Abstract

Microlens arrays have been widely used for different optoelectronic applications. The demand for compact optical devices necessitates the deployment of even smaller microlens arrays; however, as the spacing between individual lenses reduces and the lens diameter approaches the length scale of the incident wavelength of light, diffraction starts playing a critical role and produces a significant impact on the final focusing properties of the optical field. In this paper, we analyze the focusing characteristics of all-dielectric ultra-compact metasurface lens arrays for efficient optical device applications, constructed by kinds of broadband planar lenses composed of subwavelength nano-scatterers. By using the 3D finite-difference time-domain (FDTD) method, focusing and diffraction-based crosstalk effects caused by the changing physical spacing between adjacent metalenses, the diameter of microlenses, the operating wavelength, and the array size are rigorously investigated. Analysis of the achieved results show that a larger spacing, a larger lens size, and a shorter wavelength can lead to a weaker focusing crosstalk effect. Moreover, the crosstalk effect does not have a significant dependence on the array’s overall size. This research study may provide an important technological reference to designing an array of all-dielectric planar metasurface lenses with a well-controlled focusing performance and may pave the way further toward the application of metasurface lens arrays in compact optical sensing, coupling, and detecting system designs.

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

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References

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2018 (1)

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
[Crossref] [PubMed]

2017 (5)

I. Staude and J. Schilling, “Metamaterial-inspired silicon nanophotonics,” Nat. Photonics 11(5), 274–284 (2017).
[Crossref]

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017).
[Crossref] [PubMed]

A. Ranjbar and A. Grbic, “Analysis and synthesis of cascaded metasurfaces using wave matrices,” Phys. Rev. B 95(20), 205114 (2017).
[Crossref]

A. Özdemir, Z. Hayran, Y. Takashima, and H. Kurt, “Polarization independent high transmission large numerical aperture laser beam focusing and deflection by dielectric Huygens’ metasurfaces,” Opt. Commun. 401, 46–53 (2017).
[Crossref]

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[Crossref] [PubMed]

2016 (13)

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

K. E. Chong, L. Wang, I. Staude, A. R. James, J. Dominguez, S. Liu, G. S. Subramania, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Efficient polarization-insensitive complex wavefront control using Huygens’ metasurfaces based on dielectric resonant meta-atoms,” ACS Photonics 3(4), 514–519 (2016).
[Crossref]

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3(2), 209–214 (2016).
[Crossref]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[Crossref] [PubMed]

Y. Yu, P. Wang, Y. Zhu, and J. Diao, “Broadband Metallic Planar Microlenses in an Array: the Focusing Coupling Effect,” Nanoscale Res. Lett. 11(1), 109 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral Chiral Imaging with a Metalens,” Nano Lett. 16(7), 4595–4600 (2016).
[Crossref] [PubMed]

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1(3), 030801 (2016).
[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] [PubMed]

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
[Crossref] [PubMed]

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
[Crossref] [PubMed]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “High efficiency double-wavelength dielectric metasurface lenses with dichroic birefringent meta-atoms,” Opt. Express 24(16), 18468–18477 (2016).
[Crossref] [PubMed]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504– 1505 (2016).
[Crossref] [PubMed]

2015 (8)

S. He, Z. Wang, Q. Liu, and W. Wang, “Study of focal shift effect in planar GaN high contrast grating lenses,” Opt. Express 23(23), 29360–29368 (2015).
[Crossref] [PubMed]

A. Arbabi, R. M. Briggs, Y. Horie, M. Bagheri, and A. Faraon, “Efficient dielectric metasurface collimating lenses for mid-infrared quantum cascade lasers,” Opt. Express 23(26), 33310–33317 (2015).
[Crossref] [PubMed]

C. Pfeiffer and A. Grbic, “Generating stable tractor beams with dielectric metasurfaces,” Phys. Rev. B Condens. Matter Mater. Phys. 91(11), 115408 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3(6), 813–820 (2015).
[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] [PubMed]

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photon. Rev. 9(4), 412–418 (2015).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15(8), 5369–5374 (2015).
[Crossref] [PubMed]

2014 (2)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

D. H. Hwang, O. T. Kwon, W. J. Lee, J. W. Hong, and T. W. Kim, “Outcoupling efficiency of organic light-emitting diodes depending on the fill factor and size of the microlens array,” Phys. Stat. Solidi A 211(8), 1773–1777 (2014).

