Abstract

Focus-tunable lenses are indispensable to optical systems. This paper proposes an electrically modulated varifocal metalens combined with twisted nematic liquid crystals. In our design, a metalens is employed to focus on different points depending on the polarization state of incident light. We demonstrated that the varifocal metalens has a sub-millisecond response time. Furthermore, the numerical aperture of both the first and second focal points can be customized to achieve a wide range of 0.2–0.7. Moreover, the full width at half maximum approached the diffraction limit at multiple focal points. Because of the advantages of our proposed electrically modulated metalens, it has the potential for application in optical technology and biomedical science, both of which require high image quality and a rapid response time.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

2018 (8)

O. Buchnev, N. Podoliak, and V. A. Fedotov, “Liquid crystal-filled meta-pixel with switchable asymmetric reflectance and transmittance,” J. Mol. Liq. 267, 411–414 (2018).
[Crossref]

H. Zhu, T. Xu, Z. Wang, J. Li, Z. Hang, L. Zhou, S. Chen, X. Li, and L. Chen, “Flat metasurfaces to collimate electromagnetic waves with high efficiency,” Opt. Express 26(22), 28531–28543 (2018).
[Crossref]

R. Pestourie, C. Pérez-Arancibia, Z. Lin, W. Shin, F. Capasso, and S. G. Johnson, “Inverse design of large-area metasurfaces,” Opt. Express 26(26), 33732–33747 (2018).
[Crossref]

S. Colburn, A. Zhan, and A. Majumdar, “Varifocal zoom imaging with large area focal length adjustable metalenses,” Optica 5(7), 825–831 (2018).
[Crossref]

L. Yaoyao, H. Liu, F.-Q. Wang, H. Meng, J. Guo, J. Li, and Z. Wei, “High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths,” Nanomaterials 8(5), 288 (2018).
[Crossref]

S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7(6), 1041–1068 (2018).
[Crossref]

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and Applications,” Adv. Opt. Mater. 6(18), 1800554 (2018).
[Crossref]

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112(7), 073504 (2018).
[Crossref]

2017 (4)

G. Zheng, W. Wu, Z. Li, S. Zhang, M. Q. Mehmood, P. a. He, and S. Li, “Dual field-of-view step-zoom metalens,” Opt. Lett. 42(7), 1261–1264 (2017).
[Crossref]

Y.-H. Lin, Y.-J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Cryst. Rev. 5(2), 111–143 (2017).
[Crossref]

J. Cheng, S. Inampudi, and H. Mosallaei, “Optimization-based Dielectric Metasurfaces for Angle-Selective Multifunctional Beam Deflection,” Sci. Rep. 7(1), 12228 (2017).
[Crossref]

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

2016 (1)

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref]

2015 (4)

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6(1), 7069 (2015).
[Crossref]

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C.-W. Qiu, and S. Zhang, “Longitudinal Multifoci Metalens for Circularly Polarized Light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

W. Wang, Z. Guo, K. Zhou, Y. Sun, F. Shen, Y. Li, S. Qu, and S. Liu, “Polarization-independent longitudinal multi-focusing metalens,” Opt. Express 23(23), 29855–29866 (2015).
[Crossref]

N. Yu and F. Capasso, “Optical Metasurfaces and Prospect of Their Applications Including Fiber Optics,” J. Lightwave Technol. 33(12), 2344–2358 (2015).
[Crossref]

2013 (2)

2012 (2)

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref]

C. Gennarelli, A. Capozzoli, L. J. Foged, J. Fordham, and D. van Rensburg, #xeb, and l. Janse, “Recent Advances in Near-Field to Far-Field Transformation Techniques,” Int. J. Antenn. Propag. 2012, 1–3 (2012).
[Crossref]

C. Gennarelli, A. Capozzoli, L. J. Foged, J. Fordham, and D. van Rensburg, #xeb, and l. Janse, “Recent Advances in Near-Field to Far-Field Transformation Techniques,” Int. J. Antenn. Propag. 2012, 1–3 (2012).
[Crossref]

2011 (4)

