Abstract

The robustness of the polarization spatial distribution of vector beams upon propagation is crucial for a number of applications, including optical communications and materials processing. This study has been commonly centered on Gouy phase effects on focused vector beams. In this work, we present a theoretical and experimental analysis of the Gouy phase’s effects on the propagation of pure and hybrid vector beams. Experimental results at various axial planes, before and past the focus, are obtained by using a simplified liquid-crystal spatial light modulator-based optical system that allows the easy generation of these beams. Furthermore, a new alternative optical set-up that is devoid of moving elements is demonstrated, which simplifies this study. We experimentally verify the differences between pure and hybrid vector beams upon propagation. While the first ones remain stable, hybrid vector beams show Gouy phase effects that demonstrate an optical activity where the local polarization states rotate by an angle that depends on the propagation distance. Experimental results agree with the theory.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

M. M. Sánchez-López, I. Abella, D. Puerto-García, J. A. Davis, and I. Moreno, “Spectral performance of a zero-order liquid-crystal polymer commercial q-plate for the generation of vector beams at different wavelengths,” Opt. Laser Technol. 106, 168–176 (2018).
[Crossref]

P. Srinivas, C. Perumangatt, N. Lal, R. P. Singh, and B. Srinivasan, “Investigation of propagation dynamics of truncated vector vortex beams,” Opt. Lett. 43(11), 2579–2582 (2018).
[Crossref] [PubMed]

2017 (4)

Y. Zhang, X. Guo, L. Han, P. Li, S. Liu, H. Cheng, and J. Zhao, “Gouy phase induced polarization transition of focused vector vortex beams,” Opt. Express 25(21), 25725–25733 (2017).
[Crossref] [PubMed]

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,” Photon. Res. 5(1), 15–21 (2017).
[Crossref]

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[Crossref]

C. N. Alexeyev, Yu. A. Egorov, and A. V. Volyar, “Mutual transformations of fractional-order and integer-order optical vortices,” Phys. Rev. A 96(6), 63807 (2017).
[Crossref]

2016 (6)

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

X. Ling, X. Yi, Z. Dai, Y. Wang, and L. Chen, “Characterization and manipulation of full Poincaré beams on the hybrid Poincaré sphere,” J. Soc. Opt. Am. B 33(11), 2172–2176 (2016).
[Crossref]

B. Khajavi and E. J. Galvez, “High-order disclinations in space-variant polarization,” J. Opt. 18(8), 084003 (2016).
[Crossref]

I. Moreno, M. M. Sánchez-López, K. Badham, J. A. Davis, and D. M. Cottrell, “Generation of integer and fractional vector beams with q-plates encoded onto a spatial light modulator,” Opt. Lett. 41(6), 1305–1308 (2016).
[Crossref] [PubMed]

K. J. Kaltenecker, J. C. König-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).
[Crossref]

C.-H. Yang, Y.-D. Chen, S.-T. Wu, and A. Y.-G. Fuh, “Independent manipulation of topological charges and polarization patterns of optical vortices,” Sci. Rep. 6(1), 31546 (2016).
[Crossref] [PubMed]

2015 (6)

H. Wang, G. Rui, and Q. Zhan, “Dynamic propagation of optical vortices embedded in full Poincaré beams with rotationally polarization symmetry,” Opt. Commun. 351, 15–25 (2015).
[Crossref]

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a Fresnel diffraction algorithm,” Opt. Eng. 54(10), 103101 (2015).
[Crossref]

I. Moreno, J. A. Davis, T. Womble-Dahl, and D. M. Cottrell, “Azimuthal multiple-beam interference effects with combinations of vortex beams,” Opt. Lett. 40(10), 2341–2344 (2015).
[Crossref] [PubMed]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

S. G. Reddy, C. Permangatt, S. Prabhakar, A. Anwar, J. Banerji, and R. P. Singh, “Divergence of optical vortex beams,” Appl. Opt. 54(22), 6690–6693 (2015).
[Crossref] [PubMed]

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

2013 (3)

2012 (4)

2011 (2)

X.-L. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H.-T. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

P. Vaity and R. P. Singh, “Self-healing property of optical ring lattice,” Opt. Lett. 36(15), 2994–2996 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (3)

2007 (1)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

2006 (2)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [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).
[Crossref] [PubMed]

2005 (1)

2000 (1)

1998 (1)

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

1995 (1)

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

1990 (1)

Abella, I.

