luo, and S. Wen, “Spin-dependent manipulating of vector beams by tailoring polarization,” Sci. Rep. 6, 34276 (2016).
[PubMed]

J. Zhou, W. Zhang, Y. Liu, Y. Ke, Y. Liu, H. Luo, and S. Wen, “Spin-dependent manipulating of vector beams by tailoring polarization,” Sci. Rep. 6, 34276 (2016).
[PubMed]

J. Zhou, Y. Liu, Y. Ke, H. Luo, and S. Wen, “Generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases,” Opt. Lett. 40(13), 3193–3196 (2015).
[PubMed]

Liu, Z.

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photonics Res. 5(1), 15–21 (2017).

Luo, H.

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photonics Res. 5(1), 15–21 (2017).

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).

J. Zhou, W. Zhang, Y. Liu, Y. Ke, Y. Liu, H. Luo, and S. Wen, “Spin-dependent manipulating of vector beams by tailoring polarization,” Sci. Rep. 6, 34276 (2016).
[PubMed]

J. Zhou, Y. Liu, Y. Ke, H. Luo, and S. Wen, “Generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases,” Opt. Lett. 40(13), 3193–3196 (2015).
[PubMed]

Ma, C.

MacMillan, L. H.

Mansuripur, M.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Marrucci, L.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21(7), 8815–8820 (2013).
[PubMed]

McMorran, B.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Merano, M.

Milione, G.

Mineta, Y.

Mittendorff, M.

Miyaji, G.

Miyamoto, Y.

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101(5), 050501 (2008).
[PubMed]

Miyanaga, N.

Morita, R.

Nakatsuka, M.

Neely, T. W.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Neugebauer, M.

Ni, W. J.

Niv, A.

Nori, F.

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

Oka, K.

Padgett, M.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Pan, Y.

B. Gu, J. Wu, Y. Pan, and Y. Cui, “Controllable vector bottle-shaped fields generated by focused spatial-variant linearly polarized vector beams,” Appl. Phys. B 113, 165–170 (2013).

B. Gu, J. L. Wu, Y. Pan, and Y. Cui, “Achievement of needle-like focus by engineering radial-variant vector fields,” Opt. Express 21(25), 30444–30452 (2013).
[PubMed]

Paulus, G. G.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy Phase Shift for Few-Cycle Laser Pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Philip, G. M.

Porfirev, A. P.

A. P. Porfirev, A. V. Ustinov, and S. N. Khonina, “Polarization conversion when focusing cylindrically polarized vortex beams,” Sci. Rep. 6(1), 6 (2016).
[PubMed]

Ritsch-Marte, M.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Robinson, P. A.

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt. 43(2), 219–221 (1996).

Rode, A.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[PubMed]

Romero, J.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Rosales-Guzmán, C.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Rothau, S.

Rubinsztein-Dunlop, H.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Saleh, B.

Santamato, E.

Sasaki, K.

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101(5), 050501 (2008).
[PubMed]

Schadt, M.

Schattschneider, P.

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

Schneider, H.

Shu, W.

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photonics Res. 5(1), 15–21 (2017).

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).

Shvedov, V.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[PubMed]

Spreeuw, R. J. C.

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(11), 8185–8189 (1992).
[PubMed]

Stalder, M.

Stilgoe, A. B.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Subbarao, D.

Sueda, K.

Takeda, M.

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101(5), 050501 (2008).
[PubMed]

Takeuchi, S.

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101(5), 050501 (2008).
[PubMed]

Tao, S. H.

Teich, M.

Torres, J. P.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Ustinov, A. V.

A. P. Porfirev, A. V. Ustinov, and S. N. Khonina, “Polarization conversion when focusing cylindrically polarized vortex beams,” Sci. Rep. 6(1), 6 (2016).
[PubMed]

Verbeeck, J.

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

Visser, T. D.

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283(18), 3371–3375 (2010).

Viswanathan, N. K.

Walther, H.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy Phase Shift for Few-Cycle Laser Pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Walther, M.

Wang, H.

H. Cui, X. Wang, B. Gu, Y. Li, J. Chen, and H. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14(5), 055707 (2012).

Wang, H. T.

Wang, M.

S. Liu, P. Li, Y. Zhang, X. Gan, M. Wang, and J. Zhao, “Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift,” Sci. Rep. 6, 20774 (2016).
[PubMed]

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013).
[PubMed]

Wang, S.

Wang, X.

H. Cui, X. Wang, B. Gu, Y. Li, J. Chen, and H. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14(5), 055707 (2012).

Wang, X. L.

Weiner, A. M.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Wen, S.

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photonics Res. 5(1), 15–21 (2017).

