Abstract

We demonstrate large-area, closely-packed optical vortex arrays using self-assembled defects in smectic liquid crystals. Self-assembled smectic liquid crystals in a three-dimensional torus structure are called focal conic domains. Each FCD, having a micro-scale feature size, produces an optical vortex with consistent topological charge of 2. The spiral profile in the interferometry confirms the formation of an optical vortex, which is predicted by Jones matrix calculations.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  22. E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108(8), 087801 (2012).
    [CrossRef] [PubMed]
  23. R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  25. Y. H. Kim, D. K. Yoon, H. S. Jeong, O. D. Lavrentovich, H.-T. Jung, “Smectic liquid crystal defects for self-assembling of building blocks and their lithographic applications,” Adv. Funct. Mater. 21(4), 610–627 (2011).
    [CrossRef]
  26. F. Li, W. J. Doane, A. Jákli, “Magical Smectic Liquid Crystal Tube: Simple Illustration of Mechanical, Optical and Magnetic Properties of Smectic Liquid Crystals,” Jpn. J. Appl. Phys. 45(3A), 1714–1718 (2006).
    [CrossRef]
  27. C. Meyer, L. Le Cunff, M. Belloul, G. Foyart, “Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling,” Materials 2(2), 499–513 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]

2013

C. Loussert, U. Delabre, E. Brasselet, “Manipulating the Orbital Angular Momentum of Light at The Micron Scale with Nematic Disclinations in a Liquid Crystal Film,” Phys. Rev. Lett. 111(3), 037802 (2013).
[CrossRef] [PubMed]

B. Yang, E. Brasselet, “Arbitrary vortex arrays realized from optical winding of frustrated chiral liquid crystals,” J. Opt. 15(4), 044021 (2013).
[CrossRef]

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[CrossRef] [PubMed]

2012

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108(8), 087801 (2012).
[CrossRef] [PubMed]

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

E. Brasselet, A. Royon, L. Canioni, “Dense arrays of microscopic optical vortex generators from femtosecond direct laser writing of radial birefringence in glass,” Appl. Phys. Lett. 100(18), 181901 (2012).
[CrossRef]

2011

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

C. R. Doerr, L. L. Buhl, “Circular grating coupler for creating focused azimuthally and radially polarized beams,” Opt. Lett. 36(7), 1209–1211 (2011).
[CrossRef] [PubMed]

E. Brasselet, C. Loussert, “Electrically controlled topological defects in liquid crystals as tunable spin-orbit encoders for photons,” Opt. Lett. 36(5), 719–721 (2011).
[CrossRef] [PubMed]

H. T. Dai, Y. J. Liu, D. Luo, X. W. Sun, “Propagation properties of an optical vortex carried by an Airy beam: experimental implementation,” Opt. Lett. 36(9), 1617–1619 (2011).
[CrossRef] [PubMed]

Y. H. Kim, D. K. Yoon, H. S. Jeong, O. D. Lavrentovich, H.-T. Jung, “Smectic liquid crystal defects for self-assembling of building blocks and their lithographic applications,” Adv. Funct. Mater. 21(4), 610–627 (2011).
[CrossRef]

2010

H. T. Dai, Y. J. Liu, D. Luo, X. W. Sun, “Propagation dynamics of an optical vortex imposed on an Airy beam,” Opt. Lett. 35(23), 4075–4077 (2010).
[CrossRef] [PubMed]

E. Brasselet, “Spin-orbit optical cross-phase-modulation,” Phys. Rev. A 82(6), 063836 (2010).
[CrossRef]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[CrossRef] [PubMed]

E. Brasselet, M. Malinauskas, A. Žukauskas, S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[CrossRef]

2009

D. P. Ghai, S. Vyas, P. Senthilkumaran, R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282(14), 2692–2698 (2009).
[CrossRef]

E. Brasselet, N. Murazawa, H. Misawa, S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[CrossRef] [PubMed]

E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17(21), 18745–18759 (2009).
[CrossRef] [PubMed]

C. Meyer, L. Le Cunff, M. Belloul, G. Foyart, “Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling,” Materials 2(2), 499–513 (2009).
[CrossRef]

D. Mawet, E. Serabyn, K. Liewer, Ch. Hanot, S. McEldowney, D. Shemo, N. O’Brien, “Optical vectorial vortex coronagraphs using liquid crystal polymers: theory, manufacturing and laboratory demonstration,” Opt. Express 17(3), 1902–1918 (2009).
[CrossRef] [PubMed]

