Abstract

Whispering gallery modes (WGMs) around the liquid crystal droplets are sensitive to the director orientation at the interface. An electric field was applied for changing the director orientation of a nematic liquid crystal droplet surrounded by polydimethylsiloxane (PDMS), which induced vertical director orientation at the interface. WGMs were shifted by varying the electric field intensity, and WGM shift-dependent director response was calculated. From this calculation we obtained the extrapolation length of 0.35 ± 0.02 μm. These results indicate that WGM sensitivity can be used for obtaining the surface properties of liquid crystals.

© 2015 Optical Society of America

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References

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2013 (2)

J. S. Park, J. H. Kim, E. S. Lee, J. H. Park, and S. Kawata, “CARS microscopic observation of a nematic liquid crystal droplet in an electric field,” New Phys. 63(4), 466472 (2013).

C.-L. Zou, F.-J. Shu, F.-W. Sun, Z.-J. Gong, Z.-F. Han, and G.-C. Guo, “Theory of free space coupling to high-Q whispering gallery modes,” Opt. Express 21(8), 9982–9995 (2013).
[Crossref] [PubMed]

2012 (1)

W. J. Zheng and M. H. Huang, “Use of polydimethylsiloxane thin film as vertical liquid crystal alignment layer,” Thin Solid Films 520(7), 2841–2845 (2012).
[Crossref]

2011 (1)

L. He, S. K. Ozdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6(7), 428–432 (2011).
[Crossref] [PubMed]

2009 (1)

M. Humar, M. Ravnik, S. Pajk, and I. Musevic, “Electrically tunable liquid crystal optical Microresonators,” Nat. Photonics 3(10), 595–600 (2009).
[Crossref]

2008 (2)

2007 (4)

P. Zijlstra, K. L. van der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90(16), 161101 (2007).
[Crossref]

D. Keng, S. R. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91(10), 103902 (2007).
[Crossref]

A. D. Falco and G. Assanto, “Tunable wavelength-selective add–drop in liquid crystals on a silicon microresonator,” Opt. Commun. 279(1), 210–213 (2007).
[Crossref]

J.-H. Kim and H. Choi, “Technique for azimuthal anchoring measurement of nematic liquid crystals using magnetic field induced deformation,” Appl. Phys. Lett. 90(10), 101908 (2007).
[Crossref]

2006 (1)

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering gallery modes I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).

2005 (1)

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

2004 (1)

B. Maune, M. Lončar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid-crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85(3), 360–362 (2004).
[Crossref]

2003 (1)

S. Faetti and G. C. Mutinati, “Light transmission from a twisted nematic liquid crystal: Accurate methods to measure the azimuthal anchoring energy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(2 Pt 2), 026601 (2003).
[Crossref] [PubMed]

2002 (1)

A. N. Oraevsky, “Whisphering-gallery waves,” Quantum Electron. 32(5), 377–400 (2002).
[Crossref]

1998 (1)

T. C. Lubensky, D. Pettey, N. Currier, and H. Stark, “Topological defects and interactions in nematic emulsions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(1), 610–625 (1998).
[Crossref]

1996 (1)

T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(8), 4434–4437 (1996).

1994 (1)

Y. Iimura, N. Kobayashi, and S. Kobayashi, “A new method for measuring the azimuthal anchoring energy of a nematic liquid crystal,” Jpn. J. Appl. Phys. 33(3B), L434–L436 (1994).

1992 (1)

V. G. Bodnar, O. D. Lavrentovich, and V. M. Pergamenshchik, “Threshold of structural hedgehog-ring transition in drops of a nematic in an alternating electric field,” Sov. Phys. JETP 74(1), 60–67 (1992).

1988 (1)

W. Doane, A. Golemme, J. L. West, J. B. Whitehead, and B.-G. Wu, “Polymer dispersed liquid crystals for display application,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 165(1), 511–532 (1988).