J. Zhou, W. Zhang, Y. Liu, Y. Ke, Y. Liu, H. Luo, and S. Wen, “Spin-dependent manipulating of vector beams by tailoring polarization,” Sci. Rep. 6, 34276 (2016).
[PubMed]

J. Zhou, Y. Liu, Y. Ke, H. Luo, and S. Wen, “Generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases,” Opt. Lett. 40(13), 3193–3196 (2015).
[PubMed]

White, A. G.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Whiting, A.

Willner, A. E.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Winful, H. G.

Winnerl, S.

Woerdman, J. P.

A. Aiello, M. Merano, and J. P. Woerdman, “Brewster cross polarization,” Opt. Lett. 34(8), 1207–1209 (2009).
[PubMed]

M. W. Beijerbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

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(11), 8185–8189 (1992).
[PubMed]

Wolf, E.

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283(18), 3371–3375 (2010).

Wu, J.

B. Gu, J. Wu, Y. Pan, and Y. Cui, “Controllable vector bottle-shaped fields generated by focused spatial-variant linearly polarized vector beams,” Appl. Phys. B 113, 165–170 (2013).

Wu, J. L.

Xie, G.

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

Yin, X.

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).

Yuan, X. C.

Zambrini, R.

Zhan, Q.

S. Wang, D. C. Abeysinghe, and Q. Zhan, “Generation of vectorial optical fields with slot-antenna-based metasurface,” Opt. Lett. 40(20), 4711–4714 (2015).
[PubMed]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).

H. Chen, Q. Zhan, Y. Zhang, and Y. Li, “The Gouy phase shift of the highly focused radially polarized beam,” Phys. Lett. A 371(3), 259–261 (2007).

Zhang, P.

Zhang, W.

J. Zhou, W. Zhang, Y. Liu, Y. Ke, Y. Liu, H. Luo, and S. Wen, “Spin-dependent manipulating of vector beams by tailoring polarization,” Sci. Rep. 6, 34276 (2016).
[PubMed]

W. Zhang, S. Liu, P. Li, X. Jiao, and J. Zhao, “Controlling the polarization singularities of the focused azimuthally polarized beams,” Opt. Express 21(1), 974–983 (2013).
[PubMed]

Zhang, Y.

Y. Zhang, P. Li, C. Ma, S. Liu, H. Cheng, L. Han, and J. Zhao, “Efficient generation of vector beams by calibrating the phase response of a spatial light modulator,” Appl. Opt. 56(17), 4956–4960 (2017).

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[PubMed]

S. Liu, P. Li, Y. Zhang, X. Gan, M. Wang, and J. Zhao, “Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift,” Sci. Rep. 6, 20774 (2016).
[PubMed]

Y. Zhang, P. Li, S. Liu, L. Han, H. Cheng, and J. Zhao, “Optimized weak measurement for spatial spin-dependent shifts at Brewster angle,” Appl. Phys. B 122, 184 (2016).

Y. Zhang, P. Li, S. Liu, and J. Zhao, “Unveiling the photonic spin Hall effect of freely propagating fan-shaped cylindrical vector vortex beams,” Opt. Lett. 40(19), 4444–4447 (2015).
[PubMed]

H. Chen, Q. Zhan, Y. Zhang, and Y. Li, “The Gouy phase shift of the highly focused radially polarized beam,” Phys. Lett. A 371(3), 259–261 (2007).

Zhao, J.

Zhou, J.

J. Zhou, W. Zhang, Y. Liu, Y. Ke, Y. Liu, H. Luo, and S. Wen, “Spin-dependent manipulating of vector beams by tailoring polarization,” Sci. Rep. 6, 34276 (2016).
[PubMed]

J. Zhou, Y. Liu, Y. Ke, H. Luo, and S. Wen, “Generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases,” Opt. Lett. 40(13), 3193–3196 (2015).
[PubMed]

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).

Appl. Opt. (2)

Appl. Phys. B (2)

B. Gu, J. Wu, Y. Pan, and Y. Cui, “Controllable vector bottle-shaped fields generated by focused spatial-variant linearly polarized vector beams,” Appl. Phys. B 113, 165–170 (2013).

Y. Zhang, P. Li, S. Liu, L. Han, H. Cheng, and J. Zhao, “Optimized weak measurement for spatial spin-dependent shifts at Brewster angle,” Appl. Phys. B 122, 184 (2016).

