Abstract

In this paper, we propose a type of rectilinear lattices of polarization vortices, each spot in which has mutually independent, and controllable spatial polarization distributions. The lattices are generated by two holograms under special design. In the experiment, the holograms are encoded on two spatial light modulators, and the results fit very well with theory. Our scheme makes it possible to generate multiple polarization vortices with various polarization distributions simultaneously, for instance, radially and azimuthally polarized beams, and can be used in the domains as polarization-based data transmission system, optical manufacture, polarization detection and so on.

© 2016 Optical Society of America

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References

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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]
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    [Crossref] [PubMed]
  8. M. Suzuki, K. Yamane, K. Oka, Y. Toda, and R. Morita, “Extended Stokes parameters for cylindrically polarized beams,” Opt. Rev. 22(1), 179–183 (2015).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  13. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
    [Crossref]
  14. 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]
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    [Crossref]
  20. 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]
  21. L. A. Romero and F. M. Dickey, “Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings,” J. Opt. Soc. Am. A 24(8), 2280–2295 (2007).
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2016 (1)

D. Naidoo, F. S. Rous, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincare sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

2015 (3)

2014 (1)

2012 (2)

2011 (3)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, and S. Noda, “Higher-order vector beams produced by photonic-crystal lasers,” Opt. Express 19(13), 11963–11968 (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(5), 053601 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (3)

2007 (4)

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]

L. A. Romero and F. M. Dickey, “Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings,” J. Opt. Soc. Am. A 24(8), 2280–2295 (2007).
[Crossref] [PubMed]

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]

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(13), 1839–1841 (2007).
[Crossref] [PubMed]

2003 (1)

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second-Harmonic Generation Induced By Local Field Enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

1999 (1)

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser efficiency,” J. Phys. D 32(13), 1455–1461 (1999).
[Crossref]

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

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(5), 053601 (2011).
[Crossref] [PubMed]

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(11), 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(11), 8185–8189 (1992).
[Crossref] [PubMed]

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]

Beversluis, M.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second-Harmonic Generation Induced By Local Field Enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

Bouhelier, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second-Harmonic Generation Induced By Local Field Enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

Chujo, K.

Cottrell, D. M.

Dai, K.

Davis, J. A.

Dickey, F. M.

Donoso, R.

Dudley, A.

D. Naidoo, F. S. Rous, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincare sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Enderli, F.

Feurer, T.

F. Enderli and T. Feurer, “Radially polarized mode-locked Nd:YAG laser,” Opt. Lett. 34(13), 2030–2032 (2009).
[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]

Forbes, A.

D. Naidoo, F. S. Rous, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincare sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Fu, S.

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]

Gao, C.

Hamazaki, J.

Hartschuh, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second-Harmonic Generation Induced By Local Field Enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

Hernandez, T. M.

Iwahashi, S.

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]

Jin, G.

Jones, P. H.

Kawauchi, H.

Kitamura, K.

Kobayashi, Y.

Kozawa, Y.

Kurosaka, Y.

Li, C.

Litvin, I.

D. Naidoo, F. S. Rous, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincare sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Makita, M.

Maragò, O. M.

Marrucci, L.

D. Naidoo, F. S. Rous, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincare sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

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]

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]

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(5), 053601 (2011).
[Crossref] [PubMed]

Moreno, I.

Morita, R.

M. Suzuki, K. Yamane, K. Oka, Y. Toda, and R. Morita, “Extended Stokes parameters for cylindrically polarized beams,” Opt. Rev. 22(1), 179–183 (2015).
[Crossref]

J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express 18(3), 2144–2151 (2010).
[Crossref] [PubMed]

Naidoo, D.

D. Naidoo, F. S. Rous, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincare sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser efficiency,” J. Phys. D 32(13), 1455–1461 (1999).
[Crossref]

Niziev, V. G.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser efficiency,” J. Phys. D 32(13), 1455–1461 (1999).
[Crossref]

Noda, S.

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(5), 053601 (2011).
[Crossref] [PubMed]

Novotny, L.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second-Harmonic Generation Induced By Local Field Enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[Crossref] [PubMed]

Oka, K.

M. Suzuki, K. Yamane, K. Oka, Y. Toda, and R. Morita, “Extended Stokes parameters for cylindrically polarized beams,” Opt. Rev. 22(1), 179–183 (2015).
[Crossref]

Omatsu, T.

