Abstract

We present a method to generate a spatially varying lattice of polarization singularities. The periodicity and orientation of the lattice can be varied spatially by engineering phase and polarization gradients in the interfering beams. A spatial light modulator and an S-wave plate are used to control the phase and polarization gradients, respectively, in the interfering beams. A filter in the Fourier space selects the required spatial frequency components of the interfering beams. Experimentally realized lattices are presented. These spatially varying lattices may find applications in polarization dependent structured illumination, particle sorting, and optical trapping.

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

Full Article  |  PDF Article

Corrections

15 February 2019: A typographical correction was made to Ref. 6.


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References

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  1. I. Freund, “Polarization singularity indices in gaussian laser beams,” Opt. Commun. 201, 251–270 (2002).
    [Crossref]
  2. I. Freund, “Polarization singularities in optical lattices,” Opt. Lett. 29, 875–877 (2004).
    [Crossref] [PubMed]
  3. M. Berry and M. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. Royal Soc. Lond. A: Math. Phys. Eng. Sci. 457, 141–155 (2001).
    [Crossref]
  4. M. V. Berry, “The electric and magnetic polarization singularities of paraxial waves,” J. Opt. A: Pure Appl. Opt. 6, 475 (2004).
    [Crossref]
  5. M. Dennis, “Polarization singularities in paraxial vector fields: morphology and statistics,” Opt. Commun. 213, 201–221 (2002).
    [Crossref]
  6. 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]
  7. S. K. Pal and P. Senthilkumaran, “Cultivation of lemon fields,” Opt. Express 24, 28008–28013 (2016).
    [Crossref] [PubMed]
  8. Ruchi, S. K. Pal, and P. Senthilkumaran, “Generation of V-point polarization singularity lattices,” Opt. Express 25, 19326–19331 (2017).
    [Crossref] [PubMed]
  9. 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]
  10. B. S. B. Ram, P. Senthilkumaran, and A. Sharma, “Polarization-based spatial filtering for directional and nondirectional edge enhancement using an s-waveplate,” Appl. Opt. 56, 3171–3178 (2017).
    [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. W. Schoonover and T. D. Visser, “Creating polarization singularities with an n-pinhole interferometer,” in Frontiers in Optics 2009/Laser Science XXV/Fall 2009 OSA Optics & Photonics Technical Digest, (Optical Society of America, 2009), p. FWH6.
    [Crossref]
  13. S. K. Pal and P. Senthilkumaran, “Synthesis of Stokes vortices,” Opt. Lett. 44, 130–133 (2019).
  14. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
    [Crossref]
  15. O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Y. Zenkova, and A. V. Tyurin, “Circular motion of particles suspended in a gaussian beam with circular polarization validates the spin part of the internal energy flow,” Opt. Express 20, 11351–11356 (2012).
    [Crossref] [PubMed]
  16. O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, S. G. Hanson, and C. Y. Zenkova, “Orbital rotation without orbital angular momentum: mechanical action of the spin part of the internal energy flow in light beams,” Opt. Express 20, 3563–3571 (2012).
    [Crossref] [PubMed]
  17. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
    [Crossref] [PubMed]
  18. K. Ladavac and D. G. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Opt. Express 12, 1144–1149 (2004).
    [Crossref] [PubMed]
  19. P. Lochab, P. Senthilkumaran, and K. Khare, “Robust laser beam engineering using polarization and angular momentum diversity,” Opt. Express 25, 17524–17529 (2017).
    [Crossref] [PubMed]
  20. P. Lochab, P. Senthilkumaran, and K. Khare, “Designer vector beams maintaining a robust intensity profile on propagation through turbulence,” Phys. Rev. A 98, 023831 (2018).
    [Crossref]
  21. B. S. B. Ram and P. Senthilkumaran, “Edge enhancement by negative poincare–hopf index filters,” Opt. Lett. 43, 1830–1833 (2018).
    [Crossref]
  22. C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, “Spin-orbit beams for optical chirality measurement,” Appl. Phys. Lett. 112, 031101 (2018).
    [Crossref]
  23. R. C. Rumpf and J. Pazos, “Synthesis of spatially variant lattices,” Opt. Express 20, 15263–15274 (2012).
    [Crossref] [PubMed]
  24. M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105, 051102 (2014).
    [Crossref]
  25. A. Kapoor, M. Kumar, P. Senthilkumaran, and J. Joseph, “Optical vortex array in spatially varying lattice,” Opt. Commun. 365, 99–102 (2016).
    [Crossref]
  26. J. L. Digaum, J. J. Pazos, J. Chiles, J. D’Archangel, G. Padilla, A. Tatulian, R. C. Rumpf, S. Fathpour, G. D. Boreman, and S. M. Kuebler, “Tight control of light beams in photonic crystals with spatially-variant lattice orientation,” Opt. Express 22, 25788–25804 (2014).
    [Crossref] [PubMed]