2013 (3)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

L. Zou, W. Withayachumnankul, C. M. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Dielectric resonator nanoantennas at visible frequencies,” Opt. Express 21(1), 1344–1352 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (1)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

2010 (1)

2008 (4)

C. Levallois, V. Bardinal, C. Vergnenègre, T. Leïchlé, T. Camps, E. Daran, and J.-B. Doucet, “VCSEL collimation using self-aligned integrated polymer microlenses,” Proc. SPIE 6992, 69920W (2008).
[Crossref]

M. K. Wei, J. H. Lee, H. Y. Lin, Y. H. Ho, K. Y. Chen, C. C. Lin, C. F. Wu, H. Y. Lin, J. H. Tsai, and T. C. Wu, “Efficiency improvement and spectral shift of an organic light-emitting device by attaching a hexagon-based microlens array,” J. Opt. A, Pure Appl. Opt. 10(5), 055302 (2008).
[Crossref]

C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Express 16(25), 20457–20470 (2008).
[Crossref] [PubMed]

K. Tvingstedt, S. Dal Zilio, O. Inganäs, and M. Tormen, “Trapping light with micro lenses in thin film organic photovoltaic cells,” Opt. Express 16(26), 21608–21615 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (1)

2003 (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

1998 (1)

1996 (1)

G. E. Jellison and F. A. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69(3), 371–373 (1996).
[Crossref]

1993 (1)

M. Oikawa, H. Imanishi, and T. Kishimoto, “Light coupling characteristics of a planar microlens,” Electron. Commun. Jpn. Part II Electron. 76(10), 10–20 (1993).

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Amberg, M.

Arbabi, A.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “High efficiency double-wavelength dielectric metasurface lenses with dichroic birefringent meta-atoms,” Opt. Express 24(16), 18468–18477 (2016).
[Crossref] [PubMed]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[Crossref] [PubMed]

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] [PubMed]

A. Arbabi, R. M. Briggs, Y. Horie, M. Bagheri, and A. Faraon, “Efficient dielectric metasurface collimating lenses for mid-infrared quantum cascade lasers,” Opt. Express 23(26), 33310–33317 (2015).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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Arbabi, E.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “High efficiency double-wavelength dielectric metasurface lenses with dichroic birefringent meta-atoms,” Opt. Express 24(16), 18468–18477 (2016).
[Crossref] [PubMed]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
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Astilean, S.

Bagheri, M.

A. Arbabi, R. M. Briggs, Y. Horie, M. Bagheri, and A. Faraon, “Efficient dielectric metasurface collimating lenses for mid-infrared quantum cascade lasers,” Opt. Express 23(26), 33310–33317 (2015).
[Crossref] [PubMed]

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] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
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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] [PubMed]

Balthasar Mueller, J. P.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017).
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C. Levallois, V. Bardinal, C. Vergnenègre, T. Leïchlé, T. Camps, E. Daran, and J.-B. Doucet, “VCSEL collimation using self-aligned integrated polymer microlenses,” Proc. SPIE 6992, 69920W (2008).
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Bhaskaran, M.

Biener, G.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
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K. E. Chong, L. Wang, I. Staude, A. R. James, J. Dominguez, S. Liu, G. S. Subramania, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Efficient polarization-insensitive complex wavefront control using Huygens’ metasurfaces based on dielectric resonant meta-atoms,” ACS Photonics 3(4), 514–519 (2016).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15(8), 5369–5374 (2015).
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M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3(6), 813–820 (2015).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
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Briggs, R. M.

Brongersma, M. L.

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
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Campione, S.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15(8), 5369–5374 (2015).
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Camps, T.

C. Levallois, V. Bardinal, C. Vergnenègre, T. Leïchlé, T. Camps, E. Daran, and J.-B. Doucet, “VCSEL collimation using self-aligned integrated polymer microlenses,” Proc. SPIE 6992, 69920W (2008).
[Crossref]

Capasso, F.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017).
[Crossref] [PubMed]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral Chiral Imaging with a Metalens,” Nano Lett. 16(7), 4595–4600 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

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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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Catrysse, P. B.

Chavel, P.

Chen, B. H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
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B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[Crossref] [PubMed]

Chen, J.-W.

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[Crossref] [PubMed]

Chen, K. Y.

M. K. Wei, J. H. Lee, H. Y. Lin, Y. H. Ho, K. Y. Chen, C. C. Lin, C. F. Wu, H. Y. Lin, J. H. Tsai, and T. C. Wu, “Efficiency improvement and spectral shift of an organic light-emitting device by attaching a hexagon-based microlens array,” J. Opt. A, Pure Appl. Opt. 10(5), 055302 (2008).
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S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
[Crossref] [PubMed]

Chen, W. T.

