Abstract

We demonstrate polarization-selective microlensing and waveguiding of laser beams by birefringent profiles in bulk nematic fluids using numerical modelling. Specifically, we show that radial escaped nematic director profiles with negative birefringence focus and guide light with radial polarization, whereas the opposite – azimuthal – polarization passes through unaffected. A converging lens is realized in a nematic with negative birefringence, and a diverging lens in a positive birefringence material. Tuning of such single-liquid lenses by an external low-frequency electric field and by adjusting the profile and intensity of the beam itself is demonstrated, combining external control with intrinsic self-adaptive focusing. Escaped radial profiles of birefringence are shown to act as single-liquid waveguides with a single distinct eigenmode and low attenuation. Finally, this work is an approach towards creating liquid photonic elements for all-soft matter photonics.

© 2016 Optical Society of America

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References

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2016 (1)

I. Muševič, “Liquid-crystal micro-photonics,” Liq. Cryst. Rev. 4, 1 (2016).
[Crossref]

2015 (6)

N. Glazar, C. Culbreath, Y. Li, and H. Yokoyama, “Switchable liquid-crystal phase-shift mask for super-resolution photolithography based on Pancharatnam–Berry phase,” Appl. Phys. Express 8, 116501 (2015).
[Crossref]

F. Serra, M. A. Gharbi, Y. Luo, I. B. Liu, N. D. Bade, R. D. Kamien, S. Yang, and K. J. Stebe, “Curvature-driven, one-step assembly of reconfigurable smectic liquid crystal “compound eye” lenses,” Adv. Opt. Mater. 3, 1287 (2015).
[Crossref]

L. Cattaneo, M. Savoini, I. Muševič, A. Kimel, and T. Rasing, “Ultrafast all-optical response of a nematic liquid crystal,” Opt. Express 23, 14010 (2015).
[Crossref] [PubMed]

K. A. Rutkowska, K. Milenko, O. Chojnowska, R. Dabrowski, and T. R. Woliński, “Light propagation mechanism switching in a liquid crystal infiltrated microstructured polymer optical fibre,” Opto-Electron. Rev. 23, 34 (2015).
[Crossref]

A. Martinez and I. I. Smalyukh, “Light-driven dynamic Archimedes spirals and periodic oscillatory patterns of topological solitons in anisotropic soft matter,” Opt. Express 23, 4591 (2015).
[Crossref] [PubMed]

M. Nikkhou, M. Škarabot, S. Čopar, M. Ravnik, S. Žumer, and I. Muševič, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183 (2015).
[Crossref]

2014 (4)

M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclination lines,” Phys. Rev. E 90, 022503 (2014).
[Crossref]

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

M. Wahle and H.-S. Kitzerow, “Liquid crystal assisted optical fibres,” Opt. Express 22, 262 (2014).
[Crossref] [PubMed]

I. C. Khoo, “Nonlinear optics, active plasmonics and metamaterials with liquid crystals,” Prog. Quant. Electron. 38, 77 (2014).
[Crossref]

2013 (4)

H.-S. Chen and Y.-H. Lin, “An endoscopic system adopting a liquid crystal lens with an electrically tunable depth-of-field,” Opt. Express 21, 18079–18088 (2013).
[Crossref] [PubMed]

C. Loussert, U. Delabre, and 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, 037802 (2013).
[Crossref] [PubMed]

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

K. Peddireddy, V. S. R. Jampani, S. Thutupalli, S. Herminghaus, C. Bahr, and I. Muševič, “Lasing and waveguiding in smectic A liquid crystal optical fibers,” Opt. Express 21, 30233–30242 (2013).
[Crossref]

2012 (2)

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598 (2012).
[Crossref] [PubMed]

T. Porenta, M. Ravnik, and S. Žumer, “Complex field-stabilized nematic defect structures in Laguerre-Gaussian optical tweezers,” Soft Matter 8, 1865–1870 (2012).
[Crossref]

2011 (2)