M. M. Sánchez-López, I. Abella, D. Puerto-García, J. A. Davis, and I. Moreno, “Spectral performance of a zero-order liquid-crystal polymer commercial q-plate for the generation of vector beams at different wavelengths,” Opt. Laser Technol. 106, 168–176 (2018).
[Crossref]

Abrams, K.

Aït-Ameur, K.

Albero, J.

J. A. Davis, D. M. Cottrell, B. C. Schoonover, J. B. Cushing, J. Albero, and I. Moreno, “Vortex sensing analysis of radially and pseudo-radially polarized beams,” Opt. Eng. 52(5), 50502 (2013).

Alexeyev, C. N.

C. N. Alexeyev, Yu. A. Egorov, and A. V. Volyar, “Mutual transformations of fractional-order and integer-order optical vortices,” Phys. Rev. A 96(6), 63807 (2017).
[Crossref]

Alfano, R. R.

Allegre, O. J.

Allen, L.

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

Alonso, M. A.

Anwar, A.

Badham, K.

Banerji, J.

Beckley, A. M.

Bentley, J. B.

Berg, C. A.

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a Fresnel diffraction algorithm,” Opt. Eng. 54(10), 103101 (2015).
[Crossref]

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Biener, G.

Boyd, R. W.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

Brown, T. G.

Carmona, A.

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a Fresnel diffraction algorithm,” Opt. Eng. 54(10), 103101 (2015).
[Crossref]

Chen, J.

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

X.-L. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H.-T. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

Chen, L.

X. Ling, X. Yi, Z. Dai, Y. Wang, and L. Chen, “Characterization and manipulation of full Poincaré beams on the hybrid Poincaré sphere,” J. Soc. Opt. Am. B 33(11), 2172–2176 (2016).
[Crossref]

Chen, S.

Y. He, H. Ye, J. Liu, Z. Xie, X. Zhang, Y. Xiang, S. Chen, Y. Li, and D. Fan, “Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces,” IEEE Photonics J. 9(5), 1 (2017).
[Crossref]

Chen, Y.-D.

C.-H. Yang, Y.-D. Chen, S.-T. Wu, and A. Y.-G. Fuh, “Independent manipulation of topological charges and polarization patterns of optical vortices,” Sci. Rep. 6(1), 31546 (2016).
[Crossref] [PubMed]

Cheng, H.

Cottrell, D. M.

I. Moreno, M. M. Sánchez-López, K. Badham, J. A. Davis, and D. M. Cottrell, “Generation of integer and fractional vector beams with q-plates encoded onto a spatial light modulator,” Opt. Lett. 41(6), 1305–1308 (2016).
[Crossref] [PubMed]

I. Moreno, J. A. Davis, T. Womble-Dahl, and D. M. Cottrell, “Azimuthal multiple-beam interference effects with combinations of vortex beams,” Opt. Lett. 40(10), 2341–2344 (2015).
[Crossref] [PubMed]

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a Fresnel diffraction algorithm,” Opt. Eng. 54(10), 103101 (2015).
[Crossref]

J. A. Davis, D. M. Cottrell, B. C. Schoonover, J. B. Cushing, J. Albero, and I. Moreno, “Vortex sensing analysis of radially and pseudo-radially polarized beams,” Opt. Eng. 52(5), 50502 (2013).