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral Chiral Imaging with a Metalens,” Nano Lett. 16(7), 4595–4600 (2016).
[Crossref] [PubMed]

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] [PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Chen, Y. H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
[Crossref] [PubMed]

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[Crossref] [PubMed]

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K. E. Chong, L. Wang, I. Staude, A. R. James, J. Dominguez, S. Liu, G. S. Subramania, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Efficient polarization-insensitive complex wavefront control using Huygens’ metasurfaces based on dielectric resonant meta-atoms,” ACS Photonics 3(4), 514–519 (2016).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15(8), 5369–5374 (2015).
[Crossref] [PubMed]

Chu, C. H.

B. H. Chen, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, I. C. Lee, J.-W. Chen, Y. H. Chen, Y.-C. Lan, C.-H. Kuan, and D. P. Tsai, “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017).
[Crossref] [PubMed]

Colburn, S.

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3(2), 209–214 (2016).
[Crossref]

Cui, X.

Q. Zhang, T. Liao, G. Gan, M. Li, and X. Cui, “Polarization split lensing via polarization and phase control with metasurfaces at visible frequencies,” Plasmonics, 1–8 (2018).

Dal Zilio, S.

Dannberg, P.

Daran, E.

C. Levallois, V. Bardinal, C. Vergnenègre, T. Leïchlé, T. Camps, E. Daran, and J.-B. Doucet, “VCSEL collimation using self-aligned integrated polymer microlenses,” Proc. SPIE 6992, 69920W (2008).
[Crossref]

Decker, M.

K. E. Chong, L. Wang, I. Staude, A. R. James, J. Dominguez, S. Liu, G. S. Subramania, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Efficient polarization-insensitive complex wavefront control using Huygens’ metasurfaces based on dielectric resonant meta-atoms,” ACS Photonics 3(4), 514–519 (2016).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15(8), 5369–5374 (2015).
[Crossref] [PubMed]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3(6), 813–820 (2015).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Devlin, R. C.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017).
[Crossref] [PubMed]

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral Chiral Imaging with a Metalens,” Nano Lett. 16(7), 4595–4600 (2016).
[Crossref] [PubMed]

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] [PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
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Y. Yu, P. Wang, Y. Zhu, and J. Diao, “Broadband Metallic Planar Microlenses in an Array: the Focusing Coupling Effect,” Nanoscale Res. Lett. 11(1), 109 (2016).
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A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3(2), 209–214 (2016).
[Crossref]

Dominguez, J.

K. E. Chong, L. Wang, I. Staude, A. R. James, J. Dominguez, S. Liu, G. S. Subramania, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Efficient polarization-insensitive complex wavefront control using Huygens’ metasurfaces based on dielectric resonant meta-atoms,” ACS Photonics 3(4), 514–519 (2016).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15(8), 5369–5374 (2015).
[Crossref] [PubMed]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3(6), 813–820 (2015).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Doucet, J.-B.

C. Levallois, V. Bardinal, C. Vergnenègre, T. Leïchlé, T. Camps, E. Daran, and J.-B. Doucet, “VCSEL collimation using self-aligned integrated polymer microlenses,” Proc. SPIE 6992, 69920W (2008).
[Crossref]

Falkner, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3(6), 813–820 (2015).
[Crossref]

Faraon, A.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[Crossref] [PubMed]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “High efficiency double-wavelength dielectric metasurface lenses with dichroic birefringent meta-atoms,” Opt. Express 24(16), 18468–18477 (2016).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref] [PubMed]

A. Arbabi, R. M. Briggs, Y. Horie, M. Bagheri, and A. Faraon, “Efficient dielectric metasurface collimating lenses for mid-infrared quantum cascade lasers,” Opt. Express 23(26), 33310–33317 (2015).
[Crossref] [PubMed]

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] [PubMed]

Fesenmaier, C. C.

Fofang, N. T.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Fryett, T. K.

A. Zhan, S. Colburn, R. Trivedi, T. K. Fryett, C. M. Dodson, and A. Majumdar, “Low-contrast dielectric metasurface optics,” ACS Photonics 3(2), 209–214 (2016).
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Fu, Y. H.

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photon. Rev. 9(4), 412–418 (2015).
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Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gan, G.

Q. Zhang, T. Liao, G. Gan, M. Li, and X. Cui, “Polarization split lensing via polarization and phase control with metasurfaces at visible frequencies,” Plasmonics, 1–8 (2018).

