Abstract

We demonstrate that birefringent profiles of double-twist cylinders, found in some chiral nematic systems such as blue phases, can perform as polarization-selective microlenses and waveguides in the regime of negative birefringence. Specifically, we solve Maxwell’s equation using the finite-difference time-domain (FDTD) method, to simulate light propagation through double-twist cylinder birefringent structures. We show that, in case of negative material birefringence, azimuthally polarized beams experience lensing which can further be extended to waveguiding in double-twist cylinders. Lensing and waveguiding efficiency are shown to be strongly dependent on the ratio between the width of the double-twist cylinder profile and the beam width. We further characterize waveguiding in terms of losses, which are investigated in case of straight as well as curved double-twist cylinders. More generally, this work is a contribution to the design and development of (soft) birefringent profiles for optical and photonic applications.

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

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2017 (6)

Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Crys. Rev.,  5, 111–143 (2017).
[Crossref]

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
[Crossref] [PubMed]

P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16, 426 (2017).
[Crossref]

C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017).
[Crossref]

2016 (5)

D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016).
[Crossref]

M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116253903 (2016).
[Crossref] [PubMed]

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

2015 (2)

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. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

2014 (2)

M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).

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

2013 (2)

F. Fan, A. K. Srivastava, T. Du, M. C. Tseng, V. Chigrinov, and H. S. Kwok, “Low voltage tunable liquid crystal lens,” Opt. Lett. 38, 4116 (2013).
[Crossref] [PubMed]

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

2012 (1)

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
[Crossref] [PubMed]

2011 (2)

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011).
[Crossref]

J. Fukuda and S. Žumer, ”Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal,” Nat. Commun. 2, 246 (2011).
[Crossref] [PubMed]

2010 (5)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[Crossref]

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

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

S. Ko, C. Ting, A. Fuh, and T. Lin, “Polarization converters based on axially symmetric twisted nematic liquid crystal,” Opt. Express 18, 3601–3607 (2010).
[Crossref] [PubMed]

C. G. Avendaño and J. A. Reyes, “Nonlinear TM modes in cylindrical liquid crystal waveguide,” Opt. Commun. 283, 5016 (2010).
[Crossref]

2009 (2)

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

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

2007 (1)

G. R. Werner and J. R. Cary, “A stable FDTD algorithm for non-diagonal, anisotropic dielectrics,” J. Comp. Phys. 10, 1085 (2007).
[Crossref]

2005 (1)

2004 (1)

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
[Crossref]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phy. Rev. Lett. 91, 23 (2003).
[Crossref]

2002 (1)

N. Kamanina, S. Putilin, and D. Staselko, “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]

2000 (2)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929 (2000).
[Crossref]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87 (2000).
[Crossref] [PubMed]

1999 (1)

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 13 (1999).
[Crossref]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
[Crossref]

1994 (2)

H. Lin and P. Palffy-Muhoray, “Propagation of TM modes in a nonlinear liquid-crystal waveguide,” Opt. Lett. 19, 436 (1994).
[Crossref] [PubMed]

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Phys.,  114, 185–200 (1994).
[Crossref]

1992 (1)

1991 (2)

S. H. Chen and T. J. Chen, “Observation of mode selection in a radially anisotropic cylindrical waveguide with liquid-crystal cladding,” Appl. Phys. Lett. 64, 1893 (1991).
[Crossref]

H. Lin, P. Palffy-Muhoray, and M. A. Lee, “Liquid crystalline cores for optical fibers,” Mol. Cryst. Liq. Cryst. 204, 189 (1991).
[Crossref]

1989 (1)

D. C. Wright and N. D. Mermin, „ ”Crystalline liquids: the blue phases,” Rev. Mod. Phys. 61, 385–432 (1989).
[Crossref]

1976 (1)

1966 (1)

K.S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propag. 14, 302 (1966).
[Crossref]

Ackerman, P. J.

P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16, 426 (2017).
[Crossref]

Alapati, P. R.

D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016).
[Crossref]

Apostolopoulos, V.

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

April, A.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Asquini, R.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
[Crossref] [PubMed]

Assanto, G.

U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
[Crossref] [PubMed]

Avendaño, C. G.

C. G. Avendaño and J. A. Reyes, “Nonlinear TM modes in cylindrical liquid crystal waveguide,” Opt. Commun. 283, 5016 (2010).
[Crossref]

Bahr, C.

H. S. Kitzerow and C. Bahr, Chirality In Liquid Crystals (Springer Verlag, 2001).
[Crossref]

Beccherel, R.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
[Crossref] [PubMed]

Beeckman, J.

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011).
[Crossref]

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Phys.,  114, 185–200 (1994).
[Crossref]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Bhattacharjee, A.

D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016).
[Crossref]

Bhattacharjee, D.

D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016).
[Crossref]

Booth, M. J.

C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

Bortolozzo, U.

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

Brabec, T.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Brown, T. G.

Cancula, M.

M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
[Crossref]

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

Cary, J. R.

G. R. Werner and J. R. Cary, “A stable FDTD algorithm for non-diagonal, anisotropic dielectrics,” J. Comp. Phys. 10, 1085 (2007).
[Crossref]

Cattaneo, L.

Chang, R.

K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

Chen, C. C.

M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).

