Abstract

We propose theoretically and verify experimentally a method of combining a q-plate and a spiral phase plate to generate arbitrary vector vortex beams on a hybrid-order Poincaré sphere. We demonstrate that a vector vortex beam can be decomposed into a vector beam and a vortex, whereby the generation can be realized by sequentially using a q-plate and a spiral phase plate. The generated vector beam, vortex, and vector vortex beam are verified and show good agreement with the prediction. Another advantage that should be pointed out is that the spiral phase plate and q-plate are both fabricated on silica substrates, suggesting the potential possibility to integrate the two structures on a single plate. Based on a compact method of transmissive-type transformation, our scheme may have potential applications in future integrated optical devices.

© 2016 Chinese Laser Press

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References

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2016 (11)

S. Mei, M. Q. Mehmood, S. Hussain, K. Huang, X. Ling, S. Y. Siew, H. Liu, J. Teng, A. Danner, and C. Qiu, “Flat helical nanosieves,” Adv. Funct. Mater. 26, 5255–5262 (2016).
[Crossref]

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28, 2533–2539 (2016).
[Crossref]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Adv. Opt. Mater. 4, 818–833 (2016).
[Crossref]

B. Zhang, Z. Chen, H. Sun, J. Xia, and J. Ding, “Vectorial optical vortex filtering for edge enhancement,” J. Opt. 18, 035703 (2016).
[Crossref]

J. Tang, Y. Ming, Z. Chen, W. Hu, F. Xu, and Y. Lu, “Entanglement of photons with complex spatial structure in Hermite–Laguerre–Gaussian modes,” Phys. Rev. A 94, 012313 (2016).
[Crossref]

Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6, 51–70 (2016).
[Crossref]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41, 10–14 (2016).

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon. 3, 1558–1563 (2016).
[Crossref]

Y. Ke, Y. Liu, J. Zhou, Y. Liu, H. Luo, and S. Wen, “Optical integration of Pancharatnam–Berry phase lens and dynamical phase lens,” Appl. Phys. Lett. 108, 101102 (2016).
[Crossref]

M. M. Sánchezlópez, J. A. Davis, N. Hashimoto, I. Moreno, E. Hurtado, K. Badham, A. Tanabe, and S. W. Delaney, “Performance of a q-plate tunable retarder in reflection for the switchable generation of both first- and second-order vector beams,” Opt. Lett. 41, 13–16 (2016).
[Crossref]

W. Shu, Y. Liu, Y. Ke, X. Ling, Z. Liu, B. Huang, H. Luo, and X. Yin, “Propagation model for vector beams generated by metasurfaces,” Opt. Express 24, 21177–21189 (2016).
[Crossref]

2015 (5)

2014 (5)

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. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).
[Crossref]

C. Qiu, D. Palima, A. Novitsky, D. Gao, W. Ding, S. V. Zhukovsky, and J. Gluckstad, “Engineering light-matter interaction for emerging optical manipulation applications,” Nanophotonics 3, 181–201 (2014).
[Crossref]

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]

J. García-García, C. Rickenstorff-Parrao, R. Ramos-García, V. Arrizón, and A. S. Ostrovsky, “Simple technique for generating the perfect optical vortex,” Opt. Lett. 39, 5305–5308 (2014).
[Crossref]

2013 (5)

2012 (4)

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam–Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
[Crossref]

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willer, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

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]

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]

2011 (4)

2010 (2)

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref]

X. Hao, C. Kuang, T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35, 3928–3930 (2010).
[Crossref]

2009 (2)

2008 (1)

2007 (2)

2006 (3)

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

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96, 153901 (2006).
[Crossref]

2005 (1)

2004 (1)

2002 (1)

2000 (1)

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[Crossref]

1999 (1)

Y. Liu, D. Cline, and P. He, “Vacuum laser acceleration using a radially polarized CO2 laser beam,” Nucl. Instrum. Methods Phys. Res. 424, 296–303 (1999).
[Crossref]

1996 (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]

Abouraddy, A. F.

A. F. Abouraddy and K. C. Toussaint, “Three-dimensional polarization control in microscopy,” Phys. Rev. Lett. 96, 153901 (2006).
[Crossref]

Ahmed, N.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willer, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Aiello, A.

Alfano, R. R.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam–Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
[Crossref]

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]

Arbabi, A.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Adv. Opt. Mater. 4, 818–833 (2016).
[Crossref]

Arbabi, E.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Adv. Opt. Mater. 4, 818–833 (2016).
[Crossref]

Arrizón, V.

Badham, K.

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]

Biener, G.

Blit, S.

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[Crossref]

Bomzon, Z.

Born, M.

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

Cardano, F.

Chan, C. T.

J. Ng, Z. Lin, and C. T. Chan, “Theory of optical trapping by an optical vortex beam,” Phys. Rev. Lett. 104, 103601 (2010).
[Crossref]

Chen, H.

Chen, P.

Chen, X.

F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, “Vector vortex beam generation with a single plasmonic metasurface,” ACS Photon. 3, 1558–1563 (2016).
[Crossref]

Chen, Y.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).
[Crossref]

Chen, Z.

B. Zhang, Z. Chen, H. Sun, J. Xia, and J. Ding, “Vectorial optical vortex filtering for edge enhancement,” J. Opt. 18, 035703 (2016).
[Crossref]

J. Tang, Y. Ming, Z. Chen, W. Hu, F. Xu, and Y. Lu, “Entanglement of photons with complex spatial structure in Hermite–Laguerre–Gaussian modes,” Phys. Rev. A 94, 012313 (2016).
[Crossref]

Cheng, H.

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41, 10–14 (2016).

Cheng, W.

Chigrinov, V.

Cipparrone, G.