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gonzales, E.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
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A. Ranjbar and A. Grbic, “Analysis and synthesis of cascaded metasurfaces using wave matrices,” Phys. Rev. B 95(20), 205114 (2017).
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C. Pfeiffer and A. Grbic, “Generating stable tractor beams with dielectric metasurfaces,” Phys. Rev. B Condens. Matter Mater. Phys. 91(11), 115408 (2015).
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J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017).
[Crossref] [PubMed]

Han, S.

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[Crossref] [PubMed]

Hasman, E.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Hayran, Z.

A. Özdemir, Z. Hayran, Y. Takashima, and H. Kurt, “Polarization independent high transmission large numerical aperture laser beam focusing and deflection by dielectric Huygens’ metasurfaces,” Opt. Commun. 401, 46–53 (2017).
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He, S.

Ho, Y. H.

M. K. Wei, J. H. Lee, H. Y. Lin, Y. H. Ho, K. Y. Chen, C. C. Lin, C. F. Wu, H. Y. Lin, J. H. Tsai, and T. C. Wu, “Efficiency improvement and spectral shift of an organic light-emitting device by attaching a hexagon-based microlens array,” J. Opt. A, Pure Appl. Opt. 10(5), 055302 (2008).
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Hong, J. W.

D. H. Hwang, O. T. Kwon, W. J. Lee, J. W. Hong, and T. W. Kim, “Outcoupling efficiency of organic light-emitting diodes depending on the fill factor and size of the microlens array,” Phys. Stat. Solidi A 211(8), 1773–1777 (2014).

Hopkins, B.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1(3), 030801 (2016).
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Horie, Y.

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “High efficiency double-wavelength dielectric metasurface lenses with dichroic birefringent meta-atoms,” Opt. Express 24(16), 18468–18477 (2016).
[Crossref] [PubMed]

A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7, 13682 (2016).
[Crossref] [PubMed]

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M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
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M. Oikawa, H. Imanishi, and T. Kishimoto, “Light coupling characteristics of a planar microlens,” Electron. Commun. Jpn. Part II Electron. 76(10), 10–20 (1993).

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I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
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K. E. Chong, L. Wang, I. Staude, A. R. James, J. Dominguez, S. Liu, G. S. Subramania, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Efficient polarization-insensitive complex wavefront control using Huygens’ metasurfaces based on dielectric resonant meta-atoms,” ACS Photonics 3(4), 514–519 (2016).
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L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504– 1505 (2016).
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M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3(6), 813–820 (2015).
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A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express 20(18), 20599–20604 (2012).
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E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
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Kravchenko, I.

Kravchenko, I. I.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1(3), 030801 (2016).
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L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504– 1505 (2016).
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A. Özdemir, Z. Hayran, Y. Takashima, and H. Kurt, “Polarization independent high transmission large numerical aperture laser beam focusing and deflection by dielectric Huygens’ metasurfaces,” Opt. Commun. 401, 46–53 (2017).
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A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
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Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photon. Rev. 9(4), 412–418 (2015).
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D. H. Hwang, O. T. Kwon, W. J. Lee, J. W. Hong, and T. W. Kim, “Outcoupling efficiency of organic light-emitting diodes depending on the fill factor and size of the microlens array,” Phys. Stat. Solidi A 211(8), 1773–1777 (2014).

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S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
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Lan, Y.-C.

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Lee, I. C.

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D. H. Hwang, O. T. Kwon, W. J. Lee, J. W. Hong, and T. W. Kim, “Outcoupling efficiency of organic light-emitting diodes depending on the fill factor and size of the microlens array,” Phys. Stat. Solidi A 211(8), 1773–1777 (2014).

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C. Levallois, V. Bardinal, C. Vergnenègre, T. Leïchlé, T. Camps, E. Daran, and J.-B. Doucet, “VCSEL collimation using self-aligned integrated polymer microlenses,” Proc. SPIE 6992, 69920W (2008).
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Li, T.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
[Crossref] [PubMed]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504– 1505 (2016).
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M. K. Wei, J. H. Lee, H. Y. Lin, Y. H. Ho, K. Y. Chen, C. C. Lin, C. F. Wu, H. Y. Lin, J. H. Tsai, and T. C. Wu, “Efficiency improvement and spectral shift of an organic light-emitting device by attaching a hexagon-based microlens array,” J. Opt. A, Pure Appl. Opt. 10(5), 055302 (2008).
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Lin, H. Y.