Y. H. Kim, D. K. Yoon, M. C. Choi, H. S. Jeong, M. W. Kim, O. D. Lavrentovich, H.-T. Jung, “Confined self-assembly of toric focal conic domains (the effects of confined geometry on the feature size of toric focal conic domains),” Langmuir 25(3), 1685–1691 (2009).
[CrossRef] [PubMed]

2006

F. Li, W. J. Doane, A. Jákli, “Magical Smectic Liquid Crystal Tube: Simple Illustration of Mechanical, Optical and Magnetic Properties of Smectic Liquid Crystals,” Jpn. J. Appl. Phys. 45(3A), 1714–1718 (2006).
[CrossRef]

L. Marrucci, C. Manzo, D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef] [PubMed]

2005

2004

2001

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

2000

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Assanto, G.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[CrossRef] [PubMed]

Barboza, R.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[CrossRef] [PubMed]

Belloul, M.

C. Meyer, L. Le Cunff, M. Belloul, G. Foyart, “Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling,” Materials 2(2), 499–513 (2009).
[CrossRef]

Bortolozzo, U.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[CrossRef] [PubMed]

Brasselet, E.

B. Yang, E. Brasselet, “Arbitrary vortex arrays realized from optical winding of frustrated chiral liquid crystals,” J. Opt. 15(4), 044021 (2013).
[CrossRef]

C. Loussert, U. Delabre, E. Brasselet, “Manipulating the Orbital Angular Momentum of Light at The Micron Scale with Nematic Disclinations in a Liquid Crystal Film,” Phys. Rev. Lett. 111(3), 037802 (2013).
[CrossRef] [PubMed]

E. Brasselet, A. Royon, L. Canioni, “Dense arrays of microscopic optical vortex generators from femtosecond direct laser writing of radial birefringence in glass,” Appl. Phys. Lett. 100(18), 181901 (2012).
[CrossRef]

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108(8), 087801 (2012).
[CrossRef] [PubMed]

E. Brasselet, C. Loussert, “Electrically controlled topological defects in liquid crystals as tunable spin-orbit encoders for photons,” Opt. Lett. 36(5), 719–721 (2011).
[CrossRef] [PubMed]

E. Brasselet, M. Malinauskas, A. Žukauskas, S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[CrossRef]

E. Brasselet, “Spin-orbit optical cross-phase-modulation,” Phys. Rev. A 82(6), 063836 (2010).
[CrossRef]

E. Brasselet, N. Murazawa, H. Misawa, S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[CrossRef] [PubMed]

Buhl, L. L.

Cai, X.

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

Canioni, L.

E. Brasselet, A. Royon, L. Canioni, “Dense arrays of microscopic optical vortex generators from femtosecond direct laser writing of radial birefringence in glass,” Appl. Phys. Lett. 100(18), 181901 (2012).
[CrossRef]

Capasso, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Choi, M. C.

Y. H. Kim, D. K. Yoon, M. C. Choi, H. S. Jeong, M. W. Kim, O. D. Lavrentovich, H.-T. Jung, “Confined self-assembly of toric focal conic domains (the effects of confined geometry on the feature size of toric focal conic domains),” Langmuir 25(3), 1685–1691 (2009).
[CrossRef] [PubMed]

Clerc, M. G.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[CrossRef] [PubMed]

Dai, H. T.

De Martini, F.

Delabre, U.

C. Loussert, U. Delabre, E. Brasselet, “Manipulating the Orbital Angular Momentum of Light at The Micron Scale with Nematic Disclinations in a Liquid Crystal Film,” Phys. Rev. Lett. 111(3), 037802 (2013).
[CrossRef] [PubMed]

Desyatnikov, A. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[CrossRef] [PubMed]

Doane, W. J.

F. Li, W. J. Doane, A. Jákli, “Magical Smectic Liquid Crystal Tube: Simple Illustration of Mechanical, Optical and Magnetic Properties of Smectic Liquid Crystals,” Jpn. J. Appl. Phys. 45(3A), 1714–1718 (2006).
[CrossRef]

Doerr, C. R.

Foo, G.

Foyart, G.

C. Meyer, L. Le Cunff, M. Belloul, G. Foyart, “Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling,” Materials 2(2), 499–513 (2009).
[CrossRef]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Ghai, D. P.

D. P. Ghai, S. Vyas, P. Senthilkumaran, R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282(14), 2692–2698 (2009).
[CrossRef]

Grier, D.

Hanot, Ch.

Izdebskaya, Y. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[CrossRef] [PubMed]

Jákli, A.

F. Li, W. J. Doane, A. Jákli, “Magical Smectic Liquid Crystal Tube: Simple Illustration of Mechanical, Optical and Magnetic Properties of Smectic Liquid Crystals,” Jpn. J. Appl. Phys. 45(3A), 1714–1718 (2006).
[CrossRef]

Jeong, H. S.