B. F. Grewe, F. F. Voigt, M. van ’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens,” Biomed. Opt. Express 2, 2035 (2011).
[Crossref] [PubMed]

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12, 234 (2011).
[Crossref]

2010 (4)

2009 (6)

M. Ravnik and S. Žumer, “Landau-de Gennes modelling of nematic liquid crystal colloids,” Liq. Cryst. 36, 1201–1214 (2009).
[Crossref]

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

U. Tkalec, M. Ravnik, S. Žumer, and I. Muševič, “Vortexlike topological defects in nematic colloids: Chiral colloidal dimers and 2D crystals,” Phys. Rev. Lett. 103, 127801 (2009).
[Crossref] [PubMed]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[Crossref]

M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable LC optical microresonators,” Nat. Photonics 3, 595–600 (2009).
[Crossref]

I. Muševič, “Forces in nematic liquid crystals: from nanoscale interfacial forces to long-range forces in nematic colloids,” Liq. Crys. 36, 639–647 (2009).
[Crossref]

2008 (1)

2007 (1)

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6, 929 (2007).
[Crossref] [PubMed]

2006 (3)

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

O. Pishnyak, S. Sato, and O. D. Lavrentovich, “Electrically tunable lens based on a dual-frequency nematic liquid crystal,” Appl. Opt. 45, 4576 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

2005 (1)

2003 (4)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

M. Kasano, M. Ozaki, K. Yoshino, D. Ganzke, and W. Haase, “Electrically tunable waveguide laser based on ferroelectric liquid crystal,” Appl. Phys. Lett. 82, 4026 (2003).
[Crossref]

T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett. 82, 316–318 (2003).
[Crossref]

N. Chronis, G. Liu, K.-H. Jeong, and L. Lee, “Tunable liquid-filled microlens array integrated with microfluidic network,” Opt. Express 11, 2370 (2003).
[Crossref] [PubMed]

2002 (1)

N. Kamanina, S. Putilin, and D. Stasel’ko, “Nano-, pico- and femtosecond study of fullerene-doped polymer-dispersed liquid crystals: holographic recording and optical limiting effect,” Synthetic Met. 127, 129–133 (2002).
[Crossref]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

2000 (2)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

1991 (1)

H. J. Eichler and R. Macdonald, “Flow-alignment and inertial effects in picosecond laser-induced reorientation phenomena of nematic liquid crystals,” Phys. Rev. Lett. 67, 2666–2669 (1991).
[Crossref] [PubMed]

Alberucci, A.

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

Asquini, R.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598 (2012).
[Crossref] [PubMed]

Assanto, G.

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

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

G. Assanto, Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals, Wiley Series in Pure and Applied Optics (Wiley, 2012).
[Crossref]

Bade, N. D.

F. Serra, M. A. Gharbi, Y. Luo, I. B. Liu, N. D. Bade, R. D. Kamien, S. Yang, and K. J. Stebe, “Curvature-driven, one-step assembly of reconfigurable smectic liquid crystal “compound eye” lenses,” Adv. Opt. Mater. 3, 1287 (2015).
[Crossref]

Bahr, C.

Barboza, R.

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

Beccherelli, R.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598 (2012).
[Crossref] [PubMed]

Bortolozzo, U.

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

Brasselet, E.

C. Loussert, U. Delabre, and 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, 037802 (2013).
[Crossref] [PubMed]

E. Brasselet, “Singular optical reordering of liquid crystals using Gaussian beams,” J. Opt. 12, 124005 (2010).
[Crossref]

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

Buchnev, O.

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

Cancula, M.

M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclination lines,” Phys. Rev. E 90, 022503 (2014).
[Crossref]

Cattaneo, L.

Chen, H.-S.

Chen, M.-S.

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12, 234 (2011).
[Crossref]

Chojnowska, O.

K. A. Rutkowska, K. Milenko, O. Chojnowska, R. Dabrowski, and T. R. Woliński, “Light propagation mechanism switching in a liquid crystal infiltrated microstructured polymer optical fibre,” Opto-Electron. Rev. 23, 34 (2015).
[Crossref]

Chronis, N.