2019 (1)

2018 (3)

P. Lochab, P. Senthilkumaran, and K. Khare, “Designer vector beams maintaining a robust intensity profile on propagation through turbulence,” Phys. Rev. A 98, 023831 (2018).
[Crossref]

B. S. B. Ram and P. Senthilkumaran, “Edge enhancement by negative poincare–hopf index filters,” Opt. Lett. 43, 1830–1833 (2018).
[Crossref]

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, “Spin-orbit beams for optical chirality measurement,” Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

2017 (5)

2016 (2)

S. K. Pal and P. Senthilkumaran, “Cultivation of lemon fields,” Opt. Express 24, 28008–28013 (2016).
[Crossref] [PubMed]

A. Kapoor, M. Kumar, P. Senthilkumaran, and J. Joseph, “Optical vortex array in spatially varying lattice,” Opt. Commun. 365, 99–102 (2016).
[Crossref]

2014 (2)

2013 (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

2012 (4)

2007 (1)

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[Crossref]

2004 (3)

2002 (2)

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

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

2001 (1)

M. Berry and M. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. Royal Soc. Lond. A: Math. Phys. Eng. Sci. 457, 141–155 (2001).
[Crossref]

Angelsky, O. V.

Bekshaev, A. Y.

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[Crossref]

Berry, M.

M. Berry and M. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. Royal Soc. Lond. A: Math. Phys. Eng. Sci. 457, 141–155 (2001).
[Crossref]

Berry, M. V.

M. V. Berry, “The electric and magnetic polarization singularities of paraxial waves,” J. Opt. A: Pure Appl. Opt. 6, 475 (2004).
[Crossref]

Boreman, G. D.

Borwinska, M.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Chiles, J.

D’Archangel, J.

Dennis, M.

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

M. Berry and M. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. Royal Soc. Lond. A: Math. Phys. Eng. Sci. 457, 141–155 (2001).
[Crossref]

Digaum, J. L.

Fathpour, S.

Freund, I.

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

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

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[Crossref]

Grier, D. G.

Hanson, S. G.

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[Crossref]

Joseph, J.

A. Kapoor, M. Kumar, P. Senthilkumaran, and J. Joseph, “Optical vortex array in spatially varying lattice,” Opt. Commun. 365, 99–102 (2016).
[Crossref]

M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105, 051102 (2014).
[Crossref]

Kapoor, A.

A. Kapoor, M. Kumar, P. Senthilkumaran, and J. Joseph, “Optical vortex array in spatially varying lattice,” Opt. Commun. 365, 99–102 (2016).
[Crossref]

Khare, K.

P. Lochab, P. Senthilkumaran, and K. Khare, “Designer vector beams maintaining a robust intensity profile on propagation through turbulence,” Phys. Rev. A 98, 023831 (2018).
[Crossref]

P. Lochab, P. Senthilkumaran, and K. Khare, “Robust laser beam engineering using polarization and angular momentum diversity,” Opt. Express 25, 17524–17529 (2017).
[Crossref] [PubMed]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Kuebler, S. M.

Kumar, M.

A. Kapoor, M. Kumar, P. Senthilkumaran, and J. Joseph, “Optical vortex array in spatially varying lattice,” Opt. Commun. 365, 99–102 (2016).
[Crossref]

M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105, 051102 (2014).
[Crossref]

Kurzynowski, P.

Ladavac, K.

Lochab, P.

P. Lochab, P. Senthilkumaran, and K. Khare, “Designer vector beams maintaining a robust intensity profile on propagation through turbulence,” Phys. Rev. A 98, 023831 (2018).
[Crossref]

P. Lochab, P. Senthilkumaran, and K. Khare, “Robust laser beam engineering using polarization and angular momentum diversity,” Opt. Express 25, 17524–17529 (2017).
[Crossref] [PubMed]

Maksimyak, A. P.

Maksimyak, P. P.

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
[Crossref]

Mokhun, I. I.

Naik, D. N.

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, “Spin-orbit beams for optical chirality measurement,” Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

Padilla, G.