P. Ramachandran and G. Varoquaux, “Mayavi: 3D Visualization of Scientific Data,” Comput. Sci. Eng. 13(2), 40–51 (2011).
[Crossref]

C.-T. Lee, Y. Li, H.-Y. Lin, and S.-T. Wu, “Design of polarization-insensitive multi-electrode GRIN lens with a blue-phase liquid crystal,” Opt. Express 19(18), 17402–17407 (2011).
[Crossref]

Y. Li and S.-T. Wu, “Polarization independent adaptive microlens with a blue-phase liquid crystal,” Opt. Express 19(9), 8045–8050 (2011).
[Crossref]

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A Review of Electrically Tunable Focusing Liquid Crystal Lenses,” Transactions on Electrical and Electronic Materials 12(6), 234–240 (2011).
[Crossref]

2010 (2)

Y.-H. Lin, H.-S. Chen, H.-C. Lin, Y.-S. Tsou, H.-K. Hsu, and W.-Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, W. Shin, Z. Ruan, and S. Fan, “Phase front design with metallic pillar arrays,” Opt. Lett. 35(6), 844–846 (2010).
[Crossref]

2008 (1)

2005 (1)

H. Ren and S.-T. Wu, “Variable-focus liquid lens by changing aperture,” Appl. Phys. Lett. 86(21), 211107 (2005).
[Crossref]

2004 (1)

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004).
[Crossref]

1999 (1)

S. Sato, “Applications of Liquid Crystals to Variable-Focusing Lenses,” Opt. Rev. 6(6), 471–485 (1999).
[Crossref]

1993 (1)

1990 (1)

C. W. Fowler and E. S. Pateras, “Liquid crystal lens review,” Oph Phys Optics 10(2), 186–194 (1990).
[Crossref]

1981 (1)

G. Beni and S. Hackwood, “Electro-wetting displays,” Appl. Phys. Lett. 38(4), 207–209 (1981).
[Crossref]

1975 (1)

C. H. Gooch and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ⩽90 degrees,” J. Phys. D: Appl. Phys. 8(13), 1575–1584 (1975).
[Crossref]

1974 (1)

E. P. Raynes and I. A. Shanks, “Fast-switching twisted nematic electro-optical shutter and colour filter,” Electron. Lett. 10(7), 114–115 (1974).
[Crossref]

1971 (1)

M. Schadt and W. Helfrich, “Voltage-Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 18(4), 127–128 (1971).
[Crossref]

Aieta, F.

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref]

Arbabi, A.

S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7(6), 1041–1068 (2018).
[Crossref]

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6(1), 7069 (2015).
[Crossref]

Arbabi, E.

S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7(6), 1041–1068 (2018).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6(1), 7069 (2015).
[Crossref]

Ball, A. J.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6(1), 7069 (2015).
[Crossref]

Beni, G.

G. Beni and S. Hackwood, “Electro-wetting displays,” Appl. Phys. Lett. 38(4), 207–209 (1981).
[Crossref]

Blanchard, R.

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref]

Buchnev, O.

O. Buchnev, N. Podoliak, and V. A. Fedotov, “Liquid crystal-filled meta-pixel with switchable asymmetric reflectance and transmittance,” J. Mol. Liq. 267, 411–414 (2018).
[Crossref]

O. Buchnev, J. Y. Ou, M. Kaczmarek, N. I. Zheludev, and V. A. Fedotov, “Electro-optical control in a plasmonic metamaterial hybridised with a liquid-crystal cell,” Opt. Express 21(2), 1633–1638 (2013).
[Crossref]

Capasso, F.

R. Pestourie, C. Pérez-Arancibia, Z. Lin, W. Shin, F. Capasso, and S. G. Johnson, “Inverse design of large-area metasurfaces,” Opt. Express 26(26), 33732–33747 (2018).
[Crossref]

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref]

N. Yu and F. Capasso, “Optical Metasurfaces and Prospect of Their Applications Including Fiber Optics,” J. Lightwave Technol. 33(12), 2344–2358 (2015).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref]

Capozzoli, A.