Clerc, M. G.

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

Coles, H.

H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics 4, 676–685 (2010).
[Crossref]

Coles, H. J.

Copar, S.

M. Nikkhou, M. Škarabot, S. Čopar, M. Ravnik, S. Žumer, and I. Muševič, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183 (2015).
[Crossref]

Crawford, G. P.

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6, 929 (2007).
[Crossref] [PubMed]

Culbreath, C.

N. Glazar, C. Culbreath, Y. Li, and H. Yokoyama, “Switchable liquid-crystal phase-shift mask for super-resolution photolithography based on Pancharatnam–Berry phase,” Appl. Phys. Express 8, 116501 (2015).
[Crossref]

d’Alessandro, A.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598 (2012).
[Crossref] [PubMed]

Dabrowski, R.

K. A. Rutkowska, K. Milenko, O. Chojnowska, R. Dabrowski, and T. R. Woliński, “Light propagation mechanism switching in a liquid crystal infiltrated microstructured polymer optical fibre,” Opto-Electron. Rev. 23, 34 (2015).
[Crossref]

de Gennes, P. G.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2 Edition (Oxford University Press, 1995).

Delabre, U.

C. Loussert, U. Delabre, and 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, 037802 (2013).
[Crossref] [PubMed]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

Eichler, H. J.

H. J. Eichler and R. Macdonald, “Flow-alignment and inertial effects in picosecond laser-induced reorientation phenomena of nematic liquid crystals,” Phys. Rev. Lett. 67, 2666–2669 (1991).
[Crossref] [PubMed]

Fuh, A. Y.-G.

Ganzke, D.

M. Kasano, M. Ozaki, K. Yoshino, D. Ganzke, and W. Haase, “Electrically tunable waveguide laser based on ferroelectric liquid crystal,” Appl. Phys. Lett. 82, 4026 (2003).
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Haase, W.

M. Kasano, M. Ozaki, K. Yoshino, D. Ganzke, and W. Haase, “Electrically tunable waveguide laser based on ferroelectric liquid crystal,” Appl. Phys. Lett. 82, 4026 (2003).
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M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable LC optical microresonators,” Nat. Photonics 3, 595–600 (2009).
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F. Serra, M. A. Gharbi, Y. Luo, I. B. Liu, N. D. Bade, R. D. Kamien, S. Yang, and K. J. Stebe, “Curvature-driven, one-step assembly of reconfigurable smectic liquid crystal “compound eye” lenses,” Adv. Opt. Mater. 3, 1287 (2015).
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R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
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Ravnik, M.

M. Nikkhou, M. Škarabot, S. Čopar, M. Ravnik, S. Žumer, and I. Muševič, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183 (2015).
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M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable LC optical microresonators,” Nat. Photonics 3, 595–600 (2009).
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K. A. Rutkowska, K. Milenko, O. Chojnowska, R. Dabrowski, and T. R. Woliński, “Light propagation mechanism switching in a liquid crystal infiltrated microstructured polymer optical fibre,” Opto-Electron. Rev. 23, 34 (2015).
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J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
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F. Serra, M. A. Gharbi, Y. Luo, I. B. Liu, N. D. Bade, R. D. Kamien, S. Yang, and K. J. Stebe, “Curvature-driven, one-step assembly of reconfigurable smectic liquid crystal “compound eye” lenses,” Adv. Opt. Mater. 3, 1287 (2015).
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R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
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Škarabot, M.

M. Nikkhou, M. Škarabot, S. Čopar, M. Ravnik, S. Žumer, and I. Muševič, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183 (2015).
[Crossref]

Smalyukh, I. I.

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Stasel’ko, D.

N. Kamanina, S. Putilin, and D. Stasel’ko, “Nano-, pico- and femtosecond study of fullerene-doped polymer-dispersed liquid crystals: holographic recording and optical limiting effect,” Synthetic Met. 127, 129–133 (2002).
[Crossref]

Stebe, K. J.

