Abstract

Metasurfaces have pioneered a new avenue for advanced wave-front engineering. Among the various types of metasurfaces, Huygens’ metasurfaces are thought to be a novel paradigm for flat optical devices. Enabled by spectrally overlapped electric resonance and magnetic resonance, Huygens’ metasurfaces are imparted with high transmission and full phase coverage of 2π, which makes them capable of realizing high-efficiency wave-front control. However, a defect of Huygens’ metasurfaces is that their phase profiles and transmissive responses are often sensitive to the interaction of neighboring Huygens’ elements. Consequently, the original assigned phase distribution can be distorted. In this work, we present our design strategy of transmissive Huygens’ metasurfaces performing anomalous refraction. We illustrate the investigation of Huygens’ elements, realizing the overlapping between an electric dipole and magnetic dipole resonance based on cross-shaped structures. We find that the traditional discrete equidistant-phase design method is not enough to realize a transmissive Huygens’ surface due to the interaction between neighboring Huygens’ elements. Therefore, we introduce an extra optimization process on the element spacing to palliate the phase distortion resulting from the element interaction. Based on this method, we successfully design unequally spaced three-element transmissive metasurfaces exhibiting anomalous refraction effect. The anomalous refractive angle of the designed Huygens’ metasurface is 30°, which exceeds the angles of most present transmissive Huygens’ metasurfaces. A transmissive efficiency of 83.5% is numerically derived at the operating wavelength. The far-field electric distribution shows that about 93% of transmissive light is directed along the 30° refractive direction. The deflection angle can be tuned by adjusting the number of Huygens’ elements in one metasurface unit cell. The design strategies used in this paper can be inspiring for other functional Huygens’ metasurface schemes.

© 2019 Chinese Laser Press

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References

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2019 (2)

2018 (5)

Z. Wang, X. Ding, K. Zhang, B. Ratni, S. N. Burokur, X. Gu, and Q. Wu, “Huygens metasurface holograms with the modulation of focal energy distribution,” Adv. Opt. Mater. 6, 1800121 (2018).
[Crossref]

L. Zhang, J. Ding, H. Y. Zheng, S. S. An, H. T. Lin, B. W. Zheng, D. Y. Du, G. F. Yin, J. Michon, and Y. F. Zhang, “Ultra-thin high-efficiency mid-infrared transmissive Huygens meta-optics,” Nat. Commun. 9, 1481 (2018).
[Crossref]

A. J. Ollanik, J. A. Smith, M. J. Belue, and M. D. Escarra, “High efficiency all-dielectric Huygens metasurfaces from the ultraviolet to the infrared,” ACS Photon. 5, 1351–1358 (2018).
[Crossref]

Y. Z. Chen and J. Mei, “All-dielectric two-dimensional metasurfaces based on electric and magnetic dipolar Mie resonances,” Europhys. Lett. 122, 54002 (2018).
[Crossref]

J. S. Eismann, M. Neugebauer, and P. Banzer, “Exciting a chiral dipole moment in an achiral nanostructure,” Optica 5, 954–959 (2018).
[Crossref]

2017 (6)

D. Arslan, K. E. Chong, A. Miroshnichenko, D. Y. Choi, D. N. Neshev, T. Pertsch, Y. S. Kivshar, and I. Staude, “Angle-selective all-dielectric Huygens’ metasurfaces,” J. Phys. D 50, 434002 (2017).
[Crossref]

V. E. Babicheva and A. B. Evlyukhin, “Resonant lattice Kerker effect in metasurfaces with electric and magnetic optical responses,” Laser Photon. Rev. 11, 1700132 (2017).
[Crossref]

S. D. Swiecicki and J. E. Sipe, “Surface-lattice resonances in two-dimensional arrays of spheres: multipolar interactions and a mode analysis,” Phys. Rev. B 95, 195406 (2017).
[Crossref]

S. Liu, A. Vaskin, S. Campione, O. Wolf, M. B. Sinclair, J. L. Reno, G. A. Keeler, I. Staude, and I. Brener, “Huygens’ metasurfaces enabled by magnetic dipole resonance tuning in split dielectric nanoresonators,” Nano Lett. 17, 4297–4303 (2017).
[Crossref]

L. Philippe and C. Pierre, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, “Multifunctional interleaved geometric-phase dielectric metasurfaces,” Light Sci. Appl. 6, e17027 (2017).
[Crossref]

2016 (7)

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, 1190–1194 (2016).
[Crossref]

L. Dianmin, F. Pengyu, H. Erez, and L. B. Mark, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2016).
[Crossref]

R. C. Devlin, K. Mohammadreza, W. T. Chen, J. Oh, and F. Capasso, “Broadband high efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. USA 113, 10473–10478 (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 wavelength,” Nano Lett. 16, 7229–7234 (2016).
[Crossref]

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

W. Y. Zhao, H. Jiang, B. Y. Liu, J. Song, and Y. Y. Jiang, “High-efficiency beam manipulation combining geometric phase with anisotropic Huygens surface,” Appl. Phys. Lett. 108, 181102 (2016).
[Crossref]

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, 18468–18477 (2016).
[Crossref]

2015 (7)

M. I. Shalaev, J. B. Sun, A. Tsukernik, A. Pandey, K. Nikolskly, and N. M. Litchinister, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

Z. Guoxing, M. Holger, K. Mitchell, L. Guixin, Z. Thomas, and Z. Shuang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10, 308–312 (2015).
[Crossref]