1985 (1)

H. Yokoyama and H. A. van Sprang, “A novel method for determining the anchoring energy function at a nematic liquid crystal-wall interface from director distortions at high fields,” J. Appl. Phys. 57(10), 4520–4526 (1985).
[Crossref]

1984 (1)

D. A. Balzarini, D. A. Dunmur, and P. Palffy-Muhoray, “High voltage birefringence measurements of elastic constants,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 102(2), 35–41 (1984).
[Crossref]

Akahane, T.

T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(8), 4434–4437 (1996).

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

D. Keng, S. R. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91(10), 103902 (2007).
[Crossref]

Assanto, G.

A. D. Falco and G. Assanto, “Tunable wavelength-selective add–drop in liquid crystals on a silicon microresonator,” Opt. Commun. 279(1), 210–213 (2007).
[Crossref]

Baehr-Jones, T.

B. Maune, M. Lončar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid-crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85(3), 360–362 (2004).
[Crossref]

Balzarini, D. A.

D. A. Balzarini, D. A. Dunmur, and P. Palffy-Muhoray, “High voltage birefringence measurements of elastic constants,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 102(2), 35–41 (1984).
[Crossref]

Bodnar, V. G.

V. G. Bodnar, O. D. Lavrentovich, and V. M. Pergamenshchik, “Threshold of structural hedgehog-ring transition in drops of a nematic in an alternating electric field,” Sov. Phys. JETP 74(1), 60–67 (1992).

Choi, H.

J.-H. Kim and H. Choi, “Technique for azimuthal anchoring measurement of nematic liquid crystals using magnetic field induced deformation,” Appl. Phys. Lett. 90(10), 101908 (2007).
[Crossref]

Currier, N.

T. C. Lubensky, D. Pettey, N. Currier, and H. Stark, “Topological defects and interactions in nematic emulsions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(1), 610–625 (1998).
[Crossref]

Doane, W.

W. Doane, A. Golemme, J. L. West, J. B. Whitehead, and B.-G. Wu, “Polymer dispersed liquid crystals for display application,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 165(1), 511–532 (1988).

Dunmur, D. A.

D. A. Balzarini, D. A. Dunmur, and P. Palffy-Muhoray, “High voltage birefringence measurements of elastic constants,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 102(2), 35–41 (1984).
[Crossref]

Faetti, S.

S. Faetti and G. C. Mutinati, “Light transmission from a twisted nematic liquid crystal: Accurate methods to measure the azimuthal anchoring energy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(2 Pt 2), 026601 (2003).
[Crossref] [PubMed]

Falco, A. D.

A. D. Falco and G. Assanto, “Tunable wavelength-selective add–drop in liquid crystals on a silicon microresonator,” Opt. Commun. 279(1), 210–213 (2007).
[Crossref]

Gauza, S.

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

Golemme, A.

W. Doane, A. Golemme, J. L. West, J. B. Whitehead, and B.-G. Wu, “Polymer dispersed liquid crystals for display application,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 165(1), 511–532 (1988).

Gong, Z.-J.

Guo, G.-C.

Han, Z.-F.

He, L.

L. He, S. K. Ozdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6(7), 428–432 (2011).
[Crossref] [PubMed]

Hochberg, M.

B. Maune, M. Lončar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid-crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85(3), 360–362 (2004).
[Crossref]

Huang, M. H.

W. J. Zheng and M. H. Huang, “Use of polydimethylsiloxane thin film as vertical liquid crystal alignment layer,” Thin Solid Films 520(7), 2841–2845 (2012).
[Crossref]

Humar, M.

M. Humar, M. Ravnik, S. Pajk, and I. Musevic, “Electrically tunable liquid crystal optical Microresonators,” Nat. Photonics 3(10), 595–600 (2009).
[Crossref]

Iimura, Y.

Y. Iimura, N. Kobayashi, and S. Kobayashi, “A new method for measuring the azimuthal anchoring energy of a nematic liquid crystal,” Jpn. J. Appl. Phys. 33(3B), L434–L436 (1994).

Ilchenko, V. S.

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering gallery modes I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).

Ioppolo, T.

Kaneko, H.

T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(8), 4434–4437 (1996).

Kawata, S.

J. S. Park, J. H. Kim, E. S. Lee, J. H. Park, and S. Kawata, “CARS microscopic observation of a nematic liquid crystal droplet in an electric field,” New Phys. 63(4), 466472 (2013).

