Abstract

Polarization singularity lattices exhibit richer features and varieties than their scalar counterparts, namely phase vortex lattices. Lattices consisting of only C-points or only V-points of different Stokes indices are possible by phase and polarization engineering. In this article we show the generation of one generic and three non-generic lattices—all abiding the enlarged sign principle in six-beam interference. Two of them are vector fields and two of them are ellipse fields. In the vector fields, one lattice consists of V-points of the same magnitude and the other consists of V-points of different magnitude of the Poincare-Hopf index. Similarly in the two ellipse fields, the same and different C-point index lattices are there. Interestingly all the C-points are of the same handedness. In one particular case the C-point lattice is interlaced with saddle points, in which formation of C-lines is also noticed. These are saddles in both azimuth and ellipticity distributions. The governing rules for realizing these lattices are given and these lattices are experimentally demonstrated.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Generation of V-point polarization singularity lattices

Ruchi, Sushanta Kumar Pal, and P. Senthilkumaran
Opt. Express 25(16) 19326-19331 (2017)

Engineered polar magneto-optical Kerr rotation through Wood–Rayleigh anomalies and magnetoplamon resonance coupling

X. Zhang, K. Cao, J. Li, X. B. Sun, Y. Y. Wang, Y. Li, X. Zhang, and X. H. Kong
OSA Continuum 2(1) 1-8 (2019)

Generation of orthogonal lattice fields

Sushanta Kumar Pal and P. Senthilkumaran
J. Opt. Soc. Am. A 36(5) 853-858 (2019)

References

  • View by:
  • |
  • |
  • |

  1. J. V. Hajnal, “Singularities in the transverse fields of electromagnetic waves. I. theory,” Proc. R. Soc. Lond. A 414, 433–446 (1987).
    [Crossref]
  2. I. Mokhun, Y. Galushko, Y. Kharitonova, Y. Viktorovskaya, and R. Khrobatin, “Elementary heterogeneously polarized field modeling,” Opt. Lett. 36, 2137–2139 (2011).
    [Crossref] [PubMed]
  3. I. Freund, “Polarization singularity indices in Gaussian laser beams,” Opt. Commun. 201, 251–270 (2002).
    [Crossref]
  4. M. R. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
    [Crossref]
  5. A. I. Mokhun, M. S. Soskin, and I. Freund, “Elliptic critical points: C-points, a-lines, and the sign rule,” Opt. Lett. 27, 995–997 (2002).
    [Crossref]
  6. I. Freund, M. S. Soskin, and A. I. Mokhun, “Elliptic critical points in paraxial optical fields,” Opt. Commun. 208, 223–253 (2002).
    [Crossref]
  7. I. Freund, “Möbius strips and twisted ribbons in intersecting Gauss-Laguerre beams,” Opt. Commun. 284, 3816–3845 (2011).
    [Crossref]
  8. I. Freund, “Polarization singularities in optical lattices,” Opt. Lett. 29, 875–877 (2004).
    [Crossref] [PubMed]
  9. 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]
  10. R. W. Schoonover and T. D. Visser, “Creating polarization singularities with an N-pinhole interferometer,” Phys. Rev. A 79, 1–7 (2009).
    [Crossref]
  11. P. Kurzynowski, W. A. Woźniak, M. Zdunek, and M. Borwińska, “Singularities of interference of three waves with different polarization states,” Opt. Express 20, 26755–26765 (2012).
    [Crossref] [PubMed]
  12. R. Yu, Y. Xin, Q. Zhao, Y. Chen, and Q. Song, “Array of polarization singularities in interference of three waves,” J. Opt. Soc. Am. A 30, 2556–2560 (2013).
    [Crossref]
  13. P. Kurzynowski, W. A. Woźniak, and M. Borwińska, “Regular lattices of polarization singularities: Their generation and properties,” J. Opt. 12, 035406 (2010).
    [Crossref]
  14. D. Ye, X. Peng, Q. Zhao, and Y. Chen, “Numerical generation of a polarization singularity array with modulated amplitude and phase,” J. Opt. Soc. Am. A 33, 1705–1709 (2016).
    [Crossref]
  15. S. K. Pal and P. Senthilkumaran, “Cultivation of lemon fields,” Opt. Express 24, 28008–28013 (2016).
    [Crossref] [PubMed]
  16. 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]
  17. S. K. Pal and P. Senthilkumaran, “Lattice of C points at intensity nulls,” Opt. Lett. 43, 1259–1262 (2018).
    [Crossref] [PubMed]
  18. Ruchi, S. K. Pal, and P. Senthilkumaran, “Generation of V-point polarization singularity lattices,” Opt. Express 25, 19326–19331 (2017).
    [Crossref] [PubMed]
  19. D. Goldstein, Polarized Light (CRC Press, 2011).
  20. M. Born and E. Wolf, Principle of Optics (Cambridge University Press, 1999).
    [Crossref]
  21. B. Bhargava Ram, Ruchi, and P. Senthilkumaran, “Angular momentum switching and orthogonal field construction of C-points,” Opt. Lett. 43, 2157–2160 (2018).
    [Crossref] [PubMed]
  22. I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
    [Crossref] [PubMed]
  23. I. Freund, “Saddles, singularities, and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995).
    [Crossref]
  24. S. K. Pal, Ruchi, and P. Senthilkumaran, “Polarization singularity index sign inversion by a half-wave plate,” Appl. Opt. 56, 6181–6190 (2017).
    [Crossref] [PubMed]