Padgett, M. J.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Piccirillo, B.

D. Naidoo, F. S. Rous, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincare sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

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]

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]

Romero, L. A.

Rous, F. S.

D. Naidoo, F. S. Rous, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincare sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

Sakai, K.

Sand, D.

Sato, S.

Shi, Y.

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Suzuki, M.

M. Suzuki, K. Yamane, K. Oka, Y. Toda, and R. Morita, “Extended Stokes parameters for cylindrically polarized beams,” Opt. Rev. 22(1), 179–183 (2015).
[Crossref]

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(5), 053601 (2011).
[Crossref] [PubMed]

Takayama, N.

Tanda, S.

Tian, Q.

Toda, Y.

M. Suzuki, K. Yamane, K. Oka, Y. Toda, and R. Morita, “Extended Stokes parameters for cylindrically polarized beams,” Opt. Rev. 22(1), 179–183 (2015).
[Crossref]

Wang, J.

Wang, Z.

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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Xin, J.

Yamane, K.

M. Suzuki, K. Yamane, K. Oka, Y. Toda, and R. Morita, “Extended Stokes parameters for cylindrically polarized beams,” Opt. Rev. 22(1), 179–183 (2015).
[Crossref]

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Yonezawa, K.

Zhan, Q.

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

Zhang, S.

Zhao, Y.

Zhong, L.

Zhou, Z.

Adv. Opt. Photonics (2)

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

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Appl. Opt. (2)

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]

Chin. Opt. Lett. (1)

J. Opt. Soc. Am. A (1)

J. Phys. D (1)

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser efficiency,” J. Phys. D 32(13), 1455–1461 (1999).
[Crossref]

Nat. Photonics (1)

D. Naidoo, F. S. Rous, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, and A. Forbes, “Controlled generation of higher-order Poincare sphere beams from a laser,” Nat. Photonics 10(5), 327–332 (2016).
[Crossref]

New J. Phys. (1)

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 (3)

Opt. Lett. (5)

Opt. Rev. (1)

M. Suzuki, K. Yamane, K. Oka, Y. Toda, and R. Morita, “Extended Stokes parameters for cylindrically polarized beams,” Opt. Rev. 22(1), 179–183 (2015).
[Crossref]

Phys. Rev. A (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(11), 8185–8189 (1992).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-Field Second-Harmonic Generation Induced By Local Field Enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[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(5), 053601 (2011).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 The experimental setup.
Fig. 2
Fig. 2 Diffraction orders −1 and + 1 with radial (|ψ1,0〉) and azimuthal (|ψ1, π/2〉) polarization. (a) The hologram encoded on SLM1. (b) The hologram encoded on SLM2. (c) Experimental results captures by the CCD without and with analyzers (P2) indicated on the left. (d) Simulated results.
Fig. 3
Fig. 3 Diffraction orders −2, −1, + 1 and + 2 with the states of |ψ-2,0〉, |ψ-1,0〉, |ψ1, π/2〉and |ψ2, π/2〉. (a) The hologram encoded on SLM1. (b) The hologram encoded on SLM2. (c) Experimental results captures by the CCD without and with analyzers (P2) indicated on the left. (d) Simulated results.
Fig. 4
Fig. 4 Diffraction orders + 1, + 2 and + 3 with the states of |ψ1,0〉, |ψ2,0〉,and |ψ3,0〉. (a) The hologram encoded on SLM1. (b) The hologram encoded on SLM2. (c) Experimental results captures by the CCD without and with analyzers (P2) indicated on the left. (d) Simulated results.

Equations (8)

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

| ψ p , φ 0 E ( φ , r ) = A ( r ) [ cos ( p φ + φ 0 ) sin ( p φ + φ 0 ) ]
ψ R p | R p + ψ L p | L p = | ψ p , 0
| R p = exp ( i p φ ) [ 1 , i ] T
| L p = exp ( i p φ ) [ 1 , i ] T
ψ R p | R p + C ψ L p | L p = C | ψ p , 1 2 σ
exp [ i θ ( x ) ] = m = + c m exp ( i m T x )
c m = T 2 π π / T π / T exp [ i θ ( x ) ] exp ( i m T x ) d x
c m = | c m | exp ( i σ ) exp ( i p φ )

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