Abstract

We mainly investigate the polarization singularities of the focused azimuthally polarized (AP) beams modulated by spiral phase and sector obstacles. The results reveal that either the spiral phase or sector obstacle can convert the central V-point to C-points, C-point dipoles, or even double V-points under certain conditions. The conversion can be selectively controlled by appropriately setting the topological charge of the spiral phase and the sector angle of the obstacle. These results may have implications for the researches on polarization, focal field manipulation, or even angular momentum of the focused cylindrically polarized beams.

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References

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2012 (2)

2011 (2)

K. Huang, P. Shi, G. W. Cao, K. Li, X. B. Zhang, and Y. P. Li, “Vector-vortex Bessel-Gauss beams and their tightly focusing properties,” Opt. Lett.36(6), 888–890 (2011).
[CrossRef] [PubMed]

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. A83(6), 063813 (2011).
[CrossRef]

2010 (1)

2009 (2)

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett.102(3), 033902 (2009).
[CrossRef] [PubMed]

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

2008 (3)

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Singular polarimetry: Evolution of polarization singularities in electromagnetic waves propagating in a weakly anisotropic medium,” Opt. Express16(2), 695–709 (2008).
[CrossRef] [PubMed]

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization singularities in 2D and 3D speckle fields,” Phys. Rev. Lett.100(20), 203902 (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]

2006 (3)

2005 (2)

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]

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett.95(25), 253901 (2005).
[CrossRef] [PubMed]

2003 (1)

2002 (3)

I. Freund, A. I. Mokhun, M. S. Soskin, O. V. Angelsky, and I. I. Mokhun, “Stokes singularity relations,” Opt. Lett.27(7), 545–547 (2002).
[CrossRef] [PubMed]

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun.201(4-6), 251–270 (2002).
[CrossRef]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(33 Pt 2B), 036602 (2002).
[CrossRef] [PubMed]

2000 (1)

1959 (1)

B. Richards and E. Wolf, “Electomagnetic Diffraction in Optical Systems: Structure of the Image Field in an Aplanatic System,” Proc. Roy. Soc. London Series A253(1274), 358–379 (1959).
[CrossRef]

Angelsky, O. V.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(33 Pt 2B), 036602 (2002).
[CrossRef] [PubMed]

I. Freund, A. I. Mokhun, M. S. Soskin, O. V. Angelsky, and I. I. Mokhun, “Stokes singularity relations,” Opt. Lett.27(7), 545–547 (2002).
[CrossRef] [PubMed]

Baba, T.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett.102(3), 033902 (2009).
[CrossRef] [PubMed]

Bliokh, K. Y.

Brown, T.

Burresi, M.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett.102(3), 033902 (2009).
[CrossRef] [PubMed]

Cao, G. W.

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. A83(6), 063813 (2011).
[CrossRef]

Chen, W.

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commum.265(2), 411–417 (2006).
[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. Photonics2(8), 501–505 (2008).
[CrossRef]

Denisenko, V.

Dennis, M. R.

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization singularities in 2D and 3D speckle fields,” Phys. Rev. Lett.100(20), 203902 (2008).
[CrossRef] [PubMed]

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett.95(25), 253901 (2005).
[CrossRef] [PubMed]

Engelen, R. J. P.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett.102(3), 033902 (2009).
[CrossRef] [PubMed]

Flossmann, F.

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization singularities in 2D and 3D speckle fields,” Phys. Rev. Lett.100(20), 203902 (2008).
[CrossRef] [PubMed]

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett.95(25), 253901 (2005).
[CrossRef] [PubMed]

Freund, I.

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. A83(6), 063813 (2011).
[CrossRef]

Hao, X.

Hasman, E.

Huang, K.

Jiao, X.

Kleiner, V.

Kozawa, Y.

Kuang, C.

Kuipers, L.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett.102(3), 033902 (2009).
[CrossRef] [PubMed]

Li, K.

