Abstract

We present a simple and efficient method to generate any cylindrical vector vortex (CVV) beams based on two cascaded metasurfaces. The metasurface works as a space-variant Panchratnam-Berry phase element and can produce any desirable vortex phase and vector polarization. The first metasurface is used to switch the sign of topological charges associated with vortex, and the second metasurface is applied to manipulate the local polarization. This method allows us to simultaneously manipulate polarization and phase of the CVV beams.

© 2014 Optical Society of America

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2014 (2)

H. Ye, C. Wan, K. Huang, T. Han, J. Teng, Y. S. Ping, and C. Qiu, “Creation of vectorial bottle-hollow beam using radially or azimuthally polarized light,” Opt. Lett. 39, 630–633 (2014).
[CrossRef] [PubMed]

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[CrossRef]

2013 (2)

2012 (4)

2011 (6)

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).
[CrossRef]

H. Chen, J. Hao, B. F. Zhang, J. Xu, J. Ding, and H. T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett. 36, 3179–3181. (2011).
[CrossRef] [PubMed]

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

A. Holleczek, A. Aiello, C. Gabriel, C. Marquardt, and G. Leuchs, “Classical and quantum properties of cylindrically polarized states of light,” Opt. Express 19, 9714–9736 (2011).
[CrossRef] [PubMed]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

2010 (2)

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[CrossRef]

Y. Kozawa and S. Sato, “Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams,” Opt. Express 18, 10828–10833 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (2)

2007 (2)

2006 (2)

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

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

2004 (2)

2003 (2)

R. Dorn, S Qubis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

2002 (2)

2000 (1)

1999 (1)

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, 8185–8189 (1992).
[CrossRef] [PubMed]

Aiello, A.

Alfano, R. R.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

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, 8185–8189 (1992).
[CrossRef] [PubMed]

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, 8185–8189 (1992).
[CrossRef] [PubMed]

Beresna, M.

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

Biener, G.

Boltasseva, A.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[CrossRef] [PubMed]

Bomzon, Z.

Born, M.

M. Born and E. Wolf, Principles of Optics (University Press, Cambridge, 1997).

Brown, T. G.

Cardano, F.

Chen, H.

Courtial, J.

Crawford, P. R.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

de Lisio, C.

Deng, D.

Ding, J.

Dorn, R.

R. Dorn, S Qubis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Fainman, Y.

Gabriel, C.

Galvez, E. J.

E. J. Galvez, S. Khadka, W. H. Schubert, and S. Nomoto, “Poincaré-beam patterns produced by nonseparable superpositions of Laguerre-Gauss and polarization modes of light,” Appl. Opt. 51, 2925–2934 (2012).
[CrossRef] [PubMed]

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

Gecevicius, M.

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

Gertus, T.

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

Gorodetski, Y.

Guo, Q.

Haglin, P. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

Han, T.

Hao, J.

Hasman, E.

Holleczek, A.

Huang, K.

Inavalli, V. V. G. K.

Karimi, E.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[CrossRef] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[CrossRef]

Kawauchi, H.

Kazansky, P. G.

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

Khadka, S.

Kildishev, A. V.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[CrossRef] [PubMed]

Kleiner, V.

Kozawa, Y.

Leger, J. R.

Lerman, G. M.

Leuchs, G.

Levy, U.

Li, S.

Ling, X.

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[CrossRef]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[CrossRef]

Litchinitser, N. M.

N. M. Litchinitser, “Structured light meets structured matter,” Science 337, 1054–1055 (2012).
[CrossRef] [PubMed]

Liu, Y.

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[CrossRef]

Luo, H.

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[CrossRef]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[CrossRef]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Marquardt, C.

Marrucci, L.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[CrossRef] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Milione, G.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Nagali, E.

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

Niv, A.

Nolan, D. A.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Nomoto, S.

Padgett, M. J.

Pang, L.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media,” Phys. Rev. Lett. 96, 163905 (2006).
[CrossRef] [PubMed]

Piccirillo, B

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

Piccirillo, B.

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[CrossRef]

Ping, Y. S.

Pysher, M. J.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

Qiu, C.

Qubis, S

R. Dorn, S Qubis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Santamato, E.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[CrossRef] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[CrossRef]

Sato, S.

Schubert, W. H.

Sciarrino, F.

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

Shalaev, V. M.

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[CrossRef] [PubMed]

Slussarenko, S.

F. Cardano, E. Karimi, S. Slussarenko, L. Marrucci, C. de Lisio, and E. Santamato, “Polarization pattern of vector vortex beams generated by q-plates with different topological charges,” Appl. Opt. 51, C1–C6 (2012).
[CrossRef] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
[CrossRef]

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[CrossRef]

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, 8185–8189 (1992).
[CrossRef] [PubMed]

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

Teng, J.

Tsai, C.

Viswanathan, N. K.

Wan, C.

Wang, H. T.

Wang, J.

Wen, S.

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[CrossRef]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[CrossRef]

Williams, R. E.

E. J. Galvez, P. R. Crawford, H. I. Sztul, M. J. Pysher, P. J. Haglin, and R. E. Williams, “Geometric phase associated with mode transformations of optical beams bearing orbital angular momentum,” Phys. Rev. Lett. 90, 203901 (2003).
[CrossRef] [PubMed]

Willner, A. E.