J. A. Davis and D. M. Cottrell, “Ray matrix analysis of the fast Fresnel transform with applications towards liquid crystal displays,” Appl. Opt. 51(5), 644–650 (2012).
[Crossref] [PubMed]

I. Moreno, J. A. Davis, I. Ruiz, and D. M. Cottrell, “Decomposition of radially and azimuthally polarized beams using a circular-polarization and vortex-sensing diffraction grating,” Opt. Express 18(7), 7173–7183 (2010).
[Crossref] [PubMed]

J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39(10), 1549–1554 (2000).
[Crossref] [PubMed]

Cui, H. X.

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

Cushing, J. B.

J. A. Davis, D. M. Cottrell, B. C. Schoonover, J. B. Cushing, J. Albero, and I. Moreno, “Vortex sensing analysis of radially and pseudo-radially polarized beams,” Opt. Eng. 52(5), 50502 (2013).

Dai, Z.

X. Ling, X. Yi, Z. Dai, Y. Wang, and L. Chen, “Characterization and manipulation of full Poincaré beams on the hybrid Poincaré sphere,” J. Soc. Opt. Am. B 33(11), 2172–2176 (2016).
[Crossref]

Davis, J. A.

M. M. Sánchez-López, I. Abella, D. Puerto-García, J. A. Davis, and I. Moreno, “Spectral performance of a zero-order liquid-crystal polymer commercial q-plate for the generation of vector beams at different wavelengths,” Opt. Laser Technol. 106, 168–176 (2018).
[Crossref]

I. Moreno, M. M. Sánchez-López, K. Badham, J. A. Davis, and D. M. Cottrell, “Generation of integer and fractional vector beams with q-plates encoded onto a spatial light modulator,” Opt. Lett. 41(6), 1305–1308 (2016).
[Crossref] [PubMed]

I. Moreno, J. A. Davis, T. Womble-Dahl, and D. M. Cottrell, “Azimuthal multiple-beam interference effects with combinations of vortex beams,” Opt. Lett. 40(10), 2341–2344 (2015).
[Crossref] [PubMed]

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a Fresnel diffraction algorithm,” Opt. Eng. 54(10), 103101 (2015).
[Crossref]

J. A. Davis, D. M. Cottrell, B. C. Schoonover, J. B. Cushing, J. Albero, and I. Moreno, “Vortex sensing analysis of radially and pseudo-radially polarized beams,” Opt. Eng. 52(5), 50502 (2013).

J. A. Davis and D. M. Cottrell, “Ray matrix analysis of the fast Fresnel transform with applications towards liquid crystal displays,” Appl. Opt. 51(5), 644–650 (2012).
[Crossref] [PubMed]

I. Moreno, J. A. Davis, I. Ruiz, and D. M. Cottrell, “Decomposition of radially and azimuthally polarized beams using a circular-polarization and vortex-sensing diffraction grating,” Opt. Express 18(7), 7173–7183 (2010).
[Crossref] [PubMed]

J. A. Davis, B. M. L. Pascoguin, I. Moreno, and A. Nava-Vega, “Circular-polarization-splitting common-path interferometer based on a zero-twist liquid-crystal display,” Opt. Lett. 34(9), 1486–1488 (2009).
[Crossref] [PubMed]

J. A. Davis and J. B. Bentley, “Azimuthal prism effect with partially blocked vortex-producing lenses,” Opt. Lett. 30(23), 3204–3206 (2005).
[Crossref] [PubMed]

J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, “Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39(10), 1549–1554 (2000).
[Crossref] [PubMed]

Dearden, G.

Debenham, W.

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a Fresnel diffraction algorithm,” Opt. Eng. 54(10), 103101 (2015).
[Crossref]

Edwardson, S. P.

Egorov, Yu. A.

C. N. Alexeyev, Yu. A. Egorov, and A. V. Volyar, “Mutual transformations of fractional-order and integer-order optical vortices,” Phys. Rev. A 96(6), 63807 (2017).
[Crossref]

Fan, D.

