Abstract

V-points normally do not occur in generic light fields as compared to C-points and L-lines. In structured optical fields, simultaneous existence of C-points, V-points and L-lines can be engineered in lattice forms. But lattices consisting only of V-points have not been realized so far. In this paper we demonstrate creation of lattices of V-point polarization singularities with translational periodicity. These lattice structures are obtained by the interference of four (six) linearly polarized plane waves arranged in symmetric umbrella geometry. The state of polarization of each beam is controlled by an S-waveplate. Since in a periodic lattice of polarization singularities the net charge in a unit cell is zero, the lattices are populated with positive and negative index V-point singularities. All the first order degenerate states of V-point singularities can be realized in the same setup by selective excitation of the S-waveplate.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  4. J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
    [Crossref]
  5. S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46, 2893–2898 (2007).
    [Crossref] [PubMed]
  6. J. Xavier, S. Vyas, P. Senthilkumaran, and J. Joseph, “Tailored complex 3D vortex lattice structures by perturbed multiples of three plane waves,” Appl. Opt. 51, 1872–1878 (2012).
    [Crossref] [PubMed]
  7. G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75,066613 (2007).
    [Crossref]
  8. R. W. Schoonover and T. D. Visser, “Creating polarization singularities with N pinhole interferometer,” Phys. Rev. A 79, 043809(1–7) (2009).
    [Crossref]
  9. I. Freund, “Polarization Singularities in optical lattices,” Opt. Lett. 29, 875–877 (2004).
    [Crossref] [PubMed]
  10. S. K. Pal and P. Senthilkumaran, “Cultivation of lemon fields,” Opt. Express 24, 28008–28013 (2016).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  15. M. R. Dennis, “Polarization Singularities in paraxial vector fields:morphology and statisics,” Opt. Commun. 213, 201–221 (2002).
    [Crossref]
  16. J. F. Nye, “Lines of circular polarization in electromagnetic fields,” Proc. Roy. Soc. A 389, 279–290 (1983).
    [Crossref]
  17. I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201, 251–270 (2002).
    [Crossref]
  18. I. Freund, M. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
    [Crossref]
  19. J. F. Wheeldon and H. Schriemer, “Wyckoff positions and the expression of polarization singularities in photonic crystals,” Opt. Express 17, 2111–2121 (2009).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  22. I. Freund, “Optical Möbius strips in three dimensional ellipse fields: II. Lines of linear polarization,” Opt. Commun. 283, 16–28 (2010).
    [Crossref]

2017 (3)

2016 (2)

2015 (1)

2013 (1)

2012 (2)

2010 (1)

I. Freund, “Optical Möbius strips in three dimensional ellipse fields: II. Lines of linear polarization,” Opt. Commun. 283, 16–28 (2010).
[Crossref]

2009 (2)

R. W. Schoonover and T. D. Visser, “Creating polarization singularities with N pinhole interferometer,” Phys. Rev. A 79, 043809(1–7) (2009).
[Crossref]

J. F. Wheeldon and H. Schriemer, “Wyckoff positions and the expression of polarization singularities in photonic crystals,” Opt. Express 17, 2111–2121 (2009).
[Crossref] [PubMed]

2007 (2)

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75,066613 (2007).
[Crossref]

S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46, 2893–2898 (2007).
[Crossref] [PubMed]

2004 (1)

2002 (4)

A. I. Mokhun, M. S. Soskin, and I. Freund, “Elliptic critical points: C-points, α-lines, and the sign rule,” Opt. Lett. 27, 995–997 (2002).
[Crossref]

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

I. Freund, M. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
[Crossref]

M. R. Dennis, “Polarization Singularities in paraxial vector fields:morphology and statisics,” Opt. Commun. 213, 201–221 (2002).
[Crossref]

2001 (1)

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[Crossref]

1994 (1)

P. Senthilkumaran and R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105(3–4), 158–160 (1994).
[Crossref]

1983 (1)

J. F. Nye, “Lines of circular polarization in electromagnetic fields,” Proc. Roy. Soc. A 389, 279–290 (1983).
[Crossref]

Borwinska, M.

Cai, Y.

Chen, Y.

Dennis, M. R.

M. R. Dennis, “Polarization Singularities in paraxial vector fields:morphology and statisics,” Opt. Commun. 213, 201–221 (2002).
[Crossref]

Dubik, B.

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[Crossref]

Freund, I.

I. Freund, “Optical Möbius strips in three dimensional ellipse fields: II. Lines of linear polarization,” Opt. Commun. 283, 16–28 (2010).
[Crossref]

I. Freund, “Polarization Singularities in optical lattices,” Opt. Lett. 29, 875–877 (2004).
[Crossref] [PubMed]

A. I. Mokhun, M. S. Soskin, and I. Freund, “Elliptic critical points: C-points, α-lines, and the sign rule,” Opt. Lett. 27, 995–997 (2002).
[Crossref]

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

I. Freund, M. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
[Crossref]

Gbur, G.

Joseph, J.

Kurzynowski, P.

