Abstract

We propose and demonstrate an all-solid-state tunable binary phase Fresnel lens with electrically controllable focal length. The lens is composed of a binary phase Fresnel zone plate, a circular acrylic frame, and a dielectric elastomer (DE) actuator which is made of a thin DE layer and two compliant electrodes using silver nanowires. Under electric potential, the actuator produces in-plane deformation in a radial direction that can compress the Fresnel zones. The electrically-induced deformation compresses the Fresnel zones to be contracted as high as 9.1% and changes the focal length, getting shorter from 20.0 cm to 14.5 cm. The measured change in the focal length of the fabricated lens is consistent with the result estimated from numerical simulation.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  5. S. Yun, S. Park, B. Park, S. Nam, S. K. Park, and K. Kyung, “A thin film active-lens with translational control for dynamically programmable optical zoom,” Appl. Phys. Lett. 107(8), 081907 (2015).
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2016 (2)

X. Li, L. Wei, R. H. Poelma, S. Vollebregt, J. Wei, H. P. Urbach, P. M. Sarro, and G. Q. Zhang, “Stretchable binary Fresnel lens for focus tuning,” Sci. Rep. 6(1), 25348 (2016).
[Crossref] [PubMed]

K. Philipp, A. Smolarski, N. Koukourakis, A. Fischer, M. Stürmer, U. Wallrabe, and J. W. Czarske, “Volumetric HiLo microscopy employing an electrically tunable lens,” Opt. Express 24(13), 15029–15041 (2016).
[Crossref] [PubMed]

2015 (2)

S. Yun, S. Park, B. Park, S. Nam, S. K. Park, and K. Kyung, “A thin film active-lens with translational control for dynamically programmable optical zoom,” Appl. Phys. Lett. 107(8), 081907 (2015).
[Crossref]

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4(1), 6378 (2015).
[Crossref] [PubMed]

2012 (1)

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100(23), 231105 (2012).
[Crossref] [PubMed]

2011 (1)

B. Li, H. Chen, J. Qiang, S. Hu, Z. Zhu, and Y. Wang, “Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation,” J. Phys. D Appl. Phys. 44(15), 155301 (2011).
[Crossref]

2010 (2)

2009 (1)

S. Rosset, M. Niklaus, P. Dubois, and H. R. Shea, “Large-stroke dielectric elastomer actuators with ion-implanted electrodes,” J. Microelectromech. Syst. 18(6), 1300–1308 (2009).
[Crossref]

2007 (1)

K. Jung, J. C. Koo, J.-D. Nam, Y. K. Lee, and H. R. Choi, “Artificial annelid robot driven by soft actuators,” Bioinspir. Biomim. 2(2), S42–S49 (2007).
[Crossref] [PubMed]

2005 (1)

C. A. Lopez, C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87(13), 134102 (2005).
[Crossref]

2003 (1)

2001 (1)

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun. 188(5-6), 291–299 (2001).
[Crossref]

2000 (2)

B. Grzybowski, D. Qin, R. Haag, and G. M. Whitesides, “Elastomeric optical elements with deformable surface topographies: applications to force measurements, tunable light transmission and light focusing,” Sens. Actuators A Phys. 86(1-2), 81–85 (2000).
[Crossref]

R. Pelrine, R. Kornbluh, Q. Pei, and J. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287(5454), 836–839 (2000).
[Crossref] [PubMed]

1991 (1)

Bhattacharya, S.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun. 188(5-6), 291–299 (2001).
[Crossref]

Carreel, B.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4(1), 6378 (2015).
[Crossref] [PubMed]

Chen, H.

B. Li, H. Chen, J. Qiang, S. Hu, Z. Zhu, and Y. Wang, “Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation,” J. Phys. D Appl. Phys. 44(15), 155301 (2011).
[Crossref]

Choi, H. R.

K. Jung, J. C. Koo, J.-D. Nam, Y. K. Lee, and H. R. Choi, “Artificial annelid robot driven by soft actuators,” Bioinspir. Biomim. 2(2), S42–S49 (2007).
[Crossref] [PubMed]

Chronis, N.

Czarske, J. W.

Dias, D.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun. 188(5-6), 291–299 (2001).
[Crossref]

Dodge, M. R.

