Abstract

We present a flexible approach to generate arbitrary vector beams with a trapezoid Sagnac interferometer. With the interferometer, the different orders of two orthogonally polarized beams from computer-generated holograms coincide with each other in Fourier spectrum domain, and coaxially combine into the vector beams. This approach provides convenient way to experimentally study the properties of vector beams with complex polarization.

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    [CrossRef]
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    [CrossRef] [PubMed]
  26. 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(16), 3179–3181 (2011).
    [CrossRef] [PubMed]
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2012

2011

2010

X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express18(10), 10786–10795 (2010).
[CrossRef] [PubMed]

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

2009

2008

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett.33(2), 122–124 (2008).
[CrossRef] [PubMed]

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

2007

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99(7), 073901 (2007).
[CrossRef] [PubMed]

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

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]

P. B. Phua, W. J. Lai, Y. L. Lim, K. S. Tiaw, B. C. Lim, H. H. Teo, and M. H. Hong, “Mimicking optical activity for generating radially polarized light,” Opt. Lett.32(4), 376–378 (2007).
[CrossRef] [PubMed]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Efficient extracavity generation of radially and azimuthally polarized beams,” Opt. Lett.32(11), 1468–1470 (2007).
[CrossRef] [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).
[CrossRef] [PubMed]

2006

Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett.31(11), 1726–1728 (2006).
[CrossRef] [PubMed]

V. G. Niziev, R. S. Chang, and A. V. Nesterov, “Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer,” Appl. Opt.45(33), 8393–8399 (2006).
[CrossRef] [PubMed]

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, “Subwavelength and super-resolution nondiffraction beam,” Appl. Phys. Lett.89(17), 171102 (2006).
[CrossRef]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett.96(7), 073903 (2006).
[CrossRef] [PubMed]

2005

2004

2003

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91(23), 233901 (2003).
[CrossRef] [PubMed]

2001

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett.79(11), 1587–1589 (2001).
[CrossRef]

2000

1996

1990

Aït-Ameur, K.

Alonzo, C. A.

Angelsky, O. V.

Bekshaev, A. Y.

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.

Bliokh, K. Y.

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett.96(7), 073903 (2006).
[CrossRef] [PubMed]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett.96(7), 073903 (2006).
[CrossRef] [PubMed]

Bomzon, Z.

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett.79(11), 1587–1589 (2001).
[CrossRef]

Brown, T.

Chang, R. S.

Chen, H.

Chen, J.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express18(10), 10786–10795 (2010).
[CrossRef] [PubMed]

Chiu, D. T.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99(7), 073901 (2007).
[CrossRef] [PubMed]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Chong, T.

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, “Subwavelength and super-resolution nondiffraction beam,” Appl. Phys. Lett.89(17), 171102 (2006).
[CrossRef]

de Saint Denis, R.

Ding, J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91(23), 233901 (2003).
[CrossRef] [PubMed]

Edgar, J. S.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99(7), 073901 (2007).
[CrossRef] [PubMed]

Feurer, T.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

Ford, D. H.

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]

Gan, X.

Glückstad, J.

Guo, C. S.

Hanson, S. G.

Hao, J.

Hasman, E.

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).
[CrossRef] [PubMed]

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett.79(11), 1587–1589 (2001).
[CrossRef]

Heckenberg, N. R.

Hierle, R.

Hong, M. H.

Jackel, S.

Jeffries, G. D. M.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99(7), 073901 (2007).
[CrossRef] [PubMed]

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]

Jiao, X.

Jones, P. H.

Kimura, W. D.

Kleiner, V.

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).
[CrossRef] [PubMed]

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett.79(11), 1587–1589 (2001).
[CrossRef]

Lai, W. J.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91(23), 233901 (2003).
[CrossRef] [PubMed]

Li, P.

Li, Y.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express18(10), 10786–10795 (2010).
[CrossRef] [PubMed]

Lim, B. C.

Lim, Y. L.

Liu, S.

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Lumer, Y.

Machavariani, G.

Makita, M.

Maksimyak, A. P.

Maksimyak, P. P.

Maragò, O. M.

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]

McGloin, D.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99(7), 073901 (2007).
[CrossRef] [PubMed]

Meier, M.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

Meir, A.

Miao, X.

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, “Subwavelength and super-resolution nondiffraction beam,” Appl. Phys. Lett.89(17), 171102 (2006).
[CrossRef]

Moshe, I.

Nesterov, A. V.

Ni, W. J.

Nieminen, T. A.

Niv, A.

Niziev, V. G.

Passilly, N.

Phua, P. B.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91(23), 233901 (2003).
[CrossRef] [PubMed]

Rashid, M.

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]

Roch, J. F.

Rodrigo, P. J.

Romano, V.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

Rubinsztein-Dunlop, H.

Schadt, M.

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, “Subwavelength and super-resolution nondiffraction beam,” Appl. Phys. Lett.89(17), 171102 (2006).
[CrossRef]

Stalder, M.

Tan, W.