Y. H. Kim, D. K. Yoon, H. S. Jeong, O. D. Lavrentovich, H.-T. Jung, “Smectic liquid crystal defects for self-assembling of building blocks and their lithographic applications,” Adv. Funct. Mater. 21(4), 610–627 (2011).
[CrossRef]

Y. H. Kim, D. K. Yoon, M. C. Choi, H. S. Jeong, M. W. Kim, O. D. Lavrentovich, H.-T. Jung, “Confined self-assembly of toric focal conic domains (the effects of confined geometry on the feature size of toric focal conic domains),” Langmuir 25(3), 1685–1691 (2009).
[CrossRef] [PubMed]

Johnson-Morris, B.

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

Jung, H.-T.

Y. H. Kim, D. K. Yoon, H. S. Jeong, O. D. Lavrentovich, H.-T. Jung, “Smectic liquid crystal defects for self-assembling of building blocks and their lithographic applications,” Adv. Funct. Mater. 21(4), 610–627 (2011).
[CrossRef]

Y. H. Kim, D. K. Yoon, M. C. Choi, H. S. Jeong, M. W. Kim, O. D. Lavrentovich, H.-T. Jung, “Confined self-assembly of toric focal conic domains (the effects of confined geometry on the feature size of toric focal conic domains),” Langmuir 25(3), 1685–1691 (2009).
[CrossRef] [PubMed]

Juodkazis, S.

E. Brasselet, M. Malinauskas, A. Žukauskas, S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[CrossRef]

E. Brasselet, N. Murazawa, H. Misawa, S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[CrossRef] [PubMed]

Karimi, E.

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Kim, M. W.

Y. H. Kim, D. K. Yoon, M. C. Choi, H. S. Jeong, M. W. Kim, O. D. Lavrentovich, H.-T. Jung, “Confined self-assembly of toric focal conic domains (the effects of confined geometry on the feature size of toric focal conic domains),” Langmuir 25(3), 1685–1691 (2009).
[CrossRef] [PubMed]

Kim, Y. H.

Y. H. Kim, D. K. Yoon, H. S. Jeong, O. D. Lavrentovich, H.-T. Jung, “Smectic liquid crystal defects for self-assembling of building blocks and their lithographic applications,” Adv. Funct. Mater. 21(4), 610–627 (2011).
[CrossRef]

Y. H. Kim, D. K. Yoon, M. C. Choi, H. S. Jeong, M. W. Kim, O. D. Lavrentovich, H.-T. Jung, “Confined self-assembly of toric focal conic domains (the effects of confined geometry on the feature size of toric focal conic domains),” Langmuir 25(3), 1685–1691 (2009).
[CrossRef] [PubMed]

Kivshar, Y. S.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[CrossRef] [PubMed]

Krolikowski, W.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[CrossRef] [PubMed]

Ladavac, K.

Lavrentovich, O. D.

Y. H. Kim, D. K. Yoon, H. S. Jeong, O. D. Lavrentovich, H.-T. Jung, “Smectic liquid crystal defects for self-assembling of building blocks and their lithographic applications,” Adv. Funct. Mater. 21(4), 610–627 (2011).
[CrossRef]

Y. H. Kim, D. K. Yoon, M. C. Choi, H. S. Jeong, M. W. Kim, O. D. Lavrentovich, H.-T. Jung, “Confined self-assembly of toric focal conic domains (the effects of confined geometry on the feature size of toric focal conic domains),” Langmuir 25(3), 1685–1691 (2009).
[CrossRef] [PubMed]

D. Voloschenko, O. D. Lavrentovich, “Optical vortices generated by dislocations in a cholesteric liquid crystal,” Opt. Lett. 25(5), 317–319 (2000).
[CrossRef] [PubMed]

Le Cunff, L.

C. Meyer, L. Le Cunff, M. Belloul, G. Foyart, “Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling,” Materials 2(2), 499–513 (2009).
[CrossRef]

Li, F.

F. Li, W. J. Doane, A. Jákli, “Magical Smectic Liquid Crystal Tube: Simple Illustration of Mechanical, Optical and Magnetic Properties of Smectic Liquid Crystals,” Jpn. J. Appl. Phys. 45(3A), 1714–1718 (2006).
[CrossRef]

Liewer, K.

Liu, Y. J.

Loussert, C.