Dubois, P.

S. Rosset, M. Niklaus, P. Dubois, and H. R. Shea, “Large-stroke dielectric elastomer actuators with ion-implanted electrodes,” J. Microelectromech. Syst. 18(6), 1300–1308 (2009).
[Crossref]

Fischer, A.

Gilchrist, H.

Glockner, R.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun. 188(5-6), 291–299 (2001).
[Crossref]

Grzybowski, B.

B. Grzybowski, D. Qin, R. Haag, and G. M. Whitesides, “Elastomeric optical elements with deformable surface topographies: applications to force measurements, tunable light transmission and light focusing,” Sens. Actuators A Phys. 86(1-2), 81–85 (2000).
[Crossref]

Haag, R.

B. Grzybowski, D. Qin, R. Haag, and G. M. Whitesides, “Elastomeric optical elements with deformable surface topographies: applications to force measurements, tunable light transmission and light focusing,” Sens. Actuators A Phys. 86(1-2), 81–85 (2000).
[Crossref]

Habiby, S. F.

Hain, M.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun. 188(5-6), 291–299 (2001).
[Crossref]

Hirsa, A. H.

C. A. Lopez, C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87(13), 134102 (2005).
[Crossref]

Hu, S.

B. Li, H. Chen, J. Qiang, S. Hu, Z. Zhu, and Y. Wang, “Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation,” J. Phys. D Appl. Phys. 44(15), 155301 (2011).
[Crossref]

Hubbard, W. M.

Jeong, K. H.

Jiang, H.

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100(23), 231105 (2012).
[Crossref] [PubMed]

Joseph, J.

R. Pelrine, R. Kornbluh, Q. Pei, and J. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287(5454), 836–839 (2000).
[Crossref] [PubMed]

Jung, K.

K. Jung, J. C. Koo, J.-D. Nam, Y. K. Lee, and H. R. Choi, “Artificial annelid robot driven by soft actuators,” Bioinspir. Biomim. 2(2), S42–S49 (2007).
[Crossref] [PubMed]

Koo, J. C.

K. Jung, J. C. Koo, J.-D. Nam, Y. K. Lee, and H. R. Choi, “Artificial annelid robot driven by soft actuators,” Bioinspir. Biomim. 2(2), S42–S49 (2007).
[Crossref] [PubMed]

Kornbluh, R.

R. Pelrine, R. Kornbluh, Q. Pei, and J. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287(5454), 836–839 (2000).
[Crossref] [PubMed]

Koukourakis, N.

Kyung, K.

S. Yun, S. Park, B. Park, S. Nam, S. K. Park, and K. Kyung, “A thin film active-lens with translational control for dynamically programmable optical zoom,” Appl. Phys. Lett. 107(8), 081907 (2015).
[Crossref]

Lee, C.

C. A. Lopez, C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87(13), 134102 (2005).
[Crossref]

Lee, L.

Lee, Y. K.

K. Jung, J. C. Koo, J.-D. Nam, Y. K. Lee, and H. R. Choi, “Artificial annelid robot driven by soft actuators,” Bioinspir. Biomim. 2(2), S42–S49 (2007).
[Crossref] [PubMed]

Li, B.

B. Li, H. Chen, J. Qiang, S. Hu, Z. Zhu, and Y. Wang, “Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation,” J. Phys. D Appl. Phys. 44(15), 155301 (2011).
[Crossref]

Li, C.

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100(23), 231105 (2012).
[Crossref] [PubMed]

Li, X.

X. Li, L. Wei, R. H. Poelma, S. Vollebregt, J. Wei, H. P. Urbach, P. M. Sarro, and G. Q. Zhang, “Stretchable binary Fresnel lens for focus tuning,” Sci. Rep. 6(1), 25348 (2016).
[Crossref] [PubMed]

Liu, G.

Lopez, C. A.

C. A. Lopez, C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87(13), 134102 (2005).
[Crossref]

Manukyan, G.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4(1), 6378 (2015).
[Crossref] [PubMed]

Marrakchi, A.

Mathine, D. L.

Mishra, K.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4(1), 6378 (2015).
[Crossref] [PubMed]

Mugele, F.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4(1), 6378 (2015).
[Crossref] [PubMed]

Murade, C.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4(1), 6378 (2015).
[Crossref] [PubMed]

Nahory, R. E.