Y. He, H. Ye, J. Liu, Z. Xie, X. Zhang, Y. Xiang, S. Chen, Y. Li, and D. Fan, “Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces,” IEEE Photonics J. 9(5), 1 (2017).
[Crossref]

Fearon, E.

Fischer, B. M.

Forbes, A.

Ford, D. H.

Freeman, C. L.

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a Fresnel diffraction algorithm,” Opt. Eng. 54(10), 103101 (2015).
[Crossref]

Friberg, A.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

Fuh, A. Y.-G.

C.-H. Yang, Y.-D. Chen, S.-T. Wu, and A. Y.-G. Fuh, “Independent manipulation of topological charges and polarization patterns of optical vortices,” Sci. Rep. 6(1), 31546 (2016).
[Crossref] [PubMed]

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Galvez, E. J.

Gu, B.

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

X.-L. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H.-T. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

Guo, X.

Han, L.

Hasman, E.

Hasnaoui, A.

He, Y.

Y. He, H. Ye, J. Liu, Z. Xie, X. Zhang, Y. Xiang, S. Chen, Y. Li, and D. Fan, “Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces,” IEEE Photonics J. 9(5), 1 (2017).
[Crossref]

Helm, H.

Helm, M.

Honkanen, M.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

Huang, H.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Jin, Y.

Kaltenecker, K. J.

Karimi, E.

Ke, Y.

Khadka, S.

Khajavi, B.

B. Khajavi and E. J. Galvez, “High-order disclinations in space-variant polarization,” J. Opt. 18(8), 084003 (2016).
[Crossref]

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).
[Crossref] [PubMed]

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

Kimura, W. D.

Kleiner, V.

König-Otto, J. C.

Kotlyar, V. V.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

Kristensen, P.

Kuittinen, M.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

Kumar, V.

Lal, N.

Lautanen, J.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

Lavery, M. P. J.

Li, P.

Li, Y.

Y. He, H. Ye, J. Liu, Z. Xie, X. Zhang, Y. Xiang, S. Chen, Y. Li, and D. Fan, “Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces,” IEEE Photonics J. 9(5), 1 (2017).
[Crossref]

X.-L. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H.-T. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

Li, Y. N.

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

Ling, X.

X. Ling, X. Yi, Z. Dai, Y. Wang, and L. Chen, “Characterization and manipulation of full Poincaré beams on the hybrid Poincaré sphere,” J. Soc. Opt. Am. B 33(11), 2172–2176 (2016).
[Crossref]

Liu, J.

Y. He, H. Ye, J. Liu, Z. Xie, X. Zhang, Y. Xiang, S. Chen, Y. Li, and D. Fan, “Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces,” IEEE Photonics J. 9(5), 1 (2017).
[Crossref]

Liu, S.

Liu, Y.

Liu, Z.

Lou, K.

X.-L. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H.-T. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

Luo, H.

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Marrucci, L.

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

McNamara, D. E.

Miatto, F. M.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

Milione, G.

Mittendorff, M.

Moreno, I.

M. M. Sánchez-López, I. Abella, D. Puerto-García, J. A. Davis, and I. Moreno, “Spectral performance of a zero-order liquid-crystal polymer commercial q-plate for the generation of vector beams at different wavelengths,” Opt. Laser Technol. 106, 168–176 (2018).
[Crossref]

I. Moreno, M. M. Sánchez-López, K. Badham, J. A. Davis, and D. M. Cottrell, “Generation of integer and fractional vector beams with q-plates encoded onto a spatial light modulator,” Opt. Lett. 41(6), 1305–1308 (2016).
[Crossref] [PubMed]

I. Moreno, J. A. Davis, T. Womble-Dahl, and D. M. Cottrell, “Azimuthal multiple-beam interference effects with combinations of vortex beams,” Opt. Lett. 40(10), 2341–2344 (2015).
[Crossref] [PubMed]

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a Fresnel diffraction algorithm,” Opt. Eng. 54(10), 103101 (2015).
[Crossref]

J. A. Davis, D. M. Cottrell, B. C. Schoonover, J. B. Cushing, J. Albero, and I. Moreno, “Vortex sensing analysis of radially and pseudo-radially polarized beams,” Opt. Eng. 52(5), 50502 (2013).