C. R. Acad. Sci. (1)

L. G. Gouy, “Sur une propriété nouvelle des ondes lumineuses,” C. R. Acad. Sci. 110, 1251–1253 (1890).

Compt. Rendue Acad. Sci. (1)

L. G. Gouy, “Sur la propagation anormale des ondes,” Compt. Rendue Acad. Sci. 111, 33–35 (1890).

J. Chem. Phys. (1)

R. J. Gordon and V. J. Barge, “Effect of the Gouy phase on the coherent phase control of chemical reactions,” J. Chem. Phys. 127(20), 204302 (2007).
[PubMed]

J. Mod. Opt. (2)

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt. 43(2), 219–221 (1996).

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50(10), 1573–1580 (2003).

J. Opt. (2)

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19(1), 013001 (2017).

H. Cui, X. Wang, B. Gu, Y. Li, J. Chen, and H. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. 14(5), 055707 (2012).

Opt. Commun. (3)

M. W. Beijerbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283(18), 3371–3375 (2010).

T. Ackermann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189(1), 5–14 (2001).

Opt. Express (10)

J. Hamazaki, Y. Mineta, K. Oka, and R. Morita, “Direct observation of Gouy phase shift in a propagating optical vortex,” Opt. Express 14(18), 8382–8392 (2006).
[PubMed]

A. Whiting, A. Abouraddy, B. Saleh, M. Teich, and J. Fourkas, “Polarization-Assisted Transverse and Axial Optical Superresolution,” Opt. Express 11(15), 1714–1723 (2003).
[PubMed]

S. M. Baumann, D. M. Kalb, L. H. MacMillan, and E. J. Galvez, “Propagation dynamics of optical vortices due to Gouy phase,” Opt. Express 17(12), 9818–9827 (2009).
[PubMed]

K. Sueda, G. Miyaji, N. Miyanaga, and M. Nakatsuka, “Laguerre-Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses,” Opt. Express 12(15), 3548–3553 (2004).
[PubMed]

F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21(7), 8815–8820 (2013).
[PubMed]

S. H. Tao, X. C. Yuan, J. Lin, and R. E. Burge, “Residue orbital angular momentum in interferenced double vortex beams with unequal topological charges,” Opt. Express 14(2), 535–541 (2006).
[PubMed]

R. Zambrini and S. M. Barnett, “Angular momentum of multimode and polarization patterns,” Opt. Express 15(23), 15214–15227 (2007).
[PubMed]

B. Gu, J. L. Wu, Y. Pan, and Y. Cui, “Achievement of needle-like focus by engineering radial-variant vector fields,” Opt. Express 21(25), 30444–30452 (2013).
[PubMed]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Manipulation of the Pancharatnam phase in vectorial vortices,” Opt. Express 14(10), 4208–4220 (2006).
[PubMed]

W. Zhang, S. Liu, P. Li, X. Jiao, and J. Zhao, “Controlling the polarization singularities of the focused azimuthally polarized beams,” Opt. Express 21(1), 974–983 (2013).
[PubMed]

Opt. Lett. (13)

A. Aiello, M. Merano, and J. P. Woerdman, “Brewster cross polarization,” Opt. Lett. 34(8), 1207–1209 (2009).
[PubMed]

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21(23), 1948–1950 (1996).
[PubMed]

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements,” Opt. Lett. 29(3), 238–240 (2004).
[PubMed]

J. Zhou, Y. Liu, Y. Ke, H. Luo, and S. Wen, “Generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases,” Opt. Lett. 40(13), 3193–3196 (2015).
[PubMed]

S. Wang, D. C. Abeysinghe, and Q. Zhan, “Generation of vectorial optical fields with slot-antenna-based metasurface,” Opt. Lett. 40(20), 4711–4714 (2015).
[PubMed]

G. M. Philip, V. Kumar, G. Milione, and N. K. Viswanathan, “Manifestation of the Gouy phase in vector-vortex beams,” Opt. Lett. 37(13), 2667–2669 (2012).
[PubMed]

Y. Zhang, P. Li, S. Liu, and J. Zhao, “Unveiling the photonic spin Hall effect of freely propagating fan-shaped cylindrical vector vortex beams,” Opt. Lett. 40(19), 4444–4447 (2015).
[PubMed]

X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
[PubMed]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[PubMed]

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013).
[PubMed]

M. Neugebauer, S. Grosche, S. Rothau, G. Leuchs, and P. Banzer, “Lateral spin transport in paraxial beams of light,” Opt. Lett. 41(15), 3499–3502 (2016).
[PubMed]

S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26(8), 485–487 (2001).
[PubMed]

D. Subbarao, “Topological phase in Gaussian beam optics,” Opt. Lett. 20(21), 2162–2164 (1995).
[PubMed]

Optica (1)

Photonics Res. (1)

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere,” Photonics Res. 5(1), 15–21 (2017).

