Abstract

In this Letter, we present a recipe for the generation of full Poincaré beams that contain all Stokes vortices (SVs), namely ϕ12, ϕ23, and ϕ31 vortices. Superposition of two scalar vortex beams with charges l1 and l2 (where |l1|≠|l2|) in orthogonal states of polarization (SOP) generates all three types of SVs, out of which two types of them are generic and always lie in a ring, with the third type at the center of the ring with index value (l2−l1). Thus, generation of hitherto unknown dark SVs is shown. The number of SVs in a ring is 4|l2−l1|. Index sign inversion for all SVs can be achieved by swapping l1 and l2. By changing the orthogonal pairs of SOPs of the interfering beams, the SV at the center of the ring can be changed from one to another type such that the other two types take part in the formation of the ring of generic SVs. We have also deduced the expressions for the location of all the SVs in the beam. Experimental results are presented.

© 2019 Optical Society of America

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References

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2019 (2)

W. A. Woźniak, P. Kurzynowski, and A. Popiołek-Masajada, Opt. Commun. 441, 155 (2019).
[Crossref]

S. K. Pal and P. Senthilkumaran, Opt. Lett. 44, 130 (2019).
[Crossref]

2018 (6)

2017 (4)

2015 (1)

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, New J. Phys. 17, 023011 (2015).
[Crossref]

2010 (1)

2004 (1)

M. V. Berry, J. Opt. A 6, 475 (2004).
[Crossref]

2002 (4)

2001 (1)

1987 (1)

J. V. Hajnal and J. F. Nye, Proc. R. Soc. London Ser. A 414, 433 (1987).
[Crossref]

Alonso, M. A.

Angelsky, O. V.

Beckley, A. M.

Berry, M. V.

M. V. Berry, J. Opt. A 6, 475 (2004).
[Crossref]

Boyd, R. W.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, New J. Phys. 17, 023011 (2015).
[Crossref]

Brown, T. G.

Chen, L.

Chen, X.

Dennis, M.

M. Dennis, Opt. Commun. 213, 201 (2002).
[Crossref]

Freund, I.

Hajnal, J. V.

J. V. Hajnal and J. F. Nye, Proc. R. Soc. London Ser. A 414, 433 (1987).
[Crossref]

Khare, K.

P. Lochab, P. Senthilkumaran, and K. Khare, Phys. Rev. A 98, 023831 (2018).
[Crossref]

P. Lochab, P. Senthilkumaran, and K. Khare, Opt. Express 25, 17524 (2017).
[Crossref]

Kurzynowski, P.

W. A. Woźniak, P. Kurzynowski, and A. Popiołek-Masajada, Opt. Commun. 441, 155 (2019).
[Crossref]

Lavery, M. P. J.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, New J. Phys. 17, 023011 (2015).
[Crossref]

Li, F.

Liu, H.

Lochab, P.

P. Lochab, P. Senthilkumaran, and K. Khare, Phys. Rev. A 98, 023831 (2018).
[Crossref]

P. Lochab, P. Senthilkumaran, and K. Khare, Opt. Express 25, 17524 (2017).
[Crossref]

Miatto, F. M.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, New J. Phys. 17, 023011 (2015).
[Crossref]

Mokhun, A. I.

Mokhun, I. I.

Naik, D. N.

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

Nye, J. F.

J. V. Hajnal and J. F. Nye, Proc. R. Soc. London Ser. A 414, 433 (1987).
[Crossref]

Padgett, M. J.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, New J. Phys. 17, 023011 (2015).
[Crossref]

Pal, S. K.

Popiolek-Masajada, A.

W. A. Woźniak, P. Kurzynowski, and A. Popiołek-Masajada, Opt. Commun. 441, 155 (2019).
[Crossref]

Qiu, X.

Ram, B. S. B.

Ruchi,

Samlan, C. T.

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

Senthilkumaran, P.

Sharma, A.

Soskin, M. S.

Suna, R. R.

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

Viswanathan, N. K.

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

Wozniak, W. A.

W. A. Woźniak, P. Kurzynowski, and A. Popiołek-Masajada, Opt. Commun. 441, 155 (2019).
[Crossref]

Zeilinger, A.