I. Moreno, J. A. Davis, I. Ruiz, and D. M. Cottrell, “Decomposition of radially and azimuthally polarized beams using a circular-polarization and vortex-sensing diffraction grating,” Opt. Express 18(7), 7173–7183 (2010).
[Crossref] [PubMed]

J. A. Davis, B. M. L. Pascoguin, I. Moreno, and A. Nava-Vega, “Circular-polarization-splitting common-path interferometer based on a zero-twist liquid-crystal display,” Opt. Lett. 34(9), 1486–1488 (2009).
[Crossref] [PubMed]

Nava-Vega, A.

Ngcobo, S.

Nguyen, T. A.

Niv, A.

Nolan, D. A.

Nomoto, S.

Ouyang, J.

Pääkkönen, P.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

Padgett, M. J.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Pascoguin, B. M. L.

Passilly, N.

Permangatt, C.

Perrie, W.

Perumangatt, C.

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).
[Crossref] [PubMed]

Prabhakar, S.

Puerto-García, D.

M. M. Sánchez-López, I. Abella, D. Puerto-García, J. A. Davis, and I. Moreno, “Spectral performance of a zero-order liquid-crystal polymer commercial q-plate for the generation of vector beams at different wavelengths,” Opt. Laser Technol. 106, 168–176 (2018).
[Crossref]

Ramachandran, S.

Reddy, S. G.

Ren, Y.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

Rui, G.

H. Wang, G. Rui, and Q. Zhan, “Dynamic propagation of optical vortices embedded in full Poincaré beams with rotationally polarization symmetry,” Opt. Commun. 351, 15–25 (2015).
[Crossref]

Ruiz, I.

Sánchez-López, M. M.

M. M. Sánchez-López, I. Abella, D. Puerto-García, J. A. Davis, and I. Moreno, “Spectral performance of a zero-order liquid-crystal polymer commercial q-plate for the generation of vector beams at different wavelengths,” Opt. Laser Technol. 106, 168–176 (2018).
[Crossref]

I. Moreno, M. M. Sánchez-López, K. Badham, J. A. Davis, and D. M. Cottrell, “Generation of integer and fractional vector beams with q-plates encoded onto a spatial light modulator,” Opt. Lett. 41(6), 1305–1308 (2016).
[Crossref] [PubMed]

Schneider, H.

Schoonover, B. C.

J. A. Davis, D. M. Cottrell, B. C. Schoonover, J. B. Cushing, J. Albero, and I. Moreno, “Vortex sensing analysis of radially and pseudo-radially polarized beams,” Opt. Eng. 52(5), 50502 (2013).

Schubert, W. H.

Shu, W.

Singh, R. P.

Soifer, V. A.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

Sonehara, T.

Srinivas, P.

Srinivasan, B.

Tidwell, S. C.

Turunen, J.

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

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).
[Crossref] [PubMed]

Vaity, P.

Viswanathan, N. K.

Volyar, A. V.

C. N. Alexeyev, Yu. A. Egorov, and A. V. Volyar, “Mutual transformations of fractional-order and integer-order optical vortices,” Phys. Rev. A 96(6), 63807 (2017).
[Crossref]

Walther, M.

Wang, H.

H. Wang, G. Rui, and Q. Zhan, “Dynamic propagation of optical vortices embedded in full Poincaré beams with rotationally polarization symmetry,” Opt. Commun. 351, 15–25 (2015).
[Crossref]

Wang, H. T.