C. Loussert, U. Delabre, E. Brasselet, “Manipulating the Orbital Angular Momentum of Light at The Micron Scale with Nematic Disclinations in a Liquid Crystal Film,” Phys. Rev. Lett. 111(3), 037802 (2013).
[CrossRef] [PubMed]

E. Brasselet, C. Loussert, “Electrically controlled topological defects in liquid crystals as tunable spin-orbit encoders for photons,” Opt. Lett. 36(5), 719–721 (2011).
[CrossRef] [PubMed]

Luo, D.

Mair, A.

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Malinauskas, M.

E. Brasselet, M. Malinauskas, A. Žukauskas, S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[CrossRef]

Manzo, C.

L. Marrucci, C. Manzo, D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef] [PubMed]

Marrucci, L.

Mawet, D.

McEldowney, S.

Meyer, C.

C. Meyer, L. Le Cunff, M. Belloul, G. Foyart, “Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling,” Materials 2(2), 499–513 (2009).
[CrossRef]

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E. Brasselet, N. Murazawa, H. Misawa, S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[CrossRef] [PubMed]

Murazawa, N.

E. Brasselet, N. Murazawa, H. Misawa, S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[CrossRef] [PubMed]

Nagali, E.

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, S. Yu, “Integrated compact optical vortex beam emitters,” Science 338(6105), 363–366 (2012).
[CrossRef] [PubMed]

O’Brien, N.

Palacios, D. M.

Paparo, D.

L. Marrucci, C. Manzo, D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef] [PubMed]

Piccirillo, B.

Residori, S.

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[CrossRef] [PubMed]

Rode, A. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[CrossRef] [PubMed]

Royon, A.

E. Brasselet, A. Royon, L. Canioni, “Dense arrays of microscopic optical vortex generators from femtosecond direct laser writing of radial birefringence in glass,” Appl. Phys. Lett. 100(18), 181901 (2012).
[CrossRef]

Santamato, E.

Sciarrino, F.

Senthilkumaran, P.

D. P. Ghai, S. Vyas, P. Senthilkumaran, R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282(14), 2692–2698 (2009).
[CrossRef]

Serabyn, E.

Shemo, D.

Shvedov, V. G.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[CrossRef] [PubMed]

Sirohi, R. S.

D. P. Ghai, S. Vyas, P. Senthilkumaran, R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282(14), 2692–2698 (2009).
[CrossRef]

Sorel, M.

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

Strain, M. J.

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

Sun, X. W.

Swartzlander, G. A.

Tetienne, J.-P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Thompson, M. G.

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

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A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

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R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[CrossRef] [PubMed]

Voloschenko, D.

Vyas, S.

D. P. Ghai, S. Vyas, P. Senthilkumaran, R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282(14), 2692–2698 (2009).
[CrossRef]

Wang, J.

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

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Yang, B.

B. Yang, E. Brasselet, “Arbitrary vortex arrays realized from optical winding of frustrated chiral liquid crystals,” J. Opt. 15(4), 044021 (2013).
[CrossRef]

Yoon, D. K.

Y. H. Kim, D. K. Yoon, H. S. Jeong, O. D. Lavrentovich, H.-T. Jung, “Smectic liquid crystal defects for self-assembling of building blocks and their lithographic applications,” Adv. Funct. Mater. 21(4), 610–627 (2011).
[CrossRef]

Y. H. Kim, D. K. Yoon, M. C. Choi, H. S. Jeong, M. W. Kim, O. D. Lavrentovich, H.-T. Jung, “Confined self-assembly of toric focal conic domains (the effects of confined geometry on the feature size of toric focal conic domains),” Langmuir 25(3), 1685–1691 (2009).
[CrossRef] [PubMed]

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

Yu, S.

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

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Zhu, J.

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

Žukauskas, A.

E. Brasselet, M. Malinauskas, A. Žukauskas, S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[CrossRef]

Adv. Funct. Mater.

Y. H. Kim, D. K. Yoon, H. S. Jeong, O. D. Lavrentovich, H.-T. Jung, “Smectic liquid crystal defects for self-assembling of building blocks and their lithographic applications,” Adv. Funct. Mater. 21(4), 610–627 (2011).
[CrossRef]

Appl. Phys. Lett.

E. Brasselet, M. Malinauskas, A. Žukauskas, S. Juodkazis, “Photopolymerized microscopic vortex beam generators: Precise delivery of optical orbital angular momentum,” Appl. Phys. Lett. 97(21), 211108 (2010).
[CrossRef]

E. Brasselet, A. Royon, L. Canioni, “Dense arrays of microscopic optical vortex generators from femtosecond direct laser writing of radial birefringence in glass,” Appl. Phys. Lett. 100(18), 181901 (2012).
[CrossRef]

J. Opt.

B. Yang, E. Brasselet, “Arbitrary vortex arrays realized from optical winding of frustrated chiral liquid crystals,” J. Opt. 15(4), 044021 (2013).
[CrossRef]

Jpn. J. Appl. Phys.