2018 (2)

2017 (3)

2016 (2)

2015 (1)

2013 (1)

2012 (1)

2011 (2)

2010 (1)

P. Kurzynowski, W. A. Woźniak, and M. Borwińska, “Regular lattices of polarization singularities: Their generation and properties,” J. Opt. 12, 035406 (2010).
[Crossref]

2009 (1)

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

2004 (1)

2002 (4)

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

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

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

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

1995 (1)

I. Freund, “Saddles, singularities, and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995).
[Crossref]

1994 (1)

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[Crossref] [PubMed]

1987 (1)

J. V. Hajnal, “Singularities in the transverse fields of electromagnetic waves. I. theory,” Proc. R. Soc. Lond. A 414, 433–446 (1987).
[Crossref]

Born, M.

M. Born and E. Wolf, Principle of Optics (Cambridge University Press, 1999).
[Crossref]

Borwinska, M.

P. Kurzynowski, W. A. Woźniak, M. Zdunek, and M. Borwińska, “Singularities of interference of three waves with different polarization states,” Opt. Express 20, 26755–26765 (2012).
[Crossref] [PubMed]

P. Kurzynowski, W. A. Woźniak, and M. Borwińska, “Regular lattices of polarization singularities: Their generation and properties,” J. Opt. 12, 035406 (2010).
[Crossref]

Chen, Y.

Dennis, M. R.

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

Freund, I.

I. Freund, “Möbius strips and twisted ribbons in intersecting Gauss-Laguerre beams,” Opt. Commun. 284, 3816–3845 (2011).
[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, a-lines, and the sign rule,” Opt. Lett. 27, 995–997 (2002).
[Crossref]

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

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

I. Freund, “Saddles, singularities, and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995).
[Crossref]

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[Crossref] [PubMed]

Galushko, Y.

Gbur, G.

Goldstein, D.

D. Goldstein, Polarized Light (CRC Press, 2011).

Hajnal, J. V.

J. V. Hajnal, “Singularities in the transverse fields of electromagnetic waves. I. theory,” Proc. R. Soc. Lond. A 414, 433–446 (1987).
[Crossref]

Kharitonova, Y.

Khrobatin, R.

Kurzynowski, P.

P. Kurzynowski, W. A. Woźniak, M. Zdunek, and M. Borwińska, “Singularities of interference of three waves with different polarization states,” Opt. Express 20, 26755–26765 (2012).
[Crossref] [PubMed]

P. Kurzynowski, W. A. Woźniak, and M. Borwińska, “Regular lattices of polarization singularities: Their generation and properties,” J. Opt. 12, 035406 (2010).
[Crossref]

Mokhun, A. I.

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

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

Mokhun, I.

Pal, S. K.

Pang, X.

Peng, X.

Ram, B. Bhargava

Ruchi,

Schoonover, R. W.

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

Senthilkumaran, P.

Shvartsman, N.