Liang, C.

Masajada, J.

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[Crossref]

Mi, C.

Mokhun, A. I.

I. Freund, M. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
[Crossref]

A. I. Mokhun, M. S. Soskin, and I. Freund, “Elliptic critical points: C-points, α-lines, and the sign rule,” Opt. Lett. 27, 995–997 (2002).
[Crossref]

Nye, J. F.

J. F. Nye, “Lines of circular polarization in electromagnetic fields,” Proc. Roy. Soc. A 389, 279–290 (1983).
[Crossref]

Paganin, D. M.

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75,066613 (2007).
[Crossref]

Pal, S. K.

Pang, X.

Peng, X.

Ponomarenko, S. A.

Ruben, G.

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75,066613 (2007).
[Crossref]

Ruchi,

S. K. Pal, Ruchi, and P. Senthilkumaran, “C-point and V-point singularity lattice formation and index sign conversion methods,” Opt. Commun. 393, 156–168 (2017).
[Crossref]

S. K. Pal, Ruchi, and P. Senthilkumaran, “Polarization singularity index sign inversion by a half waveplate,” Appl. Opt. 56, 6181–6190 (2017).
[Crossref]

Schoonover, R. W.

R. W. Schoonover and T. D. Visser, “Creating polarization singularities with N pinhole interferometer,” Phys. Rev. A 79, 043809(1–7) (2009).
[Crossref]

Schriemer, H.

Senthilkumaran, P.

Sirohi, R. S.

P. Senthilkumaran and R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105(3–4), 158–160 (1994).
[Crossref]

Song, Q.

Soskin, M.

I. Freund, M. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
[Crossref]

Soskin, M. S.

Visser, T. D.

X. Pang, G. Gbur, and T. D. Visser, “Cycle of phase, coherence and polarization singularities in Young’s three-pinhole experiment,” Opt. Express 23, 34093–34108 (2015).
[Crossref]

R. W. Schoonover and T. D. Visser, “Creating polarization singularities with N pinhole interferometer,” Phys. Rev. A 79, 043809(1–7) (2009).
[Crossref]

Vyas, S.

Wang, F.

Wheeldon, J. F.

Wozniak, W.A.

Xavier, J.

Xin, Y.

Ye, D.

Yu, R.

Zdunek, M.

Zhao, C.

Zhao, Q.

Appl. Opt. (3)

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

Opt. Commun. (7)

M. R. Dennis, “Polarization Singularities in paraxial vector fields:morphology and statisics,” Opt. Commun. 213, 201–221 (2002).
[Crossref]

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

I. Freund, M. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
[Crossref]

P. Senthilkumaran and R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105(3–4), 158–160 (1994).
[Crossref]

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[Crossref]

I. Freund, “Optical Möbius strips in three dimensional ellipse fields: II. Lines of linear polarization,” Opt. Commun. 283, 16–28 (2010).
[Crossref]

S. K. Pal, Ruchi, and P. Senthilkumaran, “C-point and V-point singularity lattice formation and index sign conversion methods,” Opt. Commun. 393, 156–168 (2017).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. A (1)

R. W. Schoonover and T. D. Visser, “Creating polarization singularities with N pinhole interferometer,” Phys. Rev. A 79, 043809(1–7) (2009).
[Crossref]

Phys. Rev. E (1)

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75,066613 (2007).
[Crossref]

Proc. Roy. Soc. A (1)

J. F. Nye, “Lines of circular polarization in electromagnetic fields,” Proc. Roy. Soc. A 389, 279–290 (1983).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Transverse plane projection of the k → m onto a circle is shown by black dots for n = 4 (a)–(c) and n = 6 (d)–(f) plane waves. Red arrows show plane of polarization of individual beam. SOPs are arranged radially (α = 0°) in (a) and (d) ; azimuthally (α = 90°) in (c) and (f); superposition states of RP and AP (α = 45°) in (b) and (e).

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Fig. 2
Fig. 2 Four beam Interference : (a) Computed resultant intensity; (b) Stokes phase for α = 0° (RP); (c) Phase contours corresponding to RP; (d)–(f): Simulated SOP distributions for different values of α; (g)–(i) Experimentally obtained SOP distributions.

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Fig. 3
Fig. 3 Six beam Interference : (a) Computed resultant intensity; (b) Stokes phase for α = 0° (RP); (c) Corresponding Phase contour map ; Row 2 and Row 3 show polarization patterns for a central V-point with η = +1 and η = −1 respectively.

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Fig. 4
Fig. 4 Experimental results for six beam interference: (a) Resultant intensity distribution; SOP distributions for η = +1 (b)–(d) and η = −1 (e)–(f) at the center of each hexagon.

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Equations (4)

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k → m = k m x x ^ + k m y y ^ + k m z z ^
n ^ m = cos α ρ ^ m + sin α φ ^ m
E → m = n ^ m E 0 exp ( i ( k → m . r → m ) )
E R = E X x ^ + E Y y ^ = ∑ m = 1 n E → m n ^ m

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