Nam, J.-D.

K. Jung, J. C. Koo, J.-D. Nam, Y. K. Lee, and H. R. Choi, “Artificial annelid robot driven by soft actuators,” Bioinspir. Biomim. 2(2), S42–S49 (2007).
[Crossref] [PubMed]

Nam, S.

S. Yun, S. Park, B. Park, S. Nam, S. K. Park, and K. Kyung, “A thin film active-lens with translational control for dynamically programmable optical zoom,” Appl. Phys. Lett. 107(8), 081907 (2015).
[Crossref]

Niklaus, M.

S. Rosset, M. Niklaus, P. Dubois, and H. R. Shea, “Large-stroke dielectric elastomer actuators with ion-implanted electrodes,” J. Microelectromech. Syst. 18(6), 1300–1308 (2009).
[Crossref]

Oh, J. M.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4(1), 6378 (2015).
[Crossref] [PubMed]

Park, B.

S. Yun, S. Park, B. Park, S. Nam, S. K. Park, and K. Kyung, “A thin film active-lens with translational control for dynamically programmable optical zoom,” Appl. Phys. Lett. 107(8), 081907 (2015).
[Crossref]

Park, S.

S. Yun, S. Park, B. Park, S. Nam, S. K. Park, and K. Kyung, “A thin film active-lens with translational control for dynamically programmable optical zoom,” Appl. Phys. Lett. 107(8), 081907 (2015).
[Crossref]

Park, S. K.

S. Yun, S. Park, B. Park, S. Nam, S. K. Park, and K. Kyung, “A thin film active-lens with translational control for dynamically programmable optical zoom,” Appl. Phys. Lett. 107(8), 081907 (2015).
[Crossref]

Pei, Q.

R. Pelrine, R. Kornbluh, Q. Pei, and J. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287(5454), 836–839 (2000).
[Crossref] [PubMed]

Pelrine, R.

R. Pelrine, R. Kornbluh, Q. Pei, and J. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287(5454), 836–839 (2000).
[Crossref] [PubMed]

Peyghambarian, N.

Peyman, G.

Philipp, K.

Poelma, R. H.

X. Li, L. Wei, R. H. Poelma, S. Vollebregt, J. Wei, H. P. Urbach, P. M. Sarro, and G. Q. Zhang, “Stretchable binary Fresnel lens for focus tuning,” Sci. Rep. 6(1), 25348 (2016).
[Crossref] [PubMed]

Qiang, J.

B. Li, H. Chen, J. Qiang, S. Hu, Z. Zhu, and Y. Wang, “Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation,” J. Phys. D Appl. Phys. 44(15), 155301 (2011).
[Crossref]

Qin, D.

B. Grzybowski, D. Qin, R. Haag, and G. M. Whitesides, “Elastomeric optical elements with deformable surface topographies: applications to force measurements, tunable light transmission and light focusing,” Sens. Actuators A Phys. 86(1-2), 81–85 (2000).
[Crossref]

Rastani, K.

Reza Dodge, M.

Roghair, I.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4(1), 6378 (2015).
[Crossref] [PubMed]

Rosset, S.

S. Rosset, M. Niklaus, P. Dubois, and H. R. Shea, “Large-stroke dielectric elastomer actuators with ion-implanted electrodes,” J. Microelectromech. Syst. 18(6), 1300–1308 (2009).
[Crossref]

Sarro, P. M.

X. Li, L. Wei, R. H. Poelma, S. Vollebregt, J. Wei, H. P. Urbach, P. M. Sarro, and G. Q. Zhang, “Stretchable binary Fresnel lens for focus tuning,” Sci. Rep. 6(1), 25348 (2016).
[Crossref] [PubMed]

Schwiegerling, J.

Shea, H. R.

S. Rosset, M. Niklaus, P. Dubois, and H. R. Shea, “Large-stroke dielectric elastomer actuators with ion-implanted electrodes,” J. Microelectromech. Syst. 18(6), 1300–1308 (2009).
[Crossref]

Smolarski, A.

Stankovic, S.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun. 188(5-6), 291–299 (2001).
[Crossref]

Stürmer, M.