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, “Subwavelength and super-resolution nondiffraction beam,” Appl. Phys. Lett.89(17), 171102 (2006).
[CrossRef]

Teo, H. H.

Tiaw, K. S.

Tidwell, S. C.

Toussaint, K. C.

Treussart, F.

Tripathi, S.

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, “Subwavelength and super-resolution nondiffraction beam,” Appl. Phys. Lett.89(17), 171102 (2006).
[CrossRef]

Wang, H. T.

Wang, Q.

Wang, X. L.

Xu, J.

Youngworth, K.

Yuan, G.

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, “Subwavelength and super-resolution nondiffraction beam,” Appl. Phys. Lett.89(17), 171102 (2006).
[CrossRef]

Zenkova, C. Y.

Zhan, Q.

Zhang, B. F.

Zhao, J.

Zhao, Y.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99(7), 073901 (2007).
[CrossRef] [PubMed]

Adv. Opt. Photon.

Appl. Opt.

Appl. Phys. Lett.

H. Wang, L. Shi, G. Yuan, X. Miao, W. Tan, and T. Chong, “Subwavelength and super-resolution nondiffraction beam,” Appl. Phys. Lett.89(17), 171102 (2006).
[CrossRef]

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett.79(11), 1587–1589 (2001).
[CrossRef]

Appl. Phys., A Mater. Sci. Process.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

New J. Phys.

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]

Opt. Express

Opt. Lett.

X. Jiao, S. Liu, Q. Wang, X. Gan, P. Li, and J. Zhao, “Redistributing energy flow and polarization of a focused azimuthally polarized beam with rotationally symmetric sector-shaped obstacles,” Opt. Lett.37(6), 1041–1043 (2012).
[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(16), 3179–3181 (2011).
[CrossRef] [PubMed]

P. H. Jones, M. Rashid, M. Makita, and O. M. Maragò, “Sagnac interferometer method for synthesis of fractional polarization vortices,” Opt. Lett.34(17), 2560–2562 (2009).
[CrossRef] [PubMed]

P. B. Phua, W. J. Lai, Y. L. Lim, K. S. Tiaw, B. C. Lim, H. H. Teo, and M. H. Hong, “Mimicking optical activity for generating radially polarized light,” Opt. Lett.32(4), 376–378 (2007).
[CrossRef] [PubMed]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Efficient extracavity generation of radially and azimuthally polarized beams,” Opt. Lett.32(11), 1468–1470 (2007).
[CrossRef] [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).
[CrossRef] [PubMed]

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Forces in optical tweezers with radially and azimuthally polarized trapping beams,” Opt. Lett.33(2), 122–124 (2008).
[CrossRef] [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).
[CrossRef] [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).
[CrossRef] [PubMed]

Q. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett.31(11), 1726–1728 (2006).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91(23), 233901 (2003).
[CrossRef] [PubMed]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett.96(7), 073903 (2006).
[CrossRef] [PubMed]

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, “Spin-to-orbital angular momentum conversion in a strongly focused optical beam,” Phys. Rev. Lett.99(7), 073901 (2007).
[CrossRef] [PubMed]

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett.105(25), 253602 (2010).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Schematic of experimental setup for generating arbitrary spatially variant polarization beams. L, lens; RD, rotating diffuser; λ/2, half-wave plate; M, mirror; PBS, polarizing beam splitter; CGH, computer-generated hologram; F, Fourier-plane filter; λ/4, quarter-wave plate; P, polarization analyzer. The insets show the patterns of CGH and the corresponding Fourier spectra, with the aperture filter marked by dotted circles.

Fig. 2
Fig. 2

Vector beams generated with one-dimensional (1D) CGH. Top: intensity distributions of light fields with polarizations marked with arrowheads; Middle and bottom: light fields passing through analyzers.

Fig. 3
Fig. 3

Vector beams generated with two-dimensional (2D) CGH. (a, b) oblique CGHs (top) and the corresponding Fourier spectra (bottom). (c-e) intensity distributions without (top) and with (middle and bottom) polarization analyzers.

Fig. 4
Fig. 4

Vector beams generated with the interference between two linear polarized beams. (a) and (b) correspond to the radial and radial-variant polarizations, respectively.

Equations (6)

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t( x,y )=[ 1+cos( 2πy/D+δ ) ]/2
E s = A 0 exp(iδ)[ 1 i ], E p = A 0 exp(i δ +i ϕ 0 )[ 1 i ]
E s + E p =2 A 0 exp[ i( δ+ δ + ϕ 0 )/2 ][ cos[ ( δ δ ϕ 0 )/2 ] sin[ ( δ δ ϕ 0 )/2 ] ]
t( x,y )={ 2+cos[ 2π( x+y )/D+ δ 1 ]+cos[ 2π( xy )/D+ δ 2 ] }/4
E s = A 0 exp(i δ 1 )[ 1 i ], E p = A 0 exp(i δ 2 )[ 1 i ]
E s + E p =2 A 0 exp[ i( δ 1 + δ 2 )/2 ][ cos[ ( δ 1 δ 2 )/2 ] sin[ ( δ 1 δ 2 )/2 ] ]

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