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102, 161101 (2013).
[Crossref]

Cline, D.

Y. Liu, D. Cline, and P. He, “Vacuum laser acceleration using a radially polarized CO2 laser beam,” Nucl. Instrum. Methods Phys. Res. 424, 296–303 (1999).
[Crossref]

Danner, A.

S. Mei, M. Q. Mehmood, S. Hussain, K. Huang, X. Ling, S. Y. Siew, H. Liu, J. Teng, A. Danner, and C. Qiu, “Flat helical nanosieves,” Adv. Funct. Mater. 26, 5255–5262 (2016).
[Crossref]

M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C. Qiu, “Visible-frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28, 2533–2539 (2016).
[Crossref]

Davidson, N.

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[Crossref]

Davis, J. A.

de Lisio, C.

Delaney, S. W.

Deng, D.

Ding, J.

Ding, W.

C. Qiu, D. Palima, A. Novitsky, D. Gao, W. Ding, S. V. Zhukovsky, and J. Gluckstad, “Engineering light-matter interaction for emerging optical manipulation applications,” Nanophotonics 3, 181–201 (2014).
[Crossref]

Dolinar, S.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willer, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Evans, S.

G. Milione, S. Evans, D. A. Nolan, and R. R. Alfano, “Higher order Pancharatnam–Berry phase and the angular momentum of light,” Phys. Rev. Lett. 108, 190401 (2012).
[Crossref]

Fainman, Y.

Faraon, A.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Adv. Opt. Mater. 4, 818–833 (2016).
[Crossref]

Fazal, I. M.

J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willer, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6, 488–496 (2012).
[Crossref]

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, and A. A. Friesem, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77, 3322–3324 (2000).
[Crossref]

Gabriel, C.

Galvez, E. J.

Gao, D.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic illustration of the HyOPS. (θ,Φ) are the spherical coordinates. The north pole |Nl and south pole |Sm represent orthogonal circularly polarized eigenstates with topological charges of l and m, and the points |Hm,l and |Vm,l represent the horizontal and vertical polarization bases, respectively. The polarization and intensity distribution of four different points are shown with l=0 and m=2.

Fig. 2.
Fig. 2.

(a) Experimental setup to generate arbitrary vector vortex beams on the HyOPS. A Gaussian beam emerging from the He–Ne laser (632.8 nm, 17 mW, Thorlabs HNL210L-EC) passes through part (I) (GLP1, QWP1, and QP) to produce a vector beam. Then the vector beam is transformed into a vector vortex beam by part (II) (SPP). Part (III) (QWP2 and GLP2) is used to measure the Stokes parameters. GLP, Glan laser polarizer; QWP, quarter-wave plate; QP, q-plate; SPP, spiral phase plate; CCD, charge-coupled device (Coherent LaserCam HR). (b) Schematic illustration of generating a vector vortex beam (right), which can be theoretically decomposed into the vector part (left) and the vortex part (middle).

Fig. 3.
Fig. 3.

(a) and (b) Theoretical and measured optical axis distributions of the q-plate (q=1/2). (c) and (d) Polariscopic images of optical axis distribution of the q-plate under crossed polarizers. Pin and Pout stand for the polarization states of the input and output beams, respectively.

Fig. 4.
Fig. 4.

(a) and (b) 3D schematic view and measured phase retardance value distribution of spiral phase plate (l=1). (c) and (d) Measured interference patterns of the generated vortex beam with a spherical wave and a plane wave.

Fig. 5.
Fig. 5.

Polarization and intensity distribution of the theoretical and experimental results of vector beams. The first row shows the theoretical results of the points (1,0,0), (0,1,0), (1,0,0) and (0,1,0) on the HOPS in order from left to right. The second row is the corresponding experimental results. The third row shows the theoretical results of points (0,0,1), (0,0,1), (0,22,22), and (22,0,22) on the HOPS. The fourth row is the corresponding experimental results.

Fig. 6.
Fig. 6.

Polarization and intensity distribution of the theoretical and experimental results of vectorial vortex beams. The first row shows the theoretical results of the points (1,0,0), (0,1,0), (1,0,0), and (0,1,0) on the HyOPS in order from left to right. The second row is the corresponding experimental results. The third row shows the theoretical results of points (0,0,1), (0,0,1), (0,22,22), and (22,0,22) on the HyOPS, The fourth row is the corresponding experimental results.

Fig. 7.
Fig. 7.

Intensity distributions of the radially and azimuthally polarized vortex beam behind the polarization analyzer at different angles (represented by the white arrows).

Equations (15)

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

|ψ=ψNl|Nl+ψSm|Sm,
|Nl=22(e^x+ie^y)exp(ilϕiϕ0/2),
|Sm=22(e^xie^y)exp(imϕ+iϕ0/2).
S0l,m=|ψNl|2+|ψSm|2,
S1l,m=2|ψNl||ψSm|cosΦ,
S2l,m=2|ψNl|ψSm|sinΦ,
S3l,m=|ψNl|2|ψSm|2,
|ψ=expi(l+m)ϕ2[ψNl|Nexpi(lm)ϕ2+ψSm|Sexpi(ml)ϕ2],
|ψ(ϑ,α)=cosϑ2|Nei(σα2+2Ψ)+sinϑ2|Sei(σα2+2Ψ),
|ψ=cosϑ2|Neiσϕ+sinϑ2|Seiσϕ.
θ=(π+δ)/2,
Φ=η.
S1=I(0°,0°)I(90°,90°)I(0°,0°)+I(90°,90°),
S2=I(45°,45°)I(135°,135°)I(45°,45°)+I(135°,135°),
S3=I(45°,0°)I(45°,0°)I(45°,0°)+I(45°,0°).

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