Tschudi, T.

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun. 188(5-6), 291–299 (2001).
[Crossref]

Urbach, H. P.

X. Li, L. Wei, R. H. Poelma, S. Vollebregt, J. Wei, H. P. Urbach, P. M. Sarro, and G. Q. Zhang, “Stretchable binary Fresnel lens for focus tuning,” Sci. Rep. 6(1), 25348 (2016).
[Crossref] [PubMed]

Valley, P.

van den Ende, D.

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4(1), 6378 (2015).
[Crossref] [PubMed]

Vollebregt, S.

X. Li, L. Wei, R. H. Poelma, S. Vollebregt, J. Wei, H. P. Urbach, P. M. Sarro, and G. Q. Zhang, “Stretchable binary Fresnel lens for focus tuning,” Sci. Rep. 6(1), 25348 (2016).
[Crossref] [PubMed]

Wallrabe, U.

Wang, Y.

B. Li, H. Chen, J. Qiang, S. Hu, Z. Zhu, and Y. Wang, “Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation,” J. Phys. D Appl. Phys. 44(15), 155301 (2011).
[Crossref]

Wei, J.

X. Li, L. Wei, R. H. Poelma, S. Vollebregt, J. Wei, H. P. Urbach, P. M. Sarro, and G. Q. Zhang, “Stretchable binary Fresnel lens for focus tuning,” Sci. Rep. 6(1), 25348 (2016).
[Crossref] [PubMed]

Wei, L.

X. Li, L. Wei, R. H. Poelma, S. Vollebregt, J. Wei, H. P. Urbach, P. M. Sarro, and G. Q. Zhang, “Stretchable binary Fresnel lens for focus tuning,” Sci. Rep. 6(1), 25348 (2016).
[Crossref] [PubMed]

Whitesides, G. M.

B. Grzybowski, D. Qin, R. Haag, and G. M. Whitesides, “Elastomeric optical elements with deformable surface topographies: applications to force measurements, tunable light transmission and light focusing,” Sens. Actuators A Phys. 86(1-2), 81–85 (2000).
[Crossref]

Yun, S.

S. Yun, S. Park, B. Park, S. Nam, S. K. Park, and K. Kyung, “A thin film active-lens with translational control for dynamically programmable optical zoom,” Appl. Phys. Lett. 107(8), 081907 (2015).
[Crossref]

Zhang, G. Q.

X. Li, L. Wei, R. H. Poelma, S. Vollebregt, J. Wei, H. P. Urbach, P. M. Sarro, and G. Q. Zhang, “Stretchable binary Fresnel lens for focus tuning,” Sci. Rep. 6(1), 25348 (2016).
[Crossref] [PubMed]

Zhu, Z.

B. Li, H. Chen, J. Qiang, S. Hu, Z. Zhu, and Y. Wang, “Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation,” J. Phys. D Appl. Phys. 44(15), 155301 (2011).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

C. A. Lopez, C. Lee, and A. H. Hirsa, “Electrochemically activated adaptive liquid lens,” Appl. Phys. Lett. 87(13), 134102 (2005).
[Crossref]

C. Li and H. Jiang, “Electrowetting-driven variable-focus microlens on flexible surfaces,” Appl. Phys. Lett. 100(23), 231105 (2012).
[Crossref] [PubMed]

S. Yun, S. Park, B. Park, S. Nam, S. K. Park, and K. Kyung, “A thin film active-lens with translational control for dynamically programmable optical zoom,” Appl. Phys. Lett. 107(8), 081907 (2015).
[Crossref]

Bioinspir. Biomim. (1)

K. Jung, J. C. Koo, J.-D. Nam, Y. K. Lee, and H. R. Choi, “Artificial annelid robot driven by soft actuators,” Bioinspir. Biomim. 2(2), S42–S49 (2007).
[Crossref] [PubMed]

J. Microelectromech. Syst. (1)

S. Rosset, M. Niklaus, P. Dubois, and H. R. Shea, “Large-stroke dielectric elastomer actuators with ion-implanted electrodes,” J. Microelectromech. Syst. 18(6), 1300–1308 (2009).
[Crossref]