C. Gennarelli, A. Capozzoli, L. J. Foged, J. Fordham, and D. van Rensburg, #xeb, and l. Janse, “Recent Advances in Near-Field to Far-Field Transformation Techniques,” Int. J. Antenn. Propag. 2012, 1–3 (2012).
[Crossref]

Catrysse, P. B.

Chen, H.-S.

Y.-H. Lin, H.-S. Chen, H.-C. Lin, Y.-S. Tsou, H.-K. Hsu, and W.-Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
[Crossref]

Chen, L.

Chen, M.

R. Fu, Z. Li, G. Zheng, M. Chen, Y. Yang, J. Tao, L. Wu, and Q. Deng, “Reconfigurable step-zoom metalens without optical and mechanical compensations,” Opt. Express 27(9), 12221–12230 (2019).
[Crossref]

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C.-W. Qiu, and S. Zhang, “Longitudinal Multifoci Metalens for Circularly Polarized Light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

Chen, M. K.

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and Applications,” Adv. Opt. Mater. 6(18), 1800554 (2018).
[Crossref]

Chen, M.-S.

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A Review of Electrically Tunable Focusing Liquid Crystal Lenses,” Transactions on Electrical and Electronic Materials 12(6), 234–240 (2011).
[Crossref]

Chen, S.

Chen, W. T.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref]

Chen, X.

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C.-W. Qiu, and S. Zhang, “Longitudinal Multifoci Metalens for Circularly Polarized Light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

Cheng, J.

J. Cheng, S. Inampudi, and H. Mosallaei, “Optimization-based Dielectric Metasurfaces for Angle-Selective Multifunctional Beam Deflection,” Sci. Rep. 7(1), 12228 (2017).
[Crossref]

Cheng, Q.

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112(7), 073504 (2018).
[Crossref]

Chigrin, D.

Chu, C. H.

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and Applications,” Adv. Opt. Mater. 6(18), 1800554 (2018).
[Crossref]

Colburn, S.

Cui, T. J.

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112(7), 073504 (2018).
[Crossref]

Decker, M.

Deng, Q.

Devlin, R.

Devlin, R. C.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref]

Fan, S.

Fang, J.

Faraon, A.

S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7(6), 1041–1068 (2018).
[Crossref]

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6(1), 7069 (2015).
[Crossref]

Fedotov, V. A.

O. Buchnev, N. Podoliak, and V. A. Fedotov, “Liquid crystal-filled meta-pixel with switchable asymmetric reflectance and transmittance,” J. Mol. Liq. 267, 411–414 (2018).
[Crossref]

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C. Gennarelli, A. Capozzoli, L. J. Foged, J. Fordham, and D. van Rensburg, #xeb, and l. Janse, “Recent Advances in Near-Field to Far-Field Transformation Techniques,” Int. J. Antenn. Propag. 2012, 1–3 (2012).
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C. W. Fowler and E. S. Pateras, “Liquid crystal lens review,” Oph Phys Optics 10(2), 186–194 (1990).
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F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
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P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
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F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
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L. Yaoyao, H. Liu, F.-Q. Wang, H. Meng, J. Guo, J. Li, and Z. Wei, “High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths,” Nanomaterials 8(5), 288 (2018).
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Hackwood, S.

G. Beni and S. Hackwood, “Electro-wetting displays,” Appl. Phys. Lett. 38(4), 207–209 (1981).
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He, P. a.

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M. Schadt and W. Helfrich, “Voltage-Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 18(4), 127–128 (1971).
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S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004).
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Horie, Y.

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6(1), 7069 (2015).
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M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and Applications,” Adv. Opt. Mater. 6(18), 1800554 (2018).
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Y.-H. Lin, H.-S. Chen, H.-C. Lin, Y.-S. Tsou, H.-K. Hsu, and W.-Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
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J. Cheng, S. Inampudi, and H. Mosallaei, “Optimization-based Dielectric Metasurfaces for Angle-Selective Multifunctional Beam Deflection,” Sci. Rep. 7(1), 12228 (2017).
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Janse, l.