Pal, S. K.

Pazos, J.

Pazos, J. J.

Ram, B. S. B.

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

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, 78 (2007).
[Crossref]

Ruchi,

Rumpf, R. C.

Samlan, C. T.

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, “Spin-orbit beams for optical chirality measurement,” Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

Schoonover, R. W.

R. W. Schoonover and T. D. Visser, “Creating polarization singularities with an n-pinhole interferometer,” in Frontiers in Optics 2009/Laser Science XXV/Fall 2009 OSA Optics & Photonics Technical Digest, (Optical Society of America, 2009), p. FWH6.
[Crossref]

Senthilkumaran, P.

S. K. Pal and P. Senthilkumaran, “Synthesis of Stokes vortices,” Opt. Lett. 44, 130–133 (2019).

B. S. B. Ram and P. Senthilkumaran, “Edge enhancement by negative poincare–hopf index filters,” Opt. Lett. 43, 1830–1833 (2018).
[Crossref]

P. Lochab, P. Senthilkumaran, and K. Khare, “Designer vector beams maintaining a robust intensity profile on propagation through turbulence,” Phys. Rev. A 98, 023831 (2018).
[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]

Ruchi, S. K. Pal, and P. Senthilkumaran, “Generation of V-point polarization singularity lattices,” Opt. Express 25, 19326–19331 (2017).
[Crossref] [PubMed]

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]

B. S. B. Ram, P. Senthilkumaran, and A. Sharma, “Polarization-based spatial filtering for directional and nondirectional edge enhancement using an s-waveplate,” Appl. Opt. 56, 3171–3178 (2017).
[Crossref]

P. Lochab, P. Senthilkumaran, and K. Khare, “Robust laser beam engineering using polarization and angular momentum diversity,” Opt. Express 25, 17524–17529 (2017).
[Crossref] [PubMed]

A. Kapoor, M. Kumar, P. Senthilkumaran, and J. Joseph, “Optical vortex array in spatially varying lattice,” Opt. Commun. 365, 99–102 (2016).
[Crossref]

S. K. Pal and P. Senthilkumaran, “Cultivation of lemon fields,” Opt. Express 24, 28008–28013 (2016).
[Crossref] [PubMed]

Sharma, A.

Suna, R. R.

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, “Spin-orbit beams for optical chirality measurement,” Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

Tatulian, A.

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Tyurin, A. V.

Visser, T. D.

R. W. Schoonover and T. D. Visser, “Creating polarization singularities with an n-pinhole interferometer,” in Frontiers in Optics 2009/Laser Science XXV/Fall 2009 OSA Optics & Photonics Technical Digest, (Optical Society of America, 2009), p. FWH6.
[Crossref]

Viswanathan, N. K.

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, “Spin-orbit beams for optical chirality measurement,” Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Wozniak, W. A.

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Zdunek, M.

Zenkova, C. Y.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

C. T. Samlan, R. R. Suna, D. N. Naik, and N. K. Viswanathan, “Spin-orbit beams for optical chirality measurement,” Appl. Phys. Lett. 112, 031101 (2018).
[Crossref]

M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105, 051102 (2014).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

M. V. Berry, “The electric and magnetic polarization singularities of paraxial waves,” J. Opt. A: Pure Appl. Opt. 6, 475 (2004).
[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, 78 (2007).
[Crossref]

Opt. Commun. (4)

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

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

A. Kapoor, M. Kumar, P. Senthilkumaran, and J. Joseph, “Optical vortex array in spatially varying lattice,” Opt. Commun. 365, 99–102 (2016).
[Crossref]

Opt. Express (9)

J. L. Digaum, J. J. Pazos, J. Chiles, J. D’Archangel, G. Padilla, A. Tatulian, R. C. Rumpf, S. Fathpour, G. D. Boreman, and S. M. Kuebler, “Tight control of light beams in photonic crystals with spatially-variant lattice orientation,” Opt. Express 22, 25788–25804 (2014).
[Crossref] [PubMed]

R. C. Rumpf and J. Pazos, “Synthesis of spatially variant lattices,” Opt. Express 20, 15263–15274 (2012).
[Crossref] [PubMed]

S. K. Pal and P. Senthilkumaran, “Cultivation of lemon fields,” Opt. Express 24, 28008–28013 (2016).
[Crossref] [PubMed]

Ruchi, S. K. Pal, and P. Senthilkumaran, “Generation of V-point polarization singularity lattices,” Opt. Express 25, 19326–19331 (2017).
[Crossref] [PubMed]