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[Crossref] [PubMed]

Song, Q.

Soskin, M. S.

I. Freund, M. S. 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, a-lines, and the sign rule,” Opt. Lett. 27, 995–997 (2002).
[Crossref]

Viktorovskaya, Y.

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 an N-pinhole interferometer,” Phys. Rev. A 79, 1–7 (2009).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principle of Optics (Cambridge University Press, 1999).
[Crossref]

Wozniak, W. A.

P. Kurzynowski, W. A. Woźniak, M. Zdunek, and M. Borwińska, “Singularities of interference of three waves with different polarization states,” Opt. Express 20, 26755–26765 (2012).
[Crossref] [PubMed]

P. Kurzynowski, W. A. Woźniak, and M. Borwińska, “Regular lattices of polarization singularities: Their generation and properties,” J. Opt. 12, 035406 (2010).
[Crossref]

Xin, Y.

Ye, D.

Yu, R.

Zdunek, M.

Zhao, Q.

Appl. Opt. (1)

J. Opt. (1)

P. Kurzynowski, W. A. Woźniak, and M. Borwińska, “Regular lattices of polarization singularities: Their generation and properties,” J. Opt. 12, 035406 (2010).
[Crossref]

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

Opt. Commun. (5)

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]

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

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

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

I. Freund, “Möbius strips and twisted ribbons in intersecting Gauss-Laguerre beams,” Opt. Commun. 284, 3816–3845 (2011).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. A (2)

I. Freund and N. Shvartsman, “Wave-field phase singularities: The sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[Crossref] [PubMed]

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

Phys. Rev. E (1)

I. Freund, “Saddles, singularities, and extrema in random phase fields,” Phys. Rev. E 52, 2348–2360 (1995).
[Crossref]

Proc. R. Soc. Lond. A (1)

J. V. Hajnal, “Singularities in the transverse fields of electromagnetic waves. I. theory,” Proc. R. Soc. Lond. A 414, 433–446 (1987).
[Crossref]

Other (2)

D. Goldstein, Polarized Light (CRC Press, 2011).

M. Born and E. Wolf, Principle of Optics (Cambridge University Press, 1999).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 The wave vectors of each of the radially polarized beams are shown as black dots on a circle in the k-space. In (a–d), the initial constant phase offset given to beams numbered 1 to 6 leads to an accumulated phase as indicated at the center.
Fig. 2
Fig. 2 Simulated six-beam interference intensity patterns (a–d) for the four lattices E60, E61, E62, and E63. Insets: S12 Stokes intensity patterns.
Fig. 3
Fig. 3 Simulated polarization distributions of phase engineered vector and ellipse fields: (a) E60; (b) E61; (c) E62; and (d) E63 (Inset-Stokes phase). Blue, red, and green colours are used to indicate left, right handed SOPs and C-lines respectively.
Fig. 4
Fig. 4 Simulated index inversed polarization distributions of the ellipse fields: (a) E60; (b) E61; (c) E62; and (d) E63 (Inset-Stokes phase).
Fig. 5
Fig. 5 Zero contours of S1 (red) and S2 (black) of the field E62. The field is sufficiently perturbed to see the exact contours of S1 = 0 and S2 = 0 at several points that are numbered. The R and I denote real and imaginary part of S12 Stokes field.
Fig. 6
Fig. 6 Experimental setup: Microscope Objective (MO); Pin hole (PH); Lenses (L); Fourier filter (FF); S-wave plate (PC); Stokes camera (SC); Spatial light modulator (SLM). (a)–(d) Phase distributions displayed onto the SLM; (e)–(h) Recorded intensity distributions of the lattices.
Fig. 7
Fig. 7 Experimentally obtained polarization distributions of fields: (a) E60; (b) E61; (c) E62; and (d) E63.
Fig. 8
Fig. 8 Experimentally obtained polarization distributions of index inversed fields: (a) E60; (b) E61; (c) E62; and (d) E63.

Tables (1)

Tables Icon

Table 1 Synthesis of Various Polarization Singularity Lattices

Equations (1)

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

E R = j = 1 6 ( E j , l ) = j = 1 6 r ^ e i ( k j r + j ϕ l / 6 ) ,

Metrics