Keng, D.

D. Keng, S. R. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91(10), 103902 (2007).
[Crossref]

Kim, J. H.

J. S. Park, J. H. Kim, E. S. Lee, J. H. Park, and S. Kawata, “CARS microscopic observation of a nematic liquid crystal droplet in an electric field,” New Phys. 63(4), 466472 (2013).

Kim, J.-H.

J.-H. Kim and H. Choi, “Technique for azimuthal anchoring measurement of nematic liquid crystals using magnetic field induced deformation,” Appl. Phys. Lett. 90(10), 101908 (2007).
[Crossref]

Kim, W.

L. He, S. K. Ozdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6(7), 428–432 (2011).
[Crossref] [PubMed]

Kimura, M.

T. Akahane, H. Kaneko, and M. Kimura, “Novel method of measuring surface torsional anchoring strength of nematic liquid crystals,” Jpn. J. Appl. Phys. 35(8), 4434–4437 (1996).

Kobayashi, N.

Y. Iimura, N. Kobayashi, and S. Kobayashi, “A new method for measuring the azimuthal anchoring energy of a nematic liquid crystal,” Jpn. J. Appl. Phys. 33(3B), L434–L436 (1994).

Kobayashi, S.

Y. Iimura, N. Kobayashi, and S. Kobayashi, “A new method for measuring the azimuthal anchoring energy of a nematic liquid crystal,” Jpn. J. Appl. Phys. 33(3B), L434–L436 (1994).

Kozhevnikov, M.

Lavrentovich, O. D.

V. G. Bodnar, O. D. Lavrentovich, and V. M. Pergamenshchik, “Threshold of structural hedgehog-ring transition in drops of a nematic in an alternating electric field,” Sov. Phys. JETP 74(1), 60–67 (1992).

Lee, E. S.

J. S. Park, J. H. Kim, E. S. Lee, J. H. Park, and S. Kawata, “CARS microscopic observation of a nematic liquid crystal droplet in an electric field,” New Phys. 63(4), 466472 (2013).

Li, J.

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

Loncar, M.

B. Maune, M. Lončar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid-crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85(3), 360–362 (2004).
[Crossref]

Lu, R.

J. Li, C. H. Wen, S. Gauza, R. Lu, and S. T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

Lubensky, T. C.

T. C. Lubensky, D. Pettey, N. Currier, and H. Stark, “Topological defects and interactions in nematic emulsions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(1), 610–625 (1998).
[Crossref]

Matsko, A. B.

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering gallery modes I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).

Maune, B.

B. Maune, M. Lončar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid-crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85(3), 360–362 (2004).
[Crossref]

McAnanama, S. R.

D. Keng, S. R. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91(10), 103902 (2007).
[Crossref]

Mosk, A. P.

P. Zijlstra, K. L. van der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90(16), 161101 (2007).
[Crossref]

Musevic, I.

M. Humar, M. Ravnik, S. Pajk, and I. Musevic, “Electrically tunable liquid crystal optical Microresonators,” Nat. Photonics 3(10), 595–600 (2009).
[Crossref]

Mutinati, G. C.

S. Faetti and G. C. Mutinati, “Light transmission from a twisted nematic liquid crystal: Accurate methods to measure the azimuthal anchoring energy,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(2 Pt 2), 026601 (2003).
[Crossref] [PubMed]

Oraevsky, A. N.

A. N. Oraevsky, “Whisphering-gallery waves,” Quantum Electron. 32(5), 377–400 (2002).
[Crossref]

Otügen, M. V.

Ozdemir, S. K.

L. He, S. K. Ozdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6(7), 428–432 (2011).
[Crossref] [PubMed]

Pajk, S.

M. Humar, M. Ravnik, S. Pajk, and I. Musevic, “Electrically tunable liquid crystal optical Microresonators,” Nat. Photonics 3(10), 595–600 (2009).
[Crossref]

Palffy-Muhoray, P.

D. A. Balzarini, D. A. Dunmur, and P. Palffy-Muhoray, “High voltage birefringence measurements of elastic constants,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 102(2), 35–41 (1984).
[Crossref]

Park, J. H.