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

Wang, H.-T.

X.-L. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H.-T. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

Wang, X. L.

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

Wang, X.-L.

X.-L. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H.-T. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

Wang, Y.

X. Ling, X. Yi, Z. Dai, Y. Wang, and L. Chen, “Characterization and manipulation of full Poincaré beams on the hybrid Poincaré sphere,” J. Soc. Opt. Am. B 33(11), 2172–2176 (2016).
[Crossref]

Wen, S.

Willner, A. E.

Winnerl, S.

Womble-Dahl, T.

Wu, S.-T.

C.-H. Yang, Y.-D. Chen, S.-T. Wu, and A. Y.-G. Fuh, “Independent manipulation of topological charges and polarization patterns of optical vortices,” Sci. Rep. 6(1), 31546 (2016).
[Crossref] [PubMed]

Xiang, Y.

Y. He, H. Ye, J. Liu, Z. Xie, X. Zhang, Y. Xiang, S. Chen, Y. Li, and D. Fan, “Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces,” IEEE Photonics J. 9(5), 1 (2017).
[Crossref]

Xie, G.

Xie, Z.

Y. He, H. Ye, J. Liu, Z. Xie, X. Zhang, Y. Xiang, S. Chen, Y. Li, and D. Fan, “Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces,” IEEE Photonics J. 9(5), 1 (2017).
[Crossref]

Yan, M. F.

Yang, C.-H.

C.-H. Yang, Y.-D. Chen, S.-T. Wu, and A. Y.-G. Fuh, “Independent manipulation of topological charges and polarization patterns of optical vortices,” Sci. Rep. 6(1), 31546 (2016).
[Crossref] [PubMed]

Ye, H.

Y. He, H. Ye, J. Liu, Z. Xie, X. Zhang, Y. Xiang, S. Chen, Y. Li, and D. Fan, “Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces,” IEEE Photonics J. 9(5), 1 (2017).
[Crossref]

Yi, X.

X. Ling, X. Yi, Z. Dai, Y. Wang, and L. Chen, “Characterization and manipulation of full Poincaré beams on the hybrid Poincaré sphere,” J. Soc. Opt. Am. B 33(11), 2172–2176 (2016).
[Crossref]

Zeilinger, A.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

Zhan, Q.

H. Wang, G. Rui, and Q. Zhan, “Dynamic propagation of optical vortices embedded in full Poincaré beams with rotationally polarization symmetry,” Opt. Commun. 351, 15–25 (2015).
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Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
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Y. He, H. Ye, J. Liu, Z. Xie, X. Zhang, Y. Xiang, S. Chen, Y. Li, and D. Fan, “Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces,” IEEE Photonics J. 9(5), 1 (2017).
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Zhang, Y.

Zhao, J.

Adv. Opt. Photonics (1)

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

Appl. Opt. (6)

IEEE Photonics J. (1)

Y. He, H. Ye, J. Liu, Z. Xie, X. Zhang, Y. Xiang, S. Chen, Y. Li, and D. Fan, “Order-controllable cylindrical vector vortex beam generation by using spatial light modulator and cascaded metasurfaces,” IEEE Photonics J. 9(5), 1 (2017).
[Crossref]

J. Mod. Opt. (1)

P. Pääkkönen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer, and A. Friberg, “Rotating optical fields,” J. Mod. Opt. 45(11), 2355–2369 (1998).
[Crossref]

J. Opt. (2)

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

B. Khajavi and E. J. Galvez, “High-order disclinations in space-variant polarization,” J. Opt. 18(8), 084003 (2016).
[Crossref]

J. Soc. Opt. Am. B (1)

X. Ling, X. Yi, Z. Dai, Y. Wang, and L. Chen, “Characterization and manipulation of full Poincaré beams on the hybrid Poincaré sphere,” J. Soc. Opt. Am. B 33(11), 2172–2176 (2016).
[Crossref]