Chen, M.

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Ting, C.

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J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011).
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S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
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Varanytsia, A.

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
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Varin, C.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
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G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
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Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Crys. Rev.,  5, 111–143 (2017).
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A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929 (2000).
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P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
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G. R. Werner and J. R. Cary, “A stable FDTD algorithm for non-diagonal, anisotropic dielectrics,” J. Comp. Phys. 10, 1085 (2007).
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C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
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S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
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M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
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M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclinations lines,” Phy. Rev. E 90, 022503 (2014).
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S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
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M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).

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D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
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Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Crys. Rev.,  5, 111–143 (2017).
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J. Fukuda and S. Žumer, ”Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal,” Nat. Commun. 2, 246 (2011).
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K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
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H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics 4, 676–685 (2010).
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M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable liquid crystal optical microresonators,” Nat. Photonics 3, 595–600 (2009).
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A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017).
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C. G. Avendaño and J. A. Reyes, “Nonlinear TM modes in cylindrical liquid crystal waveguide,” Opt. Commun. 283, 5016 (2010).
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G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
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Opt. Eng. (1)

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011).
[Crossref]

Opt. Exp. (1)

M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Phy. Rev. E (1)

M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclinations lines,” Phy. Rev. E 90, 022503 (2014).
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R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phy. Rev. Lett. 91, 23 (2003).
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J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116253903 (2016).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
[Crossref]

Proc. Nat. Ac. Sci. USA (1)

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
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S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

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D. C. Wright and N. D. Mermin, „ ”Crystalline liquids: the blue phases,” Rev. Mod. Phys. 61, 385–432 (1989).
[Crossref]

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A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929 (2000).
[Crossref]

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C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

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U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
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N. Kamanina, S. Putilin, and D. Staselko, “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]

Other (5)

H. Ren and S. T. Wu, Introduction to adaptive lenses, (Wiley, 2012).
[Crossref]

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, (Clarendon Press, Oxford, 1998).

H. S. Kitzerow and C. Bahr, Chirality In Liquid Crystals (Springer Verlag, 2001).
[Crossref]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd ed. (Artech House, London2005).

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Figures (6)

Fig. 1
Fig. 1 Double-twist cylinder as a photonic element. Azimuthally polarized light (electric field Eopt direction is illustrated with red arrows) propagating along the of double-twist birefringent profile (optical axis is represented by colored ellipsoids) observes radially dependent refractive index which can result in lensing and waveguiding.
Fig. 2
Fig. 2 Lensing on short segments of a double-twist nematic profile for different input beam widths. (A–D) Plots of light intensity at the central plane of the beam. Lensing of azimuthally polarized input beams with different input beam waists on identical double-twist profiles results in lensing with different numerical apertures. (E) Beam width profiles along the beam path for different input beam widths.
Fig. 3
Fig. 3 Lensing in birefringent double-twist cylinders for differently polarized input beams. In case of azimuthally polarized beam (A) lensing occurs, since the light experiences radially dependent refractive index. In case of radially polarized beam (B) the refractive index is uniform and no lensing occurs. In the intermediate case of radially-azimuthally polarized beam (C) only only partial lensing occurs. Double-twist profiles of the optical axis variation are shown in red, with green dashed line indicating the end of the profile region.
Fig. 4
Fig. 4 Longitudinal component of the magnetic field of azimuthally polarized beam. Lensing of azimuthally polarized beams results in occurence of strong longitudinal magnetic field component in the center of the beam. (A) Color plots of magnetic field component Hz in the cross section of the beam in three different positions along the beam path, z1, z2, z3 (marked with white dashed lines on the lower plot) are shown, indicating that Hz is greatest at the centre of the beam cross-section at the beam waist. (B) Square of absolute amplitudes of longitudinal components Hz and Ez in the beam centre, marked with yellow line on the beam yz cross-section plot.
Fig. 5
Fig. 5 Waveguiding in a double-twist cylinder birefringent profile. (A) Azimuthally polarized beams propagating inside the double twist cylinders for different input beam widths 2w0. (B) Transversal components of the electric field E of the guided beam at three different representative positions along the beam path, denoted by green arrows. They indicate partial transformation of the initial azimuthal polarization to a polarization that is partially radial. (C) Beam power in units of initial beam power P0 along the double twist cylinder for different input beam widths 2w0. (D, E) Components of the Poynting vector averaged along the beam. Note the emergence of the radially twisted component of S in the transversal plane.
Fig. 6
Fig. 6 Waveguiding in curved birefringent double-twist profiles. (A) Light intensity of the azimuthally polarized beam inside a double-twist cylinder nematic structure curved with a radius of curvature Rc. For smaller radii of curvature substantial bending losses occur. (B) Ratio between the input and output beam power after travelling a fixed length of 60λ inside a curved nematic profile as a function of the radius of curvature Rc.

Equations (4)

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

ε̳ ε 0 E t = × H , μ μ 0 H t = × E ,
ε i j = ε ¯ δ i j + 2 3 ε a mol Q i j ,
n ( r , ϕ , z ) = e ^ z cos ( k 0 r ) e ^ ϕ sin ( k 0 r ) ,
E z DTC = ( ε̳ DTC 1 ( r ) ε̳ iso E iso ) e z 0 ,

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