J. Phys. D Appl. Phys. (1)

B. Li, H. Chen, J. Qiang, S. Hu, Z. Zhu, and Y. Wang, “Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation,” J. Phys. D Appl. Phys. 44(15), 155301 (2011).
[Crossref]

Opt. Commun. (1)

M. Hain, R. Glockner, S. Bhattacharya, D. Dias, S. Stankovic, and T. Tschudi, “Fast switching liquid crystal lenses for a dual focus digital versatile disc pickup,” Opt. Commun. 188(5-6), 291–299 (2001).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Sci. Rep. (2)

K. Mishra, C. Murade, B. Carreel, I. Roghair, J. M. Oh, G. Manukyan, D. van den Ende, and F. Mugele, “Optofluidic lens with tunable focal length and asphericity,” Sci. Rep. 4(1), 6378 (2015).
[Crossref] [PubMed]

X. Li, L. Wei, R. H. Poelma, S. Vollebregt, J. Wei, H. P. Urbach, P. M. Sarro, and G. Q. Zhang, “Stretchable binary Fresnel lens for focus tuning,” Sci. Rep. 6(1), 25348 (2016).
[Crossref] [PubMed]

Science (1)

R. Pelrine, R. Kornbluh, Q. Pei, and J. Joseph, “High-speed electrically actuated elastomers with strain greater than 100%,” Science 287(5454), 836–839 (2000).
[Crossref] [PubMed]

Sens. Actuators A Phys. (1)

B. Grzybowski, D. Qin, R. Haag, and G. M. Whitesides, “Elastomeric optical elements with deformable surface topographies: applications to force measurements, tunable light transmission and light focusing,” Sens. Actuators A Phys. 86(1-2), 81–85 (2000).
[Crossref]

Other (1)

H. Zappe, Fundamentals of Micro-optics (Cambridge University Press, 2010).

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram and operating principle of a tunable binary-phase Fresnel lens. Top view (left) and cross-section view (right) in (a) and (b). When the zones of the lens contract from (a) to (b), its focal length decreases from F to F′.

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Fig. 2
Fig. 2 (a) Structural configuration of the proposed TFL lens based on a DE membrane actuator. (b) Illustrated working principle for focus tuning of TFL: initial state (V = 0) and deformed state responding to electrically-induced in-plane deformation of DE membrane (V = V0).

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Fig. 3
Fig. 3 An illustrated fabrication process of the TFL: (a) spin-casting photo-resist on a silicon wafer, (b) forming intagliated TFL structure, (c) spin-casting and thermal cross-linking of DE material, (d) peeling off the DE structure from the silicon wafer, (e) radially pre-stretching to 200%, (f) fixing with perforated acrylic frame, and (g) spry-coating the annular AgNWs electrode on both surfaces of the DE membrane under a shadow mask. A prototype of the TFL: (h) a photograph of the TFL and the AgNWs network for electrode (inset, scale bar: 2 μm), (i) microscopic images of the Fresnel zone structure and its magnified view at edge area (inset) observed using a PLu neox SensoFAR 3D optical profiler.

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Fig. 4
Fig. 4 (a) Electric voltage dependent contraction rate profile for the TFL, when driving the voltages upwards (◻) and downwards (○). The insets are photographs of the Fresnel zone plate before (0 V, lower left) and after contraction (4 kV, upper right). The bar scales in the insets are 10 mm. (b) Numerically calculated focal length with contracting rates.

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Fig. 5
Fig. 5 Focal length change of the TFL under various driving voltages.

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Fig. 6
Fig. 6 Optical intensity distributions of the TFL on the focal planes under various driving voltages of (a) 0, (b) 2, and (c) 4 kV.

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Fig. 7
Fig. 7 (a) Experimental setup for characterizing the TFL. (b) Focusing (On state) and defocusing (Off state) response of the TFL as a function of time. Applied voltages to the lens are 2.4 kV for On and 0 kV for Off state.

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Equations (5)

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

R N 2 =N R 1 2 , N = 1,2,3, ...,
F= R 1 2 λ = R N 2 Nλ ,
F'= R ' N 2 Nλ = (S R N ) 2 Nλ = S 2 F,
T= λ 2Δn ,
p= ε 0 ε r E 2 = ε 0 ε r (V/t) 2 ,

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