M. K. Wei, J. H. Lee, H. Y. Lin, Y. H. Ho, K. Y. Chen, C. C. Lin, C. F. Wu, H. Y. Lin, J. H. Tsai, and T. C. Wu, “Efficiency improvement and spectral shift of an organic light-emitting device by attaching a hexagon-based microlens array,” J. Opt. A, Pure Appl. Opt. 10(5), 055302 (2008).
[Crossref]

M. K. Wei, J. H. Lee, H. Y. Lin, Y. H. Ho, K. Y. Chen, C. C. Lin, C. F. Wu, H. Y. Lin, J. H. Tsai, and T. C. Wu, “Efficiency improvement and spectral shift of an organic light-emitting device by attaching a hexagon-based microlens array,” J. Opt. A, Pure Appl. Opt. 10(5), 055302 (2008).
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S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018).
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Liu, S.

K. E. Chong, L. Wang, I. Staude, A. R. James, J. Dominguez, S. Liu, G. S. Subramania, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Efficient polarization-insensitive complex wavefront control using Huygens’ metasurfaces based on dielectric resonant meta-atoms,” ACS Photonics 3(4), 514–519 (2016).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15(8), 5369–5374 (2015).
[Crossref] [PubMed]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Luk, T. S.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15(8), 5369–5374 (2015).
[Crossref] [PubMed]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Luk’yanchuk, B.

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
[Crossref] [PubMed]

Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photon. Rev. 9(4), 412–418 (2015).
[Crossref]

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S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1(3), 030801 (2016).
[Crossref]

Miroshnichenko, A. E.

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
[Crossref] [PubMed]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express 20(18), 20599–20604 (2012).
[Crossref] [PubMed]

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] [PubMed]

Mitchell, A.

Modine, F. A.

G. E. Jellison and F. A. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69(3), 371–373 (1996).
[Crossref]

Neshev, D. N.

K. E. Chong, L. Wang, I. Staude, A. R. James, J. Dominguez, S. Liu, G. S. Subramania, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Efficient polarization-insensitive complex wavefront control using Huygens’ metasurfaces based on dielectric resonant meta-atoms,” ACS Photonics 3(4), 514–519 (2016).
[Crossref]

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3(12), 1504– 1505 (2016).
[Crossref] [PubMed]

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photonics 1(3), 030801 (2016).
[Crossref]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-independent silicon metadevices for efficient optical wavefront control,” Nano Lett. 15(8), 5369–5374 (2015).
[Crossref] [PubMed]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3(6), 813–820 (2015).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Niv, A.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Oh, J.

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

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] [PubMed]

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral Chiral Imaging with a Metalens,” Nano Lett. 16(7), 4595–4600 (2016).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Oikawa, M.

M. Oikawa, H. Imanishi, and T. Kishimoto, “Light coupling characteristics of a planar microlens,” Electron. Commun. Jpn. Part II Electron. 76(10), 10–20 (1993).

Özdemir, A.

A. Özdemir, Z. Hayran, Y. Takashima, and H. Kurt, “Polarization independent high transmission large numerical aperture laser beam focusing and deflection by dielectric Huygens’ metasurfaces,” Opt. Commun. 401, 46–53 (2017).
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Nanoscale Res. Lett. (1)

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Opt. Commun. (1)

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Optica (1)

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J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017).
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Phys. Stat. Solidi A (1)

D. H. Hwang, O. T. Kwon, W. J. Lee, J. W. Hong, and T. W. Kim, “Outcoupling efficiency of organic light-emitting diodes depending on the fill factor and size of the microlens array,” Phys. Stat. Solidi A 211(8), 1773–1777 (2014).

Proc. Natl. Acad. Sci. U.S.A. (1)

R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. U.S.A. 113(38), 10473–10478 (2016).
[Crossref] [PubMed]

Proc. SPIE (1)

C. Levallois, V. Bardinal, C. Vergnenègre, T. Leïchlé, T. Camps, E. Daran, and J.-B. Doucet, “VCSEL collimation using self-aligned integrated polymer microlenses,” Proc. SPIE 6992, 69920W (2008).
[Crossref]

Science (4)

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354(6314), aag2472 (2016).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[Crossref] [PubMed]

Other (2)

arXiv:1803.05637 [physics.optics].

Q. Zhang, T. Liao, G. Gan, M. Li, and X. Cui, “Polarization split lensing via polarization and phase control with metasurfaces at visible frequencies,” Plasmonics, 1–8 (2018).