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Kaczmarek, M.

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F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref]

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P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4(1), 139–152 (2017).
[Crossref]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref]

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Kremers, C.

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S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004).
[Crossref]

Lee, C.-T.

Li, J.

L. Yaoyao, H. Liu, F.-Q. Wang, H. Meng, J. Guo, J. Li, and Z. Wei, “High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths,” Nanomaterials 8(5), 288 (2018).
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H. Zhu, T. Xu, Z. Wang, J. Li, Z. Hang, L. Zhou, S. Chen, X. Li, and L. Chen, “Flat metasurfaces to collimate electromagnetic waves with high efficiency,” Opt. Express 26(22), 28531–28543 (2018).
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Y.-H. Lin, H.-S. Chen, H.-C. Lin, Y.-S. Tsou, H.-K. Hsu, and W.-Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
[Crossref]

Li, X.

Li, Y.

Li, Z.

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H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A Review of Electrically Tunable Focusing Liquid Crystal Lenses,” Transactions on Electrical and Electronic Materials 12(6), 234–240 (2011).
[Crossref]

Y.-H. Lin, H.-S. Chen, H.-C. Lin, Y.-S. Tsou, H.-K. Hsu, and W.-Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
[Crossref]

Y.-H. Lin, H. Ren, Y.-H. Wu, S.-T. Wu, Y. Zhao, J. Fang, and H.-C. Lin, “Electrically tunable wettability of liquid crystal/polymer composite films,” Opt. Express 16(22), 17591–17598 (2008).
[Crossref]

Lin, H.-Y.

Lin, Y.-H.

Y.-H. Lin, Y.-J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Cryst. Rev. 5(2), 111–143 (2017).
[Crossref]

H.-C. Lin, M.-S. Chen, and Y.-H. Lin, “A Review of Electrically Tunable Focusing Liquid Crystal Lenses,” Transactions on Electrical and Electronic Materials 12(6), 234–240 (2011).
[Crossref]

Y.-H. Lin, H.-S. Chen, H.-C. Lin, Y.-S. Tsou, H.-K. Hsu, and W.-Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
[Crossref]

Y.-H. Lin, H. Ren, Y.-H. Wu, S.-T. Wu, Y. Zhao, J. Fang, and H.-C. Lin, “Electrically tunable wettability of liquid crystal/polymer composite films,” Opt. Express 16(22), 17591–17598 (2008).
[Crossref]

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Liu, A.-Q.

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and Applications,” Adv. Opt. Mater. 6(18), 1800554 (2018).
[Crossref]

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L. Yaoyao, H. Liu, F.-Q. Wang, H. Meng, J. Guo, J. Li, and Z. Wei, “High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths,” Nanomaterials 8(5), 288 (2018).
[Crossref]

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Mehmood, M. Q.

G. Zheng, W. Wu, Z. Li, S. Zhang, M. Q. Mehmood, P. a. He, and S. Li, “Dual field-of-view step-zoom metalens,” Opt. Lett. 42(7), 1261–1264 (2017).
[Crossref]

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C.-W. Qiu, and S. Zhang, “Longitudinal Multifoci Metalens for Circularly Polarized Light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

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L. Yaoyao, H. Liu, F.-Q. Wang, H. Meng, J. Guo, J. Li, and Z. Wei, “High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths,” Nanomaterials 8(5), 288 (2018).
[Crossref]

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Miroshnichenko, A. E.

Mishra, I.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref]

Morita, S.

Mosallaei, H.

J. Cheng, S. Inampudi, and H. Mosallaei, “Optimization-based Dielectric Metasurfaces for Angle-Selective Multifunctional Beam Deflection,” Sci. Rep. 7(1), 12228 (2017).
[Crossref]

Neshev, D. N.

Oh, J.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref]

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C. W. Fowler and E. S. Pateras, “Liquid crystal lens review,” Oph Phys Optics 10(2), 186–194 (1990).
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O. Buchnev, N. Podoliak, and V. A. Fedotov, “Liquid crystal-filled meta-pixel with switchable asymmetric reflectance and transmittance,” J. Mol. Liq. 267, 411–414 (2018).
[Crossref]

Qiu, C.-W.