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]

K. Ladavac and D. G. Grier, “Microoptomechanical pumps assembled and driven by holographic optical vortex arrays,” Opt. Express 12, 1144–1149 (2004).
[Crossref] [PubMed]

P. Lochab, P. Senthilkumaran, and K. Khare, “Robust laser beam engineering using polarization and angular momentum diversity,” Opt. Express 25, 17524–17529 (2017).
[Crossref] [PubMed]

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, I. I. Mokhun, S. G. Hanson, C. Y. Zenkova, and A. V. Tyurin, “Circular motion of particles suspended in a gaussian beam with circular polarization validates the spin part of the internal energy flow,” Opt. Express 20, 11351–11356 (2012).
[Crossref] [PubMed]

O. V. Angelsky, A. Y. Bekshaev, P. P. Maksimyak, A. P. Maksimyak, S. G. Hanson, and C. Y. Zenkova, “Orbital rotation without orbital angular momentum: mechanical action of the spin part of the internal energy flow in light beams,” Opt. Express 20, 3563–3571 (2012).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. Rev. A (1)

P. Lochab, P. Senthilkumaran, and K. Khare, “Designer vector beams maintaining a robust intensity profile on propagation through turbulence,” Phys. Rev. A 98, 023831 (2018).
[Crossref]

Proc. Royal Soc. Lond. A: Math. Phys. Eng. Sci. (1)

M. Berry and M. Dennis, “Polarization singularities in isotropic random vector waves,” Proc. Royal Soc. Lond. A: Math. Phys. Eng. Sci. 457, 141–155 (2001).
[Crossref]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Other (1)

R. W. Schoonover and T. D. Visser, “Creating polarization singularities with an n-pinhole interferometer,” in Frontiers in Optics 2009/Laser Science XXV/Fall 2009 OSA Optics & Photonics Technical Digest, (Optical Society of America, 2009), p. FWH6.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 (a) Momentum distribution of three interfering beams on the Bloch sphere; (b) Polarization distribution of three interfering beams on the Poincare sphere. The spread of k vectors are represented by the area enclosed by the ellipses which is only a schematic representation.
Fig. 2
Fig. 2 Simulated intensity and Stokes phase of spatially varying lattice with varying (a) periodicity, (b) orientation and (c) both periodicity and orientation. Corresponding Stokes intensities are shown as insets. (d–f) show corresponding ϕ.
Fig. 3
Fig. 3 Simulated polarization patterns of spatially varying lattices for star field (a–c) and lemon fields (d–f) are shown, where (a,d) are for periodicity variation, (b,e) for orientation variation and (c,f) for both periodicity and orientation variation respectively.
Fig. 4
Fig. 4 (a) Simulated intensity, Stokes intensity(inset), (b) Stokes phase and, (c) polarization pattern with periodicity variation in radial direction
Fig. 5
Fig. 5 (a) Experimental set up: P: polarizer; SF: spatial filter assembly; L1, L2, L3: Converging lenses; SLM: Spatial light modulator; BS: Beam splitter; FF: Fourier filter; S: S wave plate; HWP: Half wave plate; SC: Stokes camera. (b), (c) and (d): simulated phase patterns for three beam interference with periodicity variation, with both periodicity and orientation variation and with orientation variation. Focal lengths of lenses L1, L2 and L3 are 20cm, 35cm and 15cm respectively.
Fig. 6
Fig. 6 Row i, Row ii and Row iii correspond to experimental results for spatially varying lattice with only periodicity variation, both periodicity and orientation variation and only orientation variation respectively. (a, d, g) and (c, f, i) show magnified images of polarization patterns for left and right portions of intensities (b, e, h). For experimental polarization plots, size of the window is 165 × 165μm2.

Equations (4)

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

k j = 2 π λ { cos ( Θ j ) sin ( θ ) x ^ + sin ( Θ j ) sin ( θ ) y ^ + cos ( θ ) z ^ }
K j ( r ) = 2 π λ P ( r ) ( cos ( Θ j + O ( r ) ) x ^ + sin ( Θ j + O ( r ) ) y ^ + K z j z ^ )
( φ j ( r ) ) = K j ( r )
E x = j = 1 3 cos ( Θ j + O ( r ) ) exp ( i φ j ( r ) ) , E y = j = 1 3 sin ( Θ j + O ( r ) ) exp ( i φ j ( r ) )

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