F. Serra, M. A. Gharbi, Y. Luo, I. B. Liu, N. D. Bade, R. D. Kamien, S. Yang, and K. J. Stebe, “Curvature-driven, one-step assembly of reconfigurable smectic liquid crystal “compound eye” lenses,” Adv. Opt. Mater. 3, 1287 (2015).
[Crossref]

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U. Tkalec, M. Ravnik, S. Žumer, and I. Muševič, “Vortexlike topological defects in nematic colloids: Chiral colloidal dimers and 2D crystals,” Phys. Rev. Lett. 103, 127801 (2009).
[Crossref] [PubMed]

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Vidal-Henriquez, E.

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

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D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
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K. A. Rutkowska, K. Milenko, O. Chojnowska, R. Dabrowski, and T. R. Woliński, “Light propagation mechanism switching in a liquid crystal infiltrated microstructured polymer optical fibre,” Opto-Electron. Rev. 23, 34 (2015).
[Crossref]

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S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6, 929 (2007).
[Crossref] [PubMed]

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H. Ren and S.-T. Wu, Introduction to Adaptive Lenses (Wiley, 2012).
[Crossref]

Yang, S.

F. Serra, M. A. Gharbi, Y. Luo, I. B. Liu, N. D. Bade, R. D. Kamien, S. Yang, and K. J. Stebe, “Curvature-driven, one-step assembly of reconfigurable smectic liquid crystal “compound eye” lenses,” Adv. Opt. Mater. 3, 1287 (2015).
[Crossref]

T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett. 82, 316–318 (2003).
[Crossref]

Yokoyama, H.

N. Glazar, C. Culbreath, Y. Li, and H. Yokoyama, “Switchable liquid-crystal phase-shift mask for super-resolution photolithography based on Pancharatnam–Berry phase,” Appl. Phys. Express 8, 116501 (2015).
[Crossref]

Yoshino, K.

M. Kasano, M. Ozaki, K. Yoshino, D. Ganzke, and W. Haase, “Electrically tunable waveguide laser based on ferroelectric liquid crystal,” Appl. Phys. Lett. 82, 4026 (2003).
[Crossref]

Zhan, Q.

Zografopoulos, D. C.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598 (2012).
[Crossref] [PubMed]

Žumer, S.

M. Nikkhou, M. Škarabot, S. Čopar, M. Ravnik, S. Žumer, and I. Muševič, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183 (2015).
[Crossref]

M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclination lines,” Phys. Rev. E 90, 022503 (2014).
[Crossref]

T. Porenta, M. Ravnik, and S. Žumer, “Complex field-stabilized nematic defect structures in Laguerre-Gaussian optical tweezers,” Soft Matter 8, 1865–1870 (2012).
[Crossref]

U. Tkalec, M. Ravnik, S. Žumer, and I. Muševič, “Vortexlike topological defects in nematic colloids: Chiral colloidal dimers and 2D crystals,” Phys. Rev. Lett. 103, 127801 (2009).
[Crossref] [PubMed]

M. Ravnik and S. Žumer, “Landau-de Gennes modelling of nematic liquid crystal colloids,” Liq. Cryst. 36, 1201–1214 (2009).
[Crossref]

Adv. Opt. Mater. (1)

F. Serra, M. A. Gharbi, Y. Luo, I. B. Liu, N. D. Bade, R. D. Kamien, S. Yang, and K. J. Stebe, “Curvature-driven, one-step assembly of reconfigurable smectic liquid crystal “compound eye” lenses,” Adv. Opt. Mater. 3, 1287 (2015).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. Express (1)

N. Glazar, C. Culbreath, Y. Li, and H. Yokoyama, “Switchable liquid-crystal phase-shift mask for super-resolution photolithography based on Pancharatnam–Berry phase,” Appl. Phys. Express 8, 116501 (2015).
[Crossref]

Appl. Phys. Lett. (2)

