Abstract

The phenomenon of vortex beams passing through a diffraction plate with rotationally symmetric superposition of spiral pinholes array is investigated. The variations of the topological charges of vortex beams are theoretically analyzed, numerically simulated and experimentally observed. It proves that the obtained topological charge value (l) is a combination of that of incident beam (l0) and the number of the spiral structures (m). The relationship is l = Mm-l0, where M is an integer. With this study, we proved that spiral transmission structures can also achieve the variations of the topological charge of a vortex beam. And this method is simple and costless. With the advantages of this method, it might have important applications in optical communications and optical tweezers.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  8. X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
    [Crossref]
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    [Crossref]

2017 (2)

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-angular-momentum mode selection by rotationally symmetric superposition of chiral states with application to electron vortex beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref]

B. Khahavi and E. J. Galvez, “Determining topological charge of an optical beam using a wedged optical flat,” Opt. Lett. 42(8), 1516–1519 (2017).
[Crossref]

2016 (1)

2015 (1)

2014 (2)

G. Ruffato, M. Massari, and F. Romanato, “Generation of high-order Laguerre–Gaussian modes by means of spiral phase plates,” Opt. Lett. 39(17), 5094–5097 (2014).
[Crossref]

S. Topuzoski, “Fraunhofer diffraction of Laguerre–Gaussian laser beam by helical axicon,” Opt. Commun. 330(1), 184–190 (2014).
[Crossref]

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(19), 190401 (2012).
[Crossref]

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3(1), 1278 (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(10), C1–C6 (2012).
[Crossref]

2011 (2)

S. Topuzoski and L. Janicijevic, “Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating,” J. Mod. Opt. 58(2), 138–145 (2011).
[Crossref]

P. Vaity and R. P. Singh, “Self-healing property of optical ring lattice,” Opt. Lett. 36(15), 2994–2996 (2011).
[Crossref]

2010 (1)

2009 (1)

S. Topuzoski and L. Janicijevic, “Conversion of high-order Laguerre–Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun. 282(17), 3426–3432 (2009).
[Crossref]

2008 (2)

2006 (2)

2005 (1)

2003 (1)

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

1992 (2)

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]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992).
[Crossref]

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(19), 190401 (2012).
[Crossref]

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

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]

Almazov, A. A.

Apurv Chaitanya, N.

N. Apurv Chaitanya, P. Wozniak, P. Banzer, and I. De Leon, “Generation of Vortex Beams using a Plasmonic Quadrumer Nanocluster,” Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper FM2G.4.

Babiker, M.

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-angular-momentum mode selection by rotationally symmetric superposition of chiral states with application to electron vortex beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref]

Banzer, P.

N. Apurv Chaitanya, P. Wozniak, P. Banzer, and I. De Leon, “Generation of Vortex Beams using a Plasmonic Quadrumer Nanocluster,” Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper FM2G.4.

Bashkansky, M.

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

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]

Burch, M.

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Capasso, F.

P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3(1), 1278 (2012).
[Crossref]

Cardano, F.

Courtial, J.

De Leon, I.

N. Apurv Chaitanya, P. Wozniak, P. Banzer, and I. De Leon, “Generation of Vortex Beams using a Plasmonic Quadrumer Nanocluster,” Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper FM2G.4.

de Lisio, C.

Dennis, M. R.

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(19), 190401 (2012).
[Crossref]

Fatemi, F. K.

Fu, S.

Galvez, E. J.

Gao, C.

Genevet, P.

P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3(1), 1278 (2012).
[Crossref]

Heckenberg, N. R.

Hong, M. H.

Janicijevic, L.

S. Topuzoski and L. Janicijevic, “Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating,” J. Mod. Opt. 58(2), 138–145 (2011).
[Crossref]

S. Topuzoski and L. Janicijevic, “Conversion of high-order Laguerre–Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun. 282(17), 3426–3432 (2009).
[Crossref]

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Karimi, E.

Kats, M. A.

P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3(1), 1278 (2012).
[Crossref]

Khahavi, B.

Khonina, S. N.

Kim, D. J.

Kim, J. W.

Kotlyar, V. V.

Lai, W. J.

Lim, B. C.

Lin, J.

P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3(1), 1278 (2012).
[Crossref]

Maleev, I. D.

Marrucci, L.

Massari, M.

McDuff, R.

Milione, G.

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(19), 190401 (2012).
[Crossref]

Nolan, D. A.

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(19), 190401 (2012).
[Crossref]

O’Brien, J. L.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Park, D.

Phua, P. B.

Romanato, F.

Ruffato, G.

Santamato, E.

Singh, R. P.

Singh, S.

Slussarenko, S.

Smith, C. P.

Soifer, V. A.

Sorel, M.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

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]

Strain, M. J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Swartzlander, G. A.

Teo, H. H.

Thirunavukkarasu, G.

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-angular-momentum mode selection by rotationally symmetric superposition of chiral states with application to electron vortex beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref]

Thompson, M. G.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Tiaw, K. S.

Topuzoski, S.