Woerdman, J. P.

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]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (University Press, Cambridge, 1997).

Xu, J.

Yao, A. M.

Ye, H.

Yi, X.

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[CrossRef]

Yonezawa, K.

Youngworth, K. S.

Zhan, Q.

Zhang, B. F.

Zhao, Z.

Zhou, X.

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[CrossRef]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[CrossRef]

Adv. Opt. Photon. (2)

Appl. Opt. (2)

Appl. Phys. Lett. (2)

M. Beresna, M. Gecevičius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98, 201101 (2011).
[CrossRef]

Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, and S. Wen, “Realization of polarization evolution on higher-order Poincaré sphere with metasurface,” Appl. Phys. Lett. 104, 191110 (2014).
[CrossRef]

J. Opt. (1)

L. Marrucci, E. Karimi, S. Slussarenko, B Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13, 064001 (2011).
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Opt. Express (6)

Opt. Lett. (11)

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M. J. Padgett and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24, 430–432 (1999).
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H. Kawauchi, K. Yonezawa, Y. Kozawa, and S. Sato, “Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam,” Opt. Lett. 32, 1839–1841 (2007).
[CrossRef] [PubMed]

D. Deng and Q. Guo, “Analytical vectorial structure of radially polarized light beams,” Opt. Lett. 32, 2711–2713 (2007).
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Z. Zhao, J. Wang, S. Li, and A. E. Willner, “Metamaterials-based broadband generation of orbital angular momentum carrying vector beams,” Opt. Lett. 38, 932–934 (2013).
[CrossRef] [PubMed]

N. K. Viswanathan and V. V. G. K. Inavalli, “Generation of optical vector beams using a two-mode fiber,” Opt. Lett. 34, 1189–1191 (2009).
[CrossRef] [PubMed]

H. Chen, J. Hao, B. F. Zhang, J. Xu, J. Ding, and H. T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett. 36, 3179–3181. (2011).
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[CrossRef] [PubMed]

Phys. Rev. A (3)

E. Karimi, S. Slussarenko, B. Piccirillo, L. Marrucci, and E. Santamato, “Polarization-controlled evolution of light transverse modes and associated pancharatnam geometric phase in orbital angular momentum,” Phys. Rev. A 81, 053813 (2010).
[CrossRef]

X. Ling, X. Zhou, H. Luo, and S. Wen, “Steering far-field spin-dependent splitting of light by inhomogeneous anisotropic media,” Phys. Rev. A 86, 053824 (2012).
[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).
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Phys. Rev. Lett. (4)

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light,” Phys. Rev. Lett. 107, 053601 (2011).
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Figures (5)

Fig. 1
Fig. 1

Experimental setup for generating arbitrary CVV beams. Inset (a) and (b): Schematic pictures of metasurfaces with q = 0.5 and q = 1, respectively. Space-varying nanograting consisting of nanoscale waveplate with a spatially varying fast axis directions. Inset (c): Intensity distribution of the CVV beams presents doughnut profiles.

Fig. 2
Fig. 2

Stokes parameter S3 of the beams emerging from MS1. Row 1: the experimental results when QWP1 is placed at 45°. (a) and (b) are the intensity distributions when GLP4 is placed at ±45°, respectively. (c) the corresponding Stokes parameter S3. Row 2: the experimental results when QWP1 is placed at −45°. (d) and (e) are the intensity distributions when GLP4 is placed at ±45°, respectively. (f) the corresponding Stokes parameter S3.

Fig. 3
Fig. 3

The intensity distribution (upper panels) of the beam emerging from the first metasurface and the interference patterns (lower panels) after their superposition with the reference beam. (a) and (b) are intensities for the LHC and RHC polarization incidence, and (e) and (f) are interference patterns with the reference beam, respectively, for m = 1. (c) and (d) as well as (g) and (h) are the corresponding results for m = 2.

Fig. 4
Fig. 4

A set of experimentally generated CVV beams when GLP1 is placed at +45°. The first column shows the direction of the linear polarizer (GLP3). The next four columns show the intensity distributions behind the polarization analyzer at different polarization angles. The lowest row sketches the reconstructed vector fields of the output beams

Fig. 5
Fig. 5

A set of experimentally generated CVV beams when GLP1 is placed at −45°. The first column shows the direction of the linear polarizer (GLP3). The next four columns show the intensity distributions behind the polarization analyzer GLP3 at different polarization angles.

Equations (7)

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α ( r , ϕ ) = q φ + α 0 ,
T ( r , φ ) = M ( r , φ ) JM 1 ( r , ϕ ) .
M ( r , ϕ ) = ( cos α sin α sin α cos α ) ,
T ( r , φ ) = cos δ 2 ( 1 0 0 1 ) + i sin δ 2 ( cos 2 α sin 2 α sin 2 α cos 2 α ) .
E out ( r , φ ) = E 0 cos δ 2 exp ( im φ ) ( 1 σ i ) + i E 0 sin δ 2 exp [ i ( m φ + 2 σ α ) ] ( 1 σ i ) .
E out ( r , φ ) = E 0 ( r , φ ) e im φ ( cos ( 2 α θ ) sin ( 2 α θ ) ) .
E out II ( r , φ ) = E 0 ( r , φ ) e i φ ( cos ( 2 φ θ ) sin ( 2 φ θ ) ) .

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