New J. Phys. (2)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[Crossref]

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, “Divergence of an orbital-angular-momentum-carrying beam upon propagation,” New J. Phys. 17(2), 023011 (2015).
[Crossref]

Opt. Commun. (2)

M. J. Padgett and L. Allen, “The Poynting vector in Laguerre-Gaussian laser modes,” Opt. Commun. 121(1-3), 36–40 (1995).
[Crossref]

H. Wang, G. Rui, and Q. Zhan, “Dynamic propagation of optical vortices embedded in full Poincaré beams with rotationally polarization symmetry,” Opt. Commun. 351, 15–25 (2015).
[Crossref]

Opt. Eng. (2)

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a Fresnel diffraction algorithm,” Opt. Eng. 54(10), 103101 (2015).
[Crossref]

J. A. Davis, D. M. Cottrell, B. C. Schoonover, J. B. Cushing, J. Albero, and I. Moreno, “Vortex sensing analysis of radially and pseudo-radially polarized beams,” Opt. Eng. 52(5), 50502 (2013).

Opt. Express (5)

Opt. Laser Technol. (1)

M. M. Sánchez-López, I. Abella, D. Puerto-García, J. A. Davis, and I. Moreno, “Spectral performance of a zero-order liquid-crystal polymer commercial q-plate for the generation of vector beams at different wavelengths,” Opt. Laser Technol. 106, 168–176 (2018).
[Crossref]

Opt. Lett. (9)

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
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S. Ramachandran, P. Kristensen, and M. F. Yan, “Generation and propagation of radially polarized beams in optical fibers,” Opt. Lett. 34(16), 2525–2527 (2009).
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I. Moreno, M. M. Sánchez-López, K. Badham, J. A. Davis, and D. M. Cottrell, “Generation of integer and fractional vector beams with q-plates encoded onto a spatial light modulator,” Opt. Lett. 41(6), 1305–1308 (2016).
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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).
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J. A. Davis and J. B. Bentley, “Azimuthal prism effect with partially blocked vortex-producing lenses,” Opt. Lett. 30(23), 3204–3206 (2005).
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P. Vaity and R. P. Singh, “Self-healing property of optical ring lattice,” Opt. Lett. 36(15), 2994–2996 (2011).
[Crossref] [PubMed]

I. Moreno, J. A. Davis, T. Womble-Dahl, and D. M. Cottrell, “Azimuthal multiple-beam interference effects with combinations of vortex beams,” Opt. Lett. 40(10), 2341–2344 (2015).
[Crossref] [PubMed]

J. A. Davis, B. M. L. Pascoguin, I. Moreno, and A. Nava-Vega, “Circular-polarization-splitting common-path interferometer based on a zero-twist liquid-crystal display,” Opt. Lett. 34(9), 1486–1488 (2009).
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P. Srinivas, C. Perumangatt, N. Lal, R. P. Singh, and B. Srinivasan, “Investigation of propagation dynamics of truncated vector vortex beams,” Opt. Lett. 43(11), 2579–2582 (2018).
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Optica (1)

Photon. Res. (1)

Phys. Rev. A (2)

X.-L. Wang, K. Lou, J. Chen, B. Gu, Y. Li, and H.-T. Wang, “Unveiling locally linearly polarized vector fields with broken axial symmetry,” Phys. Rev. A 83(6), 063813 (2011).
[Crossref]

C. N. Alexeyev, Yu. A. Egorov, and A. V. Volyar, “Mutual transformations of fractional-order and integer-order optical vortices,” Phys. Rev. A 96(6), 63807 (2017).
[Crossref]

Phys. Rev. Lett. (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref] [PubMed]

Sci. Rep. (2)

C.-H. Yang, Y.-D. Chen, S.-T. Wu, and A. Y.-G. Fuh, “Independent manipulation of topological charges and polarization patterns of optical vortices,” Sci. Rep. 6(1), 31546 (2016).
[Crossref] [PubMed]

A. P. Porfirev, A. V. Ustinov, and S. N. Khonina, “Polarization conversion when focusing cylindrically polarized vortex beams,” Sci. Rep. 6(1), 6 (2016).
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B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd edition, (John Wiley and Sons Inc. 2007).