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C.-W. Qiu, and S. Zhang, “Longitudinal Multifoci Metalens for Circularly Polarized Light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

Qu, S.

Ramachandran, P.

P. Ramachandran and G. Varoquaux, “Mayavi: 3D Visualization of Scientific Data,” Comput. Sci. Eng. 13(2), 40–51 (2011).
[Crossref]

Raynes, E. P.

E. P. Raynes and I. A. Shanks, “Fast-switching twisted nematic electro-optical shutter and colour filter,” Electron. Lett. 10(7), 114–115 (1974).
[Crossref]

Ren, H.

Reshetnyak, V.

Y.-H. Lin, Y.-J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Cryst. Rev. 5(2), 111–143 (2017).
[Crossref]

Roques-Carmes, C.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
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M. Schadt and W. Helfrich, “Voltage-Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 18(4), 127–128 (1971).
[Crossref]

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E. P. Raynes and I. A. Shanks, “Fast-switching twisted nematic electro-optical shutter and colour filter,” Electron. Lett. 10(7), 114–115 (1974).
[Crossref]

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Shin, W.

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M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and Applications,” Adv. Opt. Mater. 6(18), 1800554 (2018).
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Tao, J.

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C. H. Gooch and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ⩽90 degrees,” J. Phys. D: Appl. Phys. 8(13), 1575–1584 (1975).
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M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and Applications,” Adv. Opt. Mater. 6(18), 1800554 (2018).
[Crossref]

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M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and Applications,” Adv. Opt. Mater. 6(18), 1800554 (2018).
[Crossref]

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Y.-H. Lin, H.-S. Chen, H.-C. Lin, Y.-S. Tsou, H.-K. Hsu, and W.-Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
[Crossref]

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C. Gennarelli, A. Capozzoli, L. J. Foged, J. Fordham, and D. van Rensburg, #xeb, and l. Janse, “Recent Advances in Near-Field to Far-Field Transformation Techniques,” Int. J. Antenn. Propag. 2012, 1–3 (2012).
[Crossref]

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P. Ramachandran and G. Varoquaux, “Mayavi: 3D Visualization of Scientific Data,” Comput. Sci. Eng. 13(2), 40–51 (2011).
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Wang, F.-Q.

L. Yaoyao, H. Liu, F.-Q. Wang, H. Meng, J. Guo, J. Li, and Z. Wei, “High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths,” Nanomaterials 8(5), 288 (2018).
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Wang, Y.-J.

Y.-H. Lin, Y.-J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Cryst. Rev. 5(2), 111–143 (2017).
[Crossref]

Wang, Z.

Wei, Z.

L. Yaoyao, H. Liu, F.-Q. Wang, H. Meng, J. Guo, J. Li, and Z. Wei, “High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths,” Nanomaterials 8(5), 288 (2018).
[Crossref]

Wen, D.

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C.-W. Qiu, and S. Zhang, “Longitudinal Multifoci Metalens for Circularly Polarized Light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

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Wu, S.-T.

Wu, W.

Wu, Y.-H.

Xu, T.

Yang, J.

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112(7), 073504 (2018).
[Crossref]

Yang, Y.

Yaoyao, L.

L. Yaoyao, H. Liu, F.-Q. Wang, H. Meng, J. Guo, J. Li, and Z. Wei, “High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths,” Nanomaterials 8(5), 288 (2018).
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N. Yu and F. Capasso, “Optical Metasurfaces and Prospect of Their Applications Including Fiber Optics,” J. Lightwave Technol. 33(12), 2344–2358 (2015).
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F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref]

Yu, Z.

Yue, F.

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C.-W. Qiu, and S. Zhang, “Longitudinal Multifoci Metalens for Circularly Polarized Light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

Zhan, A.

Zhang, C.

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112(7), 073504 (2018).
[Crossref]

Zhang, S.