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, New J. Phys. 17, 023011 (2015).
[Crossref]

Zhang, L.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

J. Opt. A (1)

M. V. Berry, J. Opt. A 6, 475 (2004).
[Crossref]

New J. Phys. (1)

M. J. Padgett, F. M. Miatto, M. P. J. Lavery, A. Zeilinger, and R. W. Boyd, New J. Phys. 17, 023011 (2015).
[Crossref]

Opt. Commun. (3)

M. Dennis, Opt. Commun. 213, 201 (2002).
[Crossref]

I. Freund, Opt. Commun. 201, 251 (2002).
[Crossref]

W. A. Woźniak, P. Kurzynowski, and A. Popiołek-Masajada, Opt. Commun. 441, 155 (2019).
[Crossref]

Opt. Express (3)

Opt. Lett. (7)

OSA Continuum (1)

Phys. Rev. A (1)

P. Lochab, P. Senthilkumaran, and K. Khare, Phys. Rev. A 98, 023831 (2018).
[Crossref]

Proc. R. Soc. London Ser. A (1)

J. V. Hajnal and J. F. Nye, Proc. R. Soc. London Ser. A 414, 433 (1987).
[Crossref]

Other (1)

P. Senthilkumaran, in Singularities in Physics and Engineering (IOP Publishing, 2018), pp. 2053–2563.

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Figures (7)

Fig. 1.
Fig. 1. Simulation, superposition of vortices of charges l 1 = 0 and l 2 = 3 in S 1 ± , S 2 ± , and S 3 ± basis respectively. (a) Resultant SOP distribution; (b) zero contours of S 1 , S 2 , and S 3 ; and (c)–(e) Stokes phases ϕ 12 , ϕ 23 , and ϕ 31 . Insets, intensities.

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Fig. 2.
Fig. 2. Simulation, SOP distributions due to interference of two vortex beams with charges l 1 and l 2 respectively, (a)–(d) in S 1 ± basis and (e)–(f) in S 3 ± basis. Below each SOP distributions, Stokes phases ϕ 12 , ϕ 23 , and ϕ 31 are shown. Insets, intensities.

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Fig. 3.
Fig. 3. Simulation, distribution of SOPs on the Poincaré sphere for beams with different Stokes indices and combination of l 1 and l 2 . Percentage of area occupied by beams on the Poincaré sphere are (a) 60%, (b) 76.5%, (c) 87.7%, and (d) 76.5%.

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Fig. 4.
Fig. 4. Experimental setup: P, polarizer; SF, spatial filter assembly; L1 and L2, lenses; PBS, polarizing beam splitter; M 1 and M 2 , mirrors; SPP 1 , SPP 2 , spiral phase plates; HWP (QWP), half (quarter) wave plate; BD, beam dump; SC, Stokes camera.

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Fig. 5.
Fig. 5. Experimentally obtained Stokes vortices (a)  ϕ 12 , (b)  ϕ 23 , and (c)  ϕ 31 , and (d) SOP distribution due to superposition of vortex beams of charges l 1 = 0 and l 2 = 4 in S 1 ± .

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Fig. 6.
Fig. 6. Experimental results for interference of vortex beams with charges l 1 and l 2 in S 3 ± basis; a1,2; b1,2; and c1,2 show Stokes phases ϕ 12 , ϕ 23 , and ϕ 31 d1 and d2 show polarization distribution of resultant beam. Insets, intensities.

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Fig. 7.
Fig. 7. Experimental results for interference of vortex beams with charges l 1 and l 2 in S 3 ± basis; b1,2; c1,2; and d1,2 show Stokes phases ϕ 12 , ϕ 23 , and ϕ 31 . (a1) and (a2) show polarization distribution of resultant beam consisting of dark C points with Stokes index σ 12 = − 5 and σ 12 = 5 , respectively. Insets, intensities.

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Equations (4)

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

E x = r | l 1 |   exp ( i l 1 ϕ ) exp ( − r 2 w 2 ) ,
E y = r | l 2 |   exp ( i l 2 ϕ ) exp ( − r 2 w 2 ) ,
y = x   tan ( ( 2 n + 1 ) π 2 ( l 2 − l 1 ) ) and x 2 + y 2 = 1 .
y = x   tan ( n π ( l 2 − l 1 ) ) and x 2 + y 2 = 1 .