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Figures (9)

Fig. 1
Fig. 1 Real and imaginary part of the refractive index (n and k) for αTiO2 as a function of wavelength.
Fig. 2
Fig. 2 Schematic structure of metasurface with periodic TiO2 nanopillars (h = 600 nm, P = 250 nm). (a) Top view and side views. (b) Numerically calculated transmission (blue solid line) and phase shift (red circle) of metasurfaces with varied diameter and fixed period P = 250 nm at wavelength λ = 0.532 μm. Transmittance and transmitted light phase variation as a function of TiO2 nanopillar diameter (D) and wavelength (λ) are shown in (c) and (d), respectively.
Fig. 3
Fig. 3 (a) Schematic of the designed broadband dielectric planar isolated metalens with d = 8 μm. TiO2 nanopillars are resting on a SiO2 substrate. The inset gives the top view of the metalens. (b) 3D FDTD simulation results of the electric-field intensity for three cases of metalens diameter at the working wavelength of λ = 532 nm and the graphs are on the same color scale. (c) 3D FDTD simulation results of the electric-field intensity for three wavelengths when d = 2 μm.
Fig. 4
Fig. 4 Dispersion of the metalens phase distribution. Numerical (solid line) simulated and ideal (dashed line) phase distribution at 200 nm above the output surface at the wavelength λ = 450 nm (red), 532 nm (blue) and 650 nm (green).
Fig. 5
Fig. 5 (a) The top view of the 2 × 2 metalens array. Simulation results of the electric-field patterns of 2 × 2 metalens array (d = 2 μm) parallel to the xz plane and at the focal planes for the 532 nm working wavelength, corresponding to a different spacing of (b) 0 μm, (c) 1 μm, and (d) 3 μm. The crosstalk effect between two adjacent metalenses placed side by side is negligible. (e) Electric-field pattern of an isolated metalens.
Fig. 6
Fig. 6 (a) The line-scanning profiles of light intensity across the focal spots of the 2 × 2 metalens array with the spacing of a = 0, 2, 4 μm, shown with the result of the isolated metalens. The crosstalk regions for different cases of the spacing can be clearly observed. (b) The derived focal length and FWHM of the focal spots as the spacing changes. The blue and red dashed lines represent the focal length and FWHM of the isolated metalens (ML).
Fig. 7
Fig. 7 (a) Simulation results of the focal length and FWHM of the metalenses in a 2 × 2 array with the working wavelength λ changing over the visible spectrum (d = 2 μm, a = 0 μm). (b) 3D FDTD simulated electric-field intensity of the focal plane of the metalens array for λ = 0.45 μm and the focusing patterns of horizontal (H) and vertical (V) cross sections. (c) The simulated electric-field intensity of the focal plane for λ = 0.65 μm and the focusing patterns of horizontal (H) and vertical (V) cross sections.
Fig. 8
Fig. 8 (a) Simulation results of the focal length and FWHM of the metalenses in a 2 × 2 array as the diameter of lenses varying from 2 to 8 μm (a = 0 μm, λ = 0.532 μm). (b) The simulated electric-field intensity `of the focal plane of the microlens array for d = 4 μm and the focusing patterns of horizontal (H) and vertical (V) cross sections. (c) The simulated results of the focal plane for d = 8 μm and the focusing patterns of horizontal (H) and vertical (V) cross sections.
Fig. 9
Fig. 9 (a) Simulation results of the focal length and FWHM of the metalenses located in the geometrical center of the array with the scale varying from 2 × 2 to 8 × 8 (a = 0 μm, λ = 0.532 μm, d = 2 μm). (b) The simulated electric-field intensity of the focal plane of the metalens array for n = 3 and the focusing patterns of horizontal (H) and vertical (V) cross sections. (c) The simulated results for n = 8 and the focusing patterns of horizontal (H) and vertical (V) cross sections.

Tables (1)

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Table 1 Derived focusing performance for different cases of the metalens spacing

Equations (5)

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ε 2 (E)={ [ AC E 0 (E E g ) 2 ( E 2 E 0 2 ) 2 + C 2 E 2 . 1 E ], E> E g , 0, E E g ,
ε 1 (E)= ε 1 ()+ 2 π P E g ξ ε 2 (ξ) ξ 2 E 2 d ξ ,
n ˜ =n+ik= ε 1 (E)+i ε 2 (E) ,
Δφ(x,y)= 2πh λ ( n eff ( D 2 ) n eff ( D 1 ) ),
φ(x,y)= 2π λ d ( f f 2 + x 2 + y 2 ),

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