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Figures (5)

Fig. 1
Fig. 1 Plot of the Gouy phase term ζ(z) in Eq. (1).
Fig. 2
Fig. 2 (a) Focusing of a Gaussian beam with a lens. The new smaller waist is located approximately at the focal plane of the lens. The waist is located at the position z = 0. An SLM and a q-plate located before the lens are used to generate the vector beam. Simulation results in (b) and (c) for the intensity pattern behind an analyzer that is vertically aligned and at various axial locations. (b) Right after the SLM and q-plate, pure and hybrid vector beams show identical patterns. (c) However, when viewed around the focal plane the pure vector beam retains its polarization structure, while the hybrid vector beam suffers a rotation α(z).
Fig. 3
Fig. 3 (a) Scheme of the first proposed optical system to generate pure and hybrid vector beams and study the Gouy phase effects. A SPP is encoded on the LCoS-SLM and the lens L2 (or the CCD camera) is shifted longitudinally to capture different axial planes near the beam waist. (b) Experimental results for the propagation of the radially polarized beams with charges ( l R , l L )=(−1, −3), ( +1, −1) and (+3, +1) The analyzer is vertically aligned in all cases.
Fig. 4
Fig. 4 Simulation results for the propagation of radially polarized beams with charges ( l R , l L )=(−1, −3), (+1, −1) and (+3, +1) in steps of 20 mm from the focus spot. The rotation of 45° occurs at about 40 mm from the focus.
Fig. 5
Fig. 5 (a) Scheme of the second proposed optical setup to generate different pure and hybrid vector beams and study Gouy phase effects. A SPP and the lens are encoded on the LCoS-SLM. The CCD camera is kept in a fixed position and the phase mask in the SLM is virtually displaced using a propagation algorithm. (b) Results for the propagation of the radially polarized beams with charges ( l R , l L )=(−1, −3), ( +1, −1) and (+3, +1). The analyzer is vertically aligned in all cases.

Equations (14)

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E l = u 0l (z) e ilθ e iΦ(l,z) ,
u 0l (z)= 1 π(|l|)! 1 ω(z) ( 2 r ω(z) ) |l| L 0 |l| ( 2 r 2 ω (z) 2 )exp( r 2 ω (z) 2 i k r 2 2R(z) ),
Φ(p,l,z)=[ |l|+2p+1 ]ζ(z),
ω(z)= ω 0 1+ ( z z 0 ) 2 .
| V(z)= u 0 l R (z) e i l R θ e i Φ R (l,z) |R+ u 0 l L (z) e i l L θ e i Φ L (l,z) |L,
Φ R (z)=[ | l R |+1 ]ζ(z) and Φ L (z)=[ | l L |+1 ]ζ(z).
Δ Φ G (z)= Φ R (z) Φ L (z)=( | l R || l L | )ζ(z).
l= 1 2 ( l R + l L ) and m= 1 2 ( l R l L ).
| V(z) u 0l e ilθ { e imθ e i Φ R (z) |R+ e +imθ e i Φ L (z) |L },
α(z)= 1 2 Δ Φ G (z)= 1 2 ( |l+m||lm| )ζ(z).
| V(z)=2 u 0l e ilθ e i 1 2 ( Φ R (z)+ Φ L (z) ) ( cos( mθ+α(z) ) sin( mθ+α(z) ) ).
ω 02 ω 01 f z 01
z 02 f 2 λ π ω 01 2
l= 1 2 ( l R + l L )= l SPP and m= 1 2 ( l R l L )= l 2q .

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