Phys. Lett. A (1)

H. Chen, Q. Zhan, Y. Zhang, and Y. Li, “The Gouy phase shift of the highly focused radially polarized beam,” Phys. Lett. A 371(3), 259–261 (2007).

Phys. Rev. A (2)

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(11), 8185–8189 (1992).
[PubMed]

W. Shu, Y. Ke, Y. Liu, X. Ling, H. Luo, and X. Yin, “Radial spin Hall effect of light,” Phys. Rev. A 93(1), 013839 (2016).

Phys. Rev. Lett. (4)

D. Kawase, Y. Miyamoto, M. Takeda, K. Sasaki, and S. Takeuchi, “Observing quantum correlation of photons in Laguerre-Gauss modes using the Gouy phase,” Phys. Rev. Lett. 101(5), 050501 (2008).
[PubMed]

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy Phase Shift for Few-Cycle Laser Pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing local field structure of focused ultrashort pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[PubMed]

Sci. Rep. (3)

A. P. Porfirev, A. V. Ustinov, and S. N. Khonina, “Polarization conversion when focusing cylindrically polarized vortex beams,” Sci. Rep. 6(1), 6 (2016).
[PubMed]

S. Liu, P. Li, Y. Zhang, X. Gan, M. Wang, and J. Zhao, “Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift,” Sci. Rep. 6, 20774 (2016).
[PubMed]

J. Zhou, W. Zhang, Y. Liu, Y. Ke, Y. Liu, H. Luo, and S. Wen, “Spin-dependent manipulating of vector beams by tailoring polarization,” Sci. Rep. 6, 34276 (2016).
[PubMed]

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Figures (6)

Fig. 1
Fig. 1 Optical systems for observing polarization transition of focused VVBs. Laser, He-Ne laser with wavelength λ = 632.8 nm; HWP, half wave plate; GTP, Glan-Taylor polarizer; VR, vortex retarder; M, photomask; F, filter; L, lens with focal length f = 15 cm; CCD, charge coupled device. The insert shows the microscopic image of the photomask with l = 1.
Fig. 2
Fig. 2 (a) Schematic illustration of generating pure third-order vector beam by cascading VRs and HWP. LPB, linearly polarized beam. CVB, cylindrical vector beam. The white arrows illustrate the local polarization directions of the beam, and the short black lines on VRs represent the local fast axis. (b)-(d) Experimentally generated vector beams with m = 1, 2, 3 and 4, respectively. The short white lines denote the measured local polarization distributions.
Fig. 3
Fig. 3 (a) Experiment configuration used to measure the phase distribution of VVB. M, photomask; F, filter; L, lens; G, Ronci grating. (b)-(d) Off-axial interferogram between radially polarized beams carrying spiral phases with topological charges l = ± 1, ± 2 and ± 3, respectively.
Fig. 4
Fig. 4 Experimentally measured intensity distributions at the focal fields. (a)-(c) Focal fields of radially polarized vortex beams with l = 0, 2 and 3; (d)-(f) focal fields of second-order VVBs with topological charge l = 0, 3 and 4, respectively. The inserts are corresponding numerical simulation results. The dimensions of all figures are 225μm x 225μm.
Fig. 5
Fig. 5 Experimentally measured intensity distributions at the focal field. (a) and (b): focal fields of VVBs m = 2 and m = 3 with spiral phase characterized by topological charge l = 1, respectively; (c) and (d): focal fields of VVBs m = 3 and m = 4 with spiral phase characterized by topological charge l = 2, respectively. The inserts are pure vector beams with identical polarization order but without spiral phase. The dimensions of all figures are 225μm x 225μm.
Fig. 6
Fig. 6 Analysis of the polarization transition area in the cross section of the focused VVBs. Top: total intensity of the focal field. Bottom: radial intensity distributions of the two spin components. (a) m = l = 1; (b) m = 1, l = 2; (c) m = 3, l = 1.

Tables (1)

Tables Icon

Table 1 GPD between |R> and |L> components when z→∞

Equations (4)

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

E = γ [ exp ( i m φ + i φ 0 / 2 ) | R + exp ( -i m φ i φ 0 / 2 ) | L ]
E = γ 1 exp [ i ( l + m ) φ + i φ 0 / 2 ] | R + γ 2 exp [ i ( l m ) φ i φ 0 / 2 ] | L ,
Δ Φ = ( | l + m | | l m | ) tan 1 ( z z R ) = { 2 m tan - 1 ( z / z R ) , l > m 2 l tan - 1 ( z / z R ) , l < m .
M m = [ cos ( m φ ) sin ( m φ ) sin ( m φ ) cos ( m φ ) ] ,

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