G. Zheng, W. Wu, Z. Li, S. Zhang, M. Q. Mehmood, P. a. He, and S. Li, “Dual field-of-view step-zoom metalens,” Opt. Lett. 42(7), 1261–1264 (2017).
[Crossref]

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C.-W. Qiu, and S. Zhang, “Longitudinal Multifoci Metalens for Circularly Polarized Light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

Zhao, J.

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112(7), 073504 (2018).
[Crossref]

Zhao, Y.

Zheludev, N. I.

Zheng, G.

Zhou, K.

Zhou, L.

Zhu, A. Y.

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref]

Zhu, H.

Zhuang, S.

Adv. Opt. Mater. (2)

X. Chen, M. Chen, M. Q. Mehmood, D. Wen, F. Yue, C.-W. Qiu, and S. Zhang, “Longitudinal Multifoci Metalens for Circularly Polarized Light,” Adv. Opt. Mater. 3(9), 1201–1206 (2015).
[Crossref]

M. L. Tseng, H.-H. Hsiao, C. H. Chu, M. K. Chen, G. Sun, A.-Q. Liu, and D. P. Tsai, “Metalenses: Advances and Applications,” Adv. Opt. Mater. 6(18), 1800554 (2018).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (6)

J. Zhao, C. Zhang, Q. Cheng, J. Yang, and T. J. Cui, “An optically transparent metasurface for broadband microwave antireflection,” Appl. Phys. Lett. 112(7), 073504 (2018).
[Crossref]

M. Schadt and W. Helfrich, “Voltage-Dependent Optical Activity of a Twisted Nematic Liquid Crystal,” Appl. Phys. Lett. 18(4), 127–128 (1971).
[Crossref]

H. Ren and S.-T. Wu, “Variable-focus liquid lens by changing aperture,” Appl. Phys. Lett. 86(21), 211107 (2005).
[Crossref]

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett. 85(7), 1128–1130 (2004).
[Crossref]

G. Beni and S. Hackwood, “Electro-wetting displays,” Appl. Phys. Lett. 38(4), 207–209 (1981).
[Crossref]

Y.-H. Lin, H.-S. Chen, H.-C. Lin, Y.-S. Tsou, H.-K. Hsu, and W.-Y. Li, “Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals,” Appl. Phys. Lett. 96(11), 113505 (2010).
[Crossref]

Comput. Sci. Eng. (1)

P. Ramachandran and G. Varoquaux, “Mayavi: 3D Visualization of Scientific Data,” Comput. Sci. Eng. 13(2), 40–51 (2011).
[Crossref]

Electron. Lett. (1)

E. P. Raynes and I. A. Shanks, “Fast-switching twisted nematic electro-optical shutter and colour filter,” Electron. Lett. 10(7), 114–115 (1974).
[Crossref]

Int. J. Antenn. Propag. (1)

C. Gennarelli, A. Capozzoli, L. J. Foged, J. Fordham, and D. van Rensburg, #xeb, and l. Janse, “Recent Advances in Near-Field to Far-Field Transformation Techniques,” Int. J. Antenn. Propag. 2012, 1–3 (2012).
[Crossref]

J. Lightwave Technol. (1)

J. Mol. Liq. (1)

O. Buchnev, N. Podoliak, and V. A. Fedotov, “Liquid crystal-filled meta-pixel with switchable asymmetric reflectance and transmittance,” J. Mol. Liq. 267, 411–414 (2018).
[Crossref]

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

C. H. Gooch and H. A. Tarry, “The optical properties of twisted nematic liquid crystal structures with twist angles ⩽90 degrees,” J. Phys. D: Appl. Phys. 8(13), 1575–1584 (1975).
[Crossref]

Liq. Cryst. Rev. (1)

Y.-H. Lin, Y.-J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Cryst. Rev. 5(2), 111–143 (2017).
[Crossref]

Nano Lett. (2)

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12(9), 4932–4936 (2012).
[Crossref]

M. Khorasaninejad, A. Y. Zhu, C. Roques-Carmes, W. T. Chen, J. Oh, I. Mishra, R. C. Devlin, and F. Capasso, “Polarization-Insensitive Metalenses at Visible Wavelengths,” Nano Lett. 16(11), 7229–7234 (2016).
[Crossref]