M. Kasano, M. Ozaki, K. Yoshino, D. Ganzke, and W. Haase, “Electrically tunable waveguide laser based on ferroelectric liquid crystal,” Appl. Phys. Lett. 82, 4026 (2003).
[Crossref]

T. Krupenkin, S. Yang, and P. Mach, “Tunable liquid microlens,” Appl. Phys. Lett. 82, 316–318 (2003).
[Crossref]

Biomed. Opt. Express (1)

J. Opt. (1)

E. Brasselet, “Singular optical reordering of liquid crystals using Gaussian beams,” J. Opt. 12, 124005 (2010).
[Crossref]

Lab. Chip. (1)

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. d’Alessandro, and R. Beccherelli, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598 (2012).
[Crossref] [PubMed]

Liq. Crys. (1)

I. Muševič, “Forces in nematic liquid crystals: from nanoscale interfacial forces to long-range forces in nematic colloids,” Liq. Crys. 36, 639–647 (2009).
[Crossref]

Liq. Cryst. (1)

M. Ravnik and S. Žumer, “Landau-de Gennes modelling of nematic liquid crystal colloids,” Liq. Cryst. 36, 1201–1214 (2009).
[Crossref]

Liq. Cryst. Rev. (1)

I. Muševič, “Liquid-crystal micro-photonics,” Liq. Cryst. Rev. 4, 1 (2016).
[Crossref]

Nat. Commun. (1)

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

S. J. Woltman, G. D. Jay, and G. P. Crawford, “Liquid-crystal materials find a new order in biomedical applications,” Nat. Mater. 6, 929 (2007).
[Crossref] [PubMed]

Nat. Photonics (2)

H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics 4, 676–685 (2010).
[Crossref]

M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable LC optical microresonators,” Nat. Photonics 3, 595–600 (2009).
[Crossref]

Nat. Phys. (1)

M. Nikkhou, M. Škarabot, S. Čopar, M. Ravnik, S. Žumer, and I. Muševič, “Light-controlled topological charge in a nematic liquid crystal,” Nat. Phys. 11, 183 (2015).
[Crossref]

Opt. Express (8)

Opt. Lett. (2)

Opto-Electron. Rev. (1)

K. A. Rutkowska, K. Milenko, O. Chojnowska, R. Dabrowski, and T. R. Woliński, “Light propagation mechanism switching in a liquid crystal infiltrated microstructured polymer optical fibre,” Opto-Electron. Rev. 23, 34 (2015).
[Crossref]

Phys. Rev. E (1)

M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclination lines,” Phys. Rev. E 90, 022503 (2014).
[Crossref]

Phys. Rev. Lett. (9)

U. Tkalec, M. Ravnik, S. Žumer, and I. Muševič, “Vortexlike topological defects in nematic colloids: Chiral colloidal dimers and 2D crystals,” Phys. Rev. Lett. 103, 127801 (2009).
[Crossref] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

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

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Prog. Quant. Electron. (1)

I. C. Khoo, “Nonlinear optics, active plasmonics and metamaterials with liquid crystals,” Prog. Quant. Electron. 38, 77 (2014).
[Crossref]

Science (2)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
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Soft Matter (1)

T. Porenta, M. Ravnik, and S. Žumer, “Complex field-stabilized nematic defect structures in Laguerre-Gaussian optical tweezers,” Soft Matter 8, 1865–1870 (2012).
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Synthetic Met. (1)

N. Kamanina, S. Putilin, and D. Stasel’ko, “Nano-, pico- and femtosecond study of fullerene-doped polymer-dispersed liquid crystals: holographic recording and optical limiting effect,” Synthetic Met. 127, 129–133 (2002).
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Trans. Electr. Electron. Mater. (1)

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A review of electrically tunable focusing liquid crystal lenses,” Trans. Electr. Electron. Mater. 12, 234 (2011).
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Figures (6)

Fig. 1
Fig. 1

Radial escaped nematic line as a photonic element. (A) An escaped profile of the nematic liquid crystal. Away from the axis, molecules are perpendicular to the escaped line, and continuously transition to a parallel orientation at the axis. (B) Radially polarized light (polarization illustrated by red arrows) propagating through a short segment of an escaped director profile observed a radially-dependent refractive index, resulting in focusing and lensing, while the polarization profile is preserved. The optical electric field Eopt, external electric field Eext, and the chosen coordinate system are shown with arrows.