F. Li, W. J. Doane, A. Jákli, “Magical Smectic Liquid Crystal Tube: Simple Illustration of Mechanical, Optical and Magnetic Properties of Smectic Liquid Crystals,” Jpn. J. Appl. Phys. 45(3A), 1714–1718 (2006).
[CrossRef]

Langmuir

Y. H. Kim, D. K. Yoon, M. C. Choi, H. S. Jeong, M. W. Kim, O. D. Lavrentovich, H.-T. Jung, “Confined self-assembly of toric focal conic domains (the effects of confined geometry on the feature size of toric focal conic domains),” Langmuir 25(3), 1685–1691 (2009).
[CrossRef] [PubMed]

Materials

C. Meyer, L. Le Cunff, M. Belloul, G. Foyart, “Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling,” Materials 2(2), 499–513 (2009).
[CrossRef]

Nature

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Opt. Commun.

D. P. Ghai, S. Vyas, P. Senthilkumaran, R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282(14), 2692–2698 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

E. Brasselet, “Spin-orbit optical cross-phase-modulation,” Phys. Rev. A 82(6), 063836 (2010).
[CrossRef]

Phys. Rev. Lett.

E. Brasselet, N. Murazawa, H. Misawa, S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[CrossRef] [PubMed]

C. Loussert, U. Delabre, E. Brasselet, “Manipulating the Orbital Angular Momentum of Light at The Micron Scale with Nematic Disclinations in a Liquid Crystal Film,” Phys. Rev. Lett. 111(3), 037802 (2013).
[CrossRef] [PubMed]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, Y. S. Kivshar, “Giant optical manipulation,” Phys. Rev. Lett. 105(11), 118103 (2010).
[CrossRef] [PubMed]

L. Marrucci, C. Manzo, D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef] [PubMed]

E. Brasselet, “Tunable optical vortex arrays from a single nematic topological defect,” Phys. Rev. Lett. 108(8), 087801 (2012).
[CrossRef] [PubMed]

R. Barboza, U. Bortolozzo, G. Assanto, E. Vidal-Henriquez, M. G. Clerc, S. Residori, “Harnessing optical vortex lattices in nematic liquid crystals,” Phys. Rev. Lett. 111(9), 093902 (2013).
[CrossRef] [PubMed]

Science

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[CrossRef] [PubMed]

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

Other

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[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Three-dimensional schematic view of the FCD. (b) Optical microscope image of the hexagonal FCD arrays between crossed linear polarizers (scale bar is 100 μm) and (c) magnified image (scale bar is 10 μm).

Fig. 2
Fig. 2

(a) The LC molecular director is represented by the polar angle θ and mapped in colors. (b) A schematically drawn cross-section of a FCD with structural parameters. R and H are fixed constants that correspond to the radius and height of the FCD, respectively. The thickness of the FCD, which depends on ρ, is defined as d. The black dot and the dashed line is drawn to derive Eq. (1).

Fig. 3
Fig. 3

(a) Numerically calculated intensity profiles between vertically crossed polarizers in different FCD size and input wavelength. (b) Experimental results of intensity profiles are in good agreement with simulation results. (c) Optical microscope images of doughnut intensity beam profiles with different input wavelength. Input light is unpolarized. (Scale bar is 2 μm.)

Fig. 4
Fig. 4

(a) The experimental setup. LHCP or RHCP gaussian reference beam interferes with the sample beam and projected onto the visible camera. Spiral fringes in the interference pattern is shown when the input beam is (b) the LHCP light and (c) the RHCP light, respectively.

Equations (6)

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θ(ρ,z)= π 2 tan 1 ( z Rρ )
ΔΦ(ρ)= 2π λ 0 d [ n eff (ρ,z) n ]dz
n eff (ρ,z)= n n [ n 2 cos 2 θ(ρ,z)+ n 2 sin 2 θ(ρ,z)] 1/2
J(ρ,φ)=isin ΔΦ(ρ) 2 [ cosmφ sinmφ sinmφ cosmφ ]+cos ΔΦ(ρ) 2 [ 1 0 0 1 ]
I out (ρ,φ)= | Ψ out (ρ,φ) | 2 = sin 2 (mφ) sin 2 ( ΔΦ(ρ) 2 )
Ψ out =J(ρ,φ)[ 1 i ]= 1 2 ( i e imφ sin ΔΦ(ρ) 2 [ 1 i ]+cos ΔΦ(ρ) 2 [ 1 i ] )

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