S. Topuzoski, “Fraunhofer diffraction of Laguerre–Gaussian laser beam by helical axicon,” Opt. Commun. 330(1), 184–190 (2014).
[Crossref]

S. Topuzoski and L. Janicijevic, “Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating,” J. Mod. Opt. 58(2), 138–145 (2011).
[Crossref]

S. Topuzoski and L. Janicijevic, “Conversion of high-order Laguerre–Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun. 282(17), 3426–3432 (2009).
[Crossref]

Vaity, P.

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

Vasnetsov, M.

Vickers, J.

Vyas, R.

Wang, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Wang, T.

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

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]

Wozniak, P.

N. Apurv Chaitanya, P. Wozniak, P. Banzer, and I. De Leon, “Generation of Vortex Beams using a Plasmonic Quadrumer Nanocluster,” Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper FM2G.4.

Yang, Y.

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-angular-momentum mode selection by rotationally symmetric superposition of chiral states with application to electron vortex beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref]

Yu, S.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Yuan, J.

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-angular-momentum mode selection by rotationally symmetric superposition of chiral states with application to electron vortex beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref]

Zambrini, R.

Zhang, S.

Zhou, G.

Zhu, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Appl. Opt. (1)

J. Mod. Opt. (1)

S. Topuzoski and L. Janicijevic, “Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating,” J. Mod. Opt. 58(2), 138–145 (2011).
[Crossref]

J. Opt. Soc. Am. A (2)

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

Nat. Commun. (1)

P. Genevet, J. Lin, M. A. Kats, and F. Capasso, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes,” Nat. Commun. 3(1), 1278 (2012).
[Crossref]

Opt. Commun. (3)

S. Topuzoski and L. Janicijevic, “Conversion of high-order Laguerre–Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon,” Opt. Commun. 282(17), 3426–3432 (2009).
[Crossref]

S. Topuzoski, “Fraunhofer diffraction of Laguerre–Gaussian laser beam by helical axicon,” Opt. Commun. 330(1), 184–190 (2014).
[Crossref]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[Crossref]

Opt. Express (4)

Opt. Lett. (6)

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]

Phys. Rev. Lett. (2)

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(19), 190401 (2012).
[Crossref]

Y. Yang, G. Thirunavukkarasu, M. Babiker, and J. Yuan, “Orbital-angular-momentum mode selection by rotationally symmetric superposition of chiral states with application to electron vortex beams,” Phys. Rev. Lett. 119(9), 094802 (2017).
[Crossref]

Science (1)

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[Crossref]

Other (1)

N. Apurv Chaitanya, P. Wozniak, P. Banzer, and I. De Leon, “Generation of Vortex Beams using a Plasmonic Quadrumer Nanocluster,” Conference on Lasers and Electro-Optics (Optical Society of America, 2018), paper FM2G.4.

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Figures (4)

Fig. 1.
Fig. 1. The illustration of the simulated and experimental setup.
Fig. 2.
Fig. 2. The simulated results of the diffracted LG beams by the RSSSPA plate and focused by a positive lens. Line I to V give five cases with different combinations of m and l0. Column (a) to (d) present the distributions of spiral pinholes, focused light intensity, total phase on the focal plane and the magnified details of the phases.
Fig. 3.
Fig. 3. The comparison between the experimental and simulated optical intensity distributions on the different planes. (a) and (b) are at the focal plane. (c) and (d) are at the focused beam waist plane. (e) and (f) are the corresponding simulated phases. The plotting scales are 300 µm for (a) to (f). (g) and (h) are experimentally measured interference patterns of the beam in (a) and a spherical wavefront.
Fig. 4.
Fig. 4. The experimental and simulated results of the condition with only one spiral pinholes curve. Here, m = 1 represents the counterclockwise rotation of the spiral curve and m=−1 represents the clockwise one.

Equations (9)

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

ψ ( r , θ , z ) = s = 0 m 1 u s ( r , θ + 2 π s m , z ) .
U p , l ( r , θ , z ) = A p , l ( r , z ) exp [ i k z i π r 2 z λ ( z 2 + z R 2 ) ] exp [ i ( 2 p + | l 0 | + 1 ) tan 1 ( z / z R ) ] exp ( i l 0 θ ) .
ψ ( r , θ , z ) = s = 0 m     1 k = 1 n U p , l ( r , θ , z ) T s , k ( r , θ , z , d ) .
u s ( r , θ , z ) = k = 1 n U p , l ( r , θ , z ) T s , k ( r , θ , z , d ) .
ϕ s , k = ϕ 0 , k + l 0 2 π s m .
ψ ( r , θ , z ) = s = 0 m 1 k = 1 n l = c φ ( r , θ + 2 π s m , z ) exp ( i ϕ s , k )   =   s = 0 m 1 k = 1 n l = c φ ( r , θ + 2 π s m , z ) exp ( i ϕ 0 , k ) exp ( i l 0 2 π s m ) .
S = s = 0 m 1 exp ( i l 2 π s m ) exp ( i l 0 2 π s m ) = s = 0 m 1 exp [ i 2 π s m ( l + l 0 ) ] = { m ,   l + l 0 = M m 0 ,   l + l 0 M m   .
ψ ( r , θ , z ) = { m k = 1 n p = 0 l = c p , l φ p , l ( r , z ) exp ( i ϕ 0 , k ) exp ( i l θ ) , l = M m l 0 0 , l M m l 0
l = M m l 0 ,   M = 0 , ± 1 , ± 2 , .

Metrics