Li, P.

Li, Y.

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. A83(6), 063813 (2011).
[CrossRef]

Li, Y. P.

Li, Y.-P.

Liu, S.

Liu, X.

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. A83(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. Photonics2(8), 501–505 (2008).
[CrossRef]

Maier, M.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett.95(25), 253901 (2005).
[CrossRef] [PubMed]

Mokhun, A. I.

I. Freund, A. I. Mokhun, M. S. Soskin, O. V. Angelsky, and I. I. Mokhun, “Stokes singularity relations,” Opt. Lett.27(7), 545–547 (2002).
[CrossRef] [PubMed]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(33 Pt 2B), 036602 (2002).
[CrossRef] [PubMed]

Mokhun, I. I.

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(33 Pt 2B), 036602 (2002).
[CrossRef] [PubMed]

I. Freund, A. I. Mokhun, M. S. Soskin, O. V. Angelsky, and I. I. Mokhun, “Stokes singularity relations,” Opt. Lett.27(7), 545–547 (2002).
[CrossRef] [PubMed]

Mori, D.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett.102(3), 033902 (2009).
[CrossRef] [PubMed]

Niv, A.

O’Holleran, K.

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization singularities in 2D and 3D speckle fields,” Phys. Rev. Lett.100(20), 203902 (2008).
[CrossRef] [PubMed]

Opheij, A.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett.102(3), 033902 (2009).
[CrossRef] [PubMed]

Padgett, M. J.

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization singularities in 2D and 3D speckle fields,” Phys. Rev. Lett.100(20), 203902 (2008).
[CrossRef] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electomagnetic Diffraction in Optical Systems: Structure of the Image Field in an Aplanatic System,” Proc. Roy. Soc. London Series A253(1274), 358–379 (1959).
[CrossRef]

Sato, S.

Schoonover, R. W.

Schwarz, U. T.

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett.95(25), 253901 (2005).
[CrossRef] [PubMed]

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]

Shi, P.

Soskin, M. S.

van Oosten, D.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett.102(3), 033902 (2009).
[CrossRef] [PubMed]

Visser, T. D.

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]

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. A83(6), 063813 (2011).
[CrossRef]

Wang, Q.

Wang, T.

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. A83(6), 063813 (2011).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, “Electomagnetic Diffraction in Optical Systems: Structure of the Image Field in an Aplanatic System,” Proc. Roy. Soc. London Series A253(1274), 358–379 (1959).
[CrossRef]

Youngworth, K.

Zhan, Q.

Zhang, X. B.

Zhang, Y.

Zhao, J.

Zhao, Y.

Adv. Opt. Photon. (1)

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. Photonics2(8), 501–505 (2008).
[CrossRef]

Opt. Commum. (1)

W. Chen and Q. Zhan, “Three-dimensional focus shaping with cylindrical vector beams,” Opt. Commum.265(2), 411–417 (2006).
[CrossRef]

Opt. Commun. (1)

I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun.201(4-6), 251–270 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lett. (8)

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. A83(6), 063813 (2011).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, “Interferometric methods in diagnostics of polarization singularities,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(33 Pt 2B), 036602 (2002).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

F. Flossmann, U. T. Schwarz, M. Maier, and M. R. Dennis, “Polarization singularities from unfolding an optical vortex through a birefringent crystal,” Phys. Rev. Lett.95(25), 253901 (2005).
[CrossRef] [PubMed]

F. Flossmann, K. O’Holleran, M. R. Dennis, and M. J. Padgett, “Polarization singularities in 2D and 3D speckle fields,” Phys. Rev. Lett.100(20), 203902 (2008).
[CrossRef] [PubMed]

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett.102(3), 033902 (2009).
[CrossRef] [PubMed]

Proc. Roy. Soc. London Series A (1)

B. Richards and E. Wolf, “Electomagnetic Diffraction in Optical Systems: Structure of the Image Field in an Aplanatic System,” Proc. Roy. Soc. London Series A253(1274), 358–379 (1959).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th (expanded) ed. (Cambridge University Press, Cambridge, 1999).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of polarization ellipse (left) and Poincare sphere (right).