Fig. 2
Fig. 2

Numerical algorithm flowchart.

Fig. 3
Fig. 3

Lensing of high-intensity beams on an escaped disclination line in the presence of an external electric field. Shades of gray show the local light intensity with the scale given by colorbar under each image, red lines show the local director profile inside the liquid crystal lens, while green dashed lines mark the lens boundary. (A–I) Competition between elastic forces, optical fields of the beam with power P and an external electric field Eext produces a rich variety of lensing patterns. Interesting director structures form in medium-strength external fields (Eext ∼ 0.5 V/μm), where beam power P has a strong effect on the director profile and lensing. As the external field strength is increased, the structure transforms into a completely radial profile with a defect line at the axis. In all cases, light intensity is almost completely axially symmetric, as is the director angle of escape and with it the observed index of refraction.

Fig. 4
Fig. 4

(A) Numerical aperture of the lens as a function of beam power in the absence of an external electric field. We see that the numerical aperture is highest for weak beams, then quickly drops as power is increased, and finally stabilizes at a lower value for high beam powers. The inset shows the director angle profiles at different beam powers. Strong beams reduce the director angle, resulting in a wide area where the director is parallel to the escaped line axis. (B) Director angle of escape at different external field strengths and a strong (P = 800 mW) light beam. When the external field is weak, below 0.5 V/μm, the director is mostly in the z direction. As the external field is increased, it gradually changes and the director becomes aligned in the xy plane. (C) The numerical aperture of the lens at different external field strengths and beam powers. The numerical aperture is highest at a distinct external field strength Eext, which depends on the beam power. Notably, changing the beam power shifts the position of this peak, demonstrating a possibility of tuning such lenses by varying either the beam power or the external field.

Fig. 5
Fig. 5

Use of long escaped director profiles as waveguides. (A) Intensity profiles of incident beams of different widths show that the beams condense to the single eigenmode, which then remains stable for long distances. (B) Total beam power as a function of position inside the waveguide shows large initial losses, but confirms that the eigenmode is stable and the waveguide does not leak at larger distances. The magnitude of the losses depends on the incident beam width w0.

Fig. 6
Fig. 6

(A) Cross-sections of the local light intensity show that the eigenmode is independent of the incident beam width w0. A Laguerre-Gaussian profile is fitted to the mode, which gives a beam width of w0 = 375 nm. Comparison to the Laguerre-Gaussian profile and the analytically obtained solution shows a discrepancy at the center, where simulation show nonzero intensity due to a presence of longitudinal polarization, while the analytic approaches assume zero intensity. (B) Spatial profile of the refractive index observed by the incident radially polarized beam and the stable waveguide mode. Discrepancies arise due to the presence of the longitudinal component at the center, as well as far away from the axis where the light intensity is very low.

Equations (3)

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ε E t = × H , μ H t = × E .
F = V ( 1 2 L Q i j x i Q i j x i elasticity 1 3 ε 0 ε a mol , opt E i opt Q i j E j opt coupling with light 1 3 ε 0 ε a mol , ext E i ext Q i j E j ext coupling with external field ) d V + + V ( 1 2 A ( T ) Tr Q 2 + 1 3 B Tr Q 3 + 1 4 C ( Tr Q 2 ) 2 nematic isotropic transition ) d V + V ( 1 2 W ( Q Q 0 ) 2 surface anchoring ) d S
[ ρ 2 + 1 ρ 2 + B ( 1 ρ 2 1 + ρ 2 ) 2 ] ψ ( ρ ) = β ψ ( ρ )

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