J. S. Park, J. H. Kim, E. S. Lee, J. H. Park, and S. Kawata, “CARS microscopic observation of a nematic liquid crystal droplet in an electric field,” New Phys. 63(4), 466472 (2013).

Park, J. S.

J. S. Park, J. H. Kim, E. S. Lee, J. H. Park, and S. Kawata, “CARS microscopic observation of a nematic liquid crystal droplet in an electric field,” New Phys. 63(4), 466472 (2013).

Pergamenshchik, V. M.

V. G. Bodnar, O. D. Lavrentovich, and V. M. Pergamenshchik, “Threshold of structural hedgehog-ring transition in drops of a nematic in an alternating electric field,” Sov. Phys. JETP 74(1), 60–67 (1992).

Pettey, D.

T. C. Lubensky, D. Pettey, N. Currier, and H. Stark, “Topological defects and interactions in nematic emulsions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(1), 610–625 (1998).
[Crossref]

Psaltis, D.

B. Maune, M. Lončar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid-crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85(3), 360–362 (2004).
[Crossref]

Qiu, Y.

B. Maune, M. Lončar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid-crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85(3), 360–362 (2004).
[Crossref]

Ravnik, M.

M. Humar, M. Ravnik, S. Pajk, and I. Musevic, “Electrically tunable liquid crystal optical Microresonators,” Nat. Photonics 3(10), 595–600 (2009).
[Crossref]

Scherer, A.

B. Maune, M. Lončar, J. Witzens, M. Hochberg, T. Baehr-Jones, D. Psaltis, A. Scherer, and Y. Qiu, “Liquid-crystal electric tuning of a photonic crystal laser,” Appl. Phys. Lett. 85(3), 360–362 (2004).
[Crossref]

Sheverev, V.

Shu, F.-J.

Stark, H.

T. C. Lubensky, D. Pettey, N. Currier, and H. Stark, “Topological defects and interactions in nematic emulsions,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 57(1), 610–625 (1998).
[Crossref]

Stepaniuk, V.

Sun, F.-W.

Teraoka, I.

D. Keng, S. R. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91(10), 103902 (2007).
[Crossref]

van der Molen, K. L.

P. Zijlstra, K. L. van der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90(16), 161101 (2007).
[Crossref]

van Sprang, H. A.

H. Yokoyama and H. A. van Sprang, “A novel method for determining the anchoring energy function at a nematic liquid crystal-wall interface from director distortions at high fields,” J. Appl. Phys. 57(10), 4520–4526 (1985).
[Crossref]

Vollmer, F.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

Wen, C. H.

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Figures (4)

Fig. 1
Fig. 1 (a) The cell structure. LC droplets were located in the middle of the cell. Droplets were mixtures of nematic LC and fluorescent dye. Electric field was applied along the vertical direction. (b) The real image of a LC droplet used in the experiment. The radius of the droplet was about 10 μm.
Fig. 2
Fig. 2 (a) Schematic diagram of the side view of a droplet. It shows the director, circulating light with polarization and electric field applied on the droplet. (b) Schematic diagram of a part of the droplet showing the relative directions of the director and electric field. For easy understanding, we exaggerated the interface as the flat substrate. In the figures, (E) is the external electric field.
Fig. 3
Fig. 3 (a) WGM spectrum vs. the electric field. (b) WGM wavelength vs. the electric field intensity. The different point shapes correspond to the different modes.
Fig. 4
Fig. 4 Experimental and fitted WGM signals. All of the data points were fitted together. The points are the measured data and the lines are the numerical fits. The different point shapes correspond to the different modes.

Equations (4)

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K d 2 θ dy 2 + ΔεE 2 sin θ cos θ = 0
ξ 2 ( dy ) 2 = cos 2 θ cos 2 θ o
0 θ ex cos 2 θ cos 2 θ o = d ex ξ
= 2 πr 1 2 π 0 2 π n ( θ ex o ) o = 2 πrn ( θ ex ) with n ( θ ex ) = 1 2 π 0 n ( θ ex )

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