Fig. 2
Fig. 2

(a) Intensity and (b) polarization state distributions of the focal field of an AP beam. The dotted and dashed lines in (a) denote the zero contours of s1 and s2, respectively, with their crossing point marked by A. The background and the short lines in (b) are the ellipticity and orientation of major axis of polarization ellipse, respectively. The dimension of the focal plane is 2λ × 2λ.

Fig. 3
Fig. 3

Intensity (top) and polarization state (bottom) distributions of the focal fields of the AP beam with additional spiral phase. (a)-(c) correspond to l = 1, 2, and 3, respectively. The dotted, dashed, and solid lines in the top row denote the zero contours of s1, s2, and s3, respectively. The background and the short lines in the bottom row are the ellipticity and orientation of major axis of polarization ellipse, respectively. The dimension of the focal plane is 2λ × 2λ.

Fig. 4
Fig. 4

Polarization states of the focal field of AP beam with spiral phase when l<0. (a)-(c) correspond to l = −1, −2, −3, respectively. The dimension of the focal plane is 2λ × 2λ.

Fig. 5
Fig. 5

Schematic diagram of the focus system (a) and the obstacle (b).

Fig. 6
Fig. 6

Intensity (top) and polarization state (bottom) distributions of the focal field of the AP beam blocked by sector obstacles. (a)-(f) correspond to Ψ = 45°, 90°, 135°, 180°, 225°, and 270°, respectively. The dimension of the focal plane is 2λ × 2λ.

Fig. 7
Fig. 7

Intensity (top) and polarization state distributions (bottom) of the focal field of the obstructed AP beam (Ψ = 180°) with spiral phase. (a)-(d) correspond to l = −1, + 1, + 2, and + 3, respectively. The dimension of the focal plane is 2λ × 2λ.

Fig. 8
Fig. 8

Intensity (top) and polarization state distributions (bottom) of the focal field of the AP beam blocked by phase obstacles. (a)-(f) correspond to Ψ = 30°, 60°, 83.5°, 90°, 110°, and 180°, respectively. The dimension of the focal plane is 2λ × 2λ.

Fig. 9
Fig. 9

Intensity (top) and polarization state distributions (bottom) of the focal field of the AP beam modulated by phase obstacle (Ψ = 180°) with spiral phase. (a)-(d) correspond to l = −1, + 1, + 2, and + 3, respectively. The dimension of the focal plane is 2λ × 2λ.

Equations (7)

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

S 0 = E x E x * + E y E y * S 1 = E x E x * E y E y * , S 2 = E x E y * + E y E x * S 3 =i( E x E y * E y E x * )
E( x,y,z )= 0 θ max dθ 0 2π Asinθ cosθ exp[ ik( xsinθcosφ+ysinθsinφ+zcosθ ) ][ sinφ e x cosφ e y 0 e z ]dφ ,
A=Δ( φ )exp( tan 2 θ tan 2 θ max +iϑ( φ,θ ) ) J 1 ( tanθ tan θ max ),
E f ( ρ,ϕ )=π i l e ilϕ 0 θ max l 0 ( θ )sinθ cosθ e ikzcosθ [ e -iϕ J l1 ( kρsinθ ) e R e iϕ J l+1 ( kρsinθ ) e L ]dθ ,
VpointCpoint if l=±n or ±( n-2 ), and l0 VpointVpoint if l±n and ±( n-2 )
Δ( φ )={ 0 ( -Ψ/2φ<Ψ/2 ) 1 (Otherwise)
Δ( φ )={ 1 ( -Ψ/2φ<Ψ/2 ) 1 (Otherwise)

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