Nanomaterials (1)

L. Yaoyao, H. Liu, F.-Q. Wang, H. Meng, J. Guo, J. Li, and Z. Wei, “High-Efficiency, Near-Diffraction Limited, Dielectric Metasurface Lenses Based on Crystalline Titanium Dioxide at Visible Wavelengths,” Nanomaterials 8(5), 288 (2018).
[Crossref]

Nanophotonics (1)

S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, “A review of dielectric optical metasurfaces for wavefront control,” Nanophotonics 7(6), 1041–1068 (2018).
[Crossref]

Nat. Commun. (1)

A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6(1), 7069 (2015).
[Crossref]

Oph Phys Optics (1)

C. W. Fowler and E. S. Pateras, “Liquid crystal lens review,” Oph Phys Optics 10(2), 186–194 (1990).
[Crossref]

Opt. Express (10)

Y.-H. Lin, H. Ren, Y.-H. Wu, S.-T. Wu, Y. Zhao, J. Fang, and H.-C. Lin, “Electrically tunable wettability of liquid crystal/polymer composite films,” Opt. Express 16(22), 17591–17598 (2008).
[Crossref]

W. Wang, Z. Guo, K. Zhou, Y. Sun, F. Shen, Y. Li, S. Qu, and S. Liu, “Polarization-independent longitudinal multi-focusing metalens,” Opt. Express 23(23), 29855–29866 (2015).
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Y. Li and S.-T. Wu, “Polarization independent adaptive microlens with a blue-phase liquid crystal,” Opt. Express 19(9), 8045–8050 (2011).
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C.-T. Lee, Y. Li, H.-Y. Lin, and S.-T. Wu, “Design of polarization-insensitive multi-electrode GRIN lens with a blue-phase liquid crystal,” Opt. Express 19(18), 17402–17407 (2011).
[Crossref]

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Supplementary Material (1)

NameDescription
» Visualization 1       Simulation results in video format for Figure 7

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Figures (8)

Fig. 1.
Fig. 1. Schematic of the unit cell structure of the electrically modulated metalens combined with TN LCs. (a) Unit cell structure; (b) side view of the electrically modulated metalens combined with TN LCs.
Fig. 2.
Fig. 2. Sweep results of unit cells over 101 steps. (a, b) Simulated sweep phase delay of unit cell structures; (c, d) simulated transmission of unit cell structures. The operation wavelength was 650 nm, and the height was 600 nm.
Fig. 3.
Fig. 3. Metalens parameters. (a) Phase versus radial distance; (b) Length and width versus radial distance.
Fig. 4.
Fig. 4. (a) Schematic of the proposed electrically modulated multi-focus metalens; (b) top view of the metalens.
Fig. 5.
Fig. 5. Schematics of the TN LC tilt angle and the electrical field fraction. (a) TN LCs in the off-state; (b) TN LCs in the on-state; (c) x-polarized and y-polarized fractions in the off-state; (d) x-polarized and y-polarized fractions in the on-state.
Fig. 6.
Fig. 6. Schematic of the TN LCs’ response times.
Fig. 7.
Fig. 7. Schematics of far fields on the x-z, y-z, and x-y planes. (a) First focal point on the x-z plane; (b) first focal point on the y-z plane; (c) first focal point on the x-y plane; (d) second focal point on the x-z plane; (d) second focal point on the y-z plane; (d) second focal point on the x-y plane (Visualization 1).
Fig. 8.
Fig. 8. Schematics for comparison between the FWHM and the diffraction limit in design 4. (a) First focal point at around 10 µm; (b) second focal point at around 45 µm.

Tables (1)

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Table 1. Comparison between four designs of the proposed metalens with respect to the diffraction limit.

Equations (2)

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φ ( x , y )  =  φ m + φ p = k 0 ( x 2 + y 2 + f 2 f )
I ( θ ) = I 0 [ 2 J 1 ( k a sin θ ) k a sin θ ]