Abstract

We propose a theoretical model to semi-quantitatively describe the modulation mechanism of multi-azimuthal masks on the focal fields of azimuthally polarized (AP) beam. With this model, we cannot only explain the redistributions of the polarization and intensity at the focal plane, but also consciously manage the focal fields by designing the mask structure parameters, such as the symmetry, area, and phase retardation of the sector photic regions. Our results may supply a guideline to realize the manipulation on the polarizations, angular momenta, and the distribution of focused fields.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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2013 (4)

2012 (2)

2011 (2)

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

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]

2009 (1)

2008 (3)

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. Photonics 2(8), 501–505 (2008).
[Crossref]

B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10(10), 103013 (2008).
[Crossref]

2007 (2)

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]

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]

2006 (3)

2005 (2)

2000 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Aolita, L.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Barnett, S.

Bentley, J. B.

Brown, T. G.

Chen, J.

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]

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. Photonics 2(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]

Courtial, J.

D’Ambrosio, V.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Davis, J. A.

Ding, J.

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]

Franke-Arnold, S.

Gan, X.

Gu, B.

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, C. S.

Heckenberg, N. R.

Jack, B.

B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10(10), 103013 (2008).
[Crossref]

Jiao, X.

Kozawa, Y.

Kwek, L. C.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Li, P.

Li, Y.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

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. P.

Liu, S.

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]

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. Photonics 2(8), 501–505 (2008).
[Crossref]

Marrucci, L.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

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]

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]

Ni, W. J.

Nieminen, T. A.

Padgett, M.

Padgett, M. J.

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

B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10(10), 103013 (2008).
[Crossref]

Peng, T.

Re, L. D.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

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.

Sato, S.

Sciarrino, F.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

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. Photonics 2(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. Photonics 2(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]

Slussarenko, S.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Spagnolo, N.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

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]

Walborn, S. P.

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

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. Photonics 2(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.

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]

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]

Wang, M.

Wang, Q.

Wang, S.

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]

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]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Xie, X.

Yang, L.

Yao, A. M.

Yao, E.

Youngworth, K. S.

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]

Zhan, Q.

Zhang, P.

Zhang, W.

Zhang, Y.

Zhao, J.

Zhao, Y.

Zhou, J.

Adv. Opt. Photon. (2)

Appl. Phys. Lett. (1)

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]

Appl. Phys., A Mater. Sci. Process. (1)

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]

Nat. Commun. (1)

V. D’Ambrosio, N. Spagnolo, L. D. Re, S. Slussarenko, Y. Li, L. C. Kwek, L. Marrucci, S. P. Walborn, L. Aolita, and F. Sciarrino, “Photonic polarization gears for ultra-sensitive angular measurements,” Nat. Commun. 4, 2432 (2013).

Nat. Photonics (1)

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. Photonics 2(8), 501–505 (2008).
[Crossref]

New J. Phys. (1)

B. Jack, M. J. Padgett, and S. Franke-Arnold, “Angular diffraction,” New J. Phys. 10(10), 103013 (2008).
[Crossref]

Opt. Express (4)

Opt. Lett. (8)

L. Yang, X. Xie, S. Wang, and J. Zhou, “Minimized spot of annular radially polarized focusing beam,” Opt. Lett. 38(8), 1331–1333 (2013).
[Crossref] [PubMed]

Y. Zhao, Q. Zhan, Y. Zhang, and Y. P. Li, “Creation of a three-dimensional optical chain for controllable particle delivery,” Opt. Lett. 30(8), 848–850 (2005).
[Crossref] [PubMed]

Y. Kozawa and S. Sato, “Focusing property of a double-ring-shaped radially polarized beam,” Opt. Lett. 31(6), 820–822 (2006).
[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]

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]

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

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]

Phys. Rev. A (1)

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]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic structure of the sector photic mask. (b) Theoretical map of polarizations at the focal plane. (c)-(e) Calculated transverse distributions of intensity (top) and Stokes parameter s3 (bottom) at the focal plane of the vector beams with l = 1, 5 and 10, respectively. Red and blue dashed ellipses correspond to the spin components UR and UL, respectively. The dimension of the focal plane is 6λ × 6λ.
Fig. 2
Fig. 2 (a1) Schematic structure of the N = 2 mask and theoretical maps of polarization for vector beams transmitted from photic regions (a2) -π/4≤φ′≤π/4, and (a3) 3π/4≤φ′≤5π/4, with the schematics of inserted. (b), (c) Intensity distributions at the pupil plane (top), transverse distributions of intensity (middle) and Stokes parameter s3 (bottom) at the focal plane of the vector beams with l = 1 (AP beam) and 5, respectively. Arrows donate the polarized direction. The dimension of the focal plane is 4λ × 4λ.
Fig. 3
Fig. 3 (a) Schematic structure of an N = 3 mask and (b) its theoretical focusing model. Transverse distributions of (c) intensity and (d) Stokes parameter s3 of the focal field. Red and blue dashed ellipses correspond to the spin components URj and ULj, respectively. The dimension of the focal plane is 4λ × 4λ.
Fig. 4
Fig. 4 Schematic structures of N = 4 masks with different transmission coefficients (top), calculated intensity (middle) and Stokes parameter s3 (bottom) of focal fields. Arrows: polarization orientation. Lines: orientations of the long axis of local polarization ellipses. The dimension of the focal plane is 4λ × 4λ.
Fig. 5
Fig. 5 (a) Schematic structure of an N = 6 mask with two kind of transmission coefficients. (b) Calculated intensity and (c) Stokes parameter s3 of focal fields. Arrows: polarization orientation. The dimension of the focal plane is 4λ × 4λ.
Fig. 6
Fig. 6 Schematics structures of anisometric masks (top) and correspondingly calculated intensity (middle) and Stokes parameter s3 (bottom) distributions of focal fields. Arrows: polarization orientation. Lines: orientations of the long axis of local polarization ellipses. The dimension of the focal plane is 4λ × 4λ.

Equations (9)

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

P j ( φ )={ t j α j β j /2 φ α j + β j /2 0else j=1,2,...,N,
E in = E 0 ( r , φ ) j=1 N P j ( φ ) ,
E in = E 0 ( r , φ ) j=1 N m= + C mj e im φ t j ,
C mj = β j 2π sinc( m β j 2 ) e im α j .
E 0 ( r , φ )= E 0 ( r )exp[ i( l φ + φ 0 ) ] e R + E 0 ( r )exp[ i( l φ + φ 0 ) ] e L ,
E in = E 0 ( r ) j=1 N m= + β j 2π sinc( m β j 2 ) t j e im( φ α j ) ( e il φ e R e il φ e L ) , = E 0 ( r ) j=1 N β j 2π t j ( E Rj e R E Lj e L )
E Rj = m= + sinc( m β j 2 ) e i( ml ) φ e - im α j , E Lj = m= + sinc( m β j 2 ) e i( lm ) φ e im α j .
E F = j=1 N β j 2π t j e ilπ/2 ( U Rj e R U Lj e L ) ,
{ U Rj = e ilφ m= + sinc( m β j 2 ) e im[ φ( α j + π 2 ) ] H ml ( r ) U Lj = e ilφ m= + sinc( m β j 2 ) e im[ φ( α j π 2 ) ] H ml ( r ) ,

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