A. Amir, H. Yu, B. Mahmood, and F. Andrei, “A dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–944 (2015).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, P. Thomas, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9, 195–213 (2015).
[Crossref]

A. Amir, H. Yu, J. B. Alexander, B. Mahmood, and F. Andrei, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

X. Ni, Z. J. Wong, M. Mrejen, Y. Wang, and X. Zhang, “An ultrathin invisibility skin cloak for visible light,” Science 349, 1310–1314 (2015).
[Crossref]

2014 (3)

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

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

Y. Zhao, X.-X. Liu, and A. Alù, “Recent advances on optical metasurfaces,” J. Opt. 16, 035403 (2014).
[Crossref]

2013 (2)

V. N. Gururaj, M. S. Vladimir, and B. Alexandra, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25, 3264–3294 (2013).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Domingguez, 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, 7824–7832 (2013).
[Crossref]

2012 (3)

P. Grahn, A. Shevchenko, and M. Kaivola, “Electromagnetic multipole theory for optical nanomaterials,” New J. Phys. 14, 093033 (2012).
[Crossref]

E. Ringe, M. R. Langille, K. Sohn, J. Zhang, J. Huang, C. A. Mirkin, R. P. Van Duyne, and L. D. Marks, “Plasmon length: a universal parameter to describe size effects in gold nanoparticles,” J. Phys. Chem. Lett. 3, 1479–1483 (2012).
[Crossref]

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, and G. Y. Guo, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
[Crossref]

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, 333–337 (2011).
[Crossref]

2010 (1)

A. B. Evlyukhin, C. Reinhardt, A. Seidel, B. S. Luk’yanchuk, and B. N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. B 82, 45404 (2010).
[Crossref]

1983 (1)

1907 (1)

L. Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philos. Mag. 14, 60–65 (1907).
[Crossref]

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, 333–337 (2011).
[Crossref]

Alexander, J. B.

A. Amir, H. Yu, J. B. Alexander, B. Mahmood, and F. Andrei, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Alexandra, B.

V. N. Gururaj, M. S. Vladimir, and B. Alexandra, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25, 3264–3294 (2013).
[Crossref]

Alù, A.

Y. Zhao, X.-X. Liu, and A. Alù, “Recent advances on optical metasurfaces,” J. Opt. 16, 035403 (2014).
[Crossref]

Amir, A.

A. Amir, H. Yu, B. Mahmood, and F. Andrei, “A dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–944 (2015).
[Crossref]

A. Amir, H. Yu, J. B. Alexander, B. Mahmood, and F. Andrei, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

An, S. S.

L. Zhang, J. Ding, H. Y. Zheng, S. S. An, H. T. Lin, B. W. Zheng, D. Y. Du, G. F. Yin, J. Michon, and Y. F. Zhang, “Ultra-thin high-efficiency mid-infrared transmissive Huygens meta-optics,” Nat. Commun. 9, 1481 (2018).
[Crossref]

Andrei, F.

A. Amir, H. Yu, J. B. Alexander, B. Mahmood, and F. Andrei, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

A. Amir, H. Yu, B. Mahmood, and F. Andrei, “A dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–944 (2015).
[Crossref]

Arbabi, A.

Arbabi, E.

Arslan, D.

D. Arslan, K. E. Chong, A. Miroshnichenko, D. Y. Choi, D. N. Neshev, T. Pertsch, Y. S. Kivshar, and I. Staude, “Angle-selective all-dielectric Huygens’ metasurfaces,” J. Phys. D 50, 434002 (2017).
[Crossref]

Babicheva, V. E.

V. E. Babicheva and A. B. Evlyukhin, “Resonant lattice Kerker effect in metasurfaces with electric and magnetic optical responses,” Laser Photon. Rev. 11, 1700132 (2017).
[Crossref]

Banzer, P.

Belue, M. J.

A. J. Ollanik, J. A. Smith, M. J. Belue, and M. D. Escarra, “High efficiency all-dielectric Huygens metasurfaces from the ultraviolet to the infrared,” ACS Photon. 5, 1351–1358 (2018).
[Crossref]

Boyraz, O.

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

Brener, I.

S. Liu, A. Vaskin, S. Campione, O. Wolf, M. B. Sinclair, J. L. Reno, G. A. Keeler, I. Staude, and I. Brener, “Huygens’ metasurfaces enabled by magnetic dipole resonance tuning in split dielectric nanoresonators,” Nano Lett. 17, 4297–4303 (2017).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, P. Thomas, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Domingguez, 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, 7824–7832 (2013).
[Crossref]

Brongersma, M. L.

E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, “Multifunctional interleaved geometric-phase dielectric metasurfaces,” Light Sci. Appl. 6, e17027 (2017).
[Crossref]

Burokur, S. N.

Z. Wang, X. Ding, K. Zhang, B. Ratni, S. N. Burokur, X. Gu, and Q. Wu, “Huygens metasurface holograms with the modulation of focal energy distribution,” Adv. Opt. Mater. 6, 1800121 (2018).
[Crossref]

Bykov, A. Y.

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9, 195–213 (2015).
[Crossref]

Campione, S.

S. Liu, A. Vaskin, S. Campione, O. Wolf, M. B. Sinclair, J. L. Reno, G. A. Keeler, I. Staude, and I. Brener, “Huygens’ metasurfaces enabled by magnetic dipole resonance tuning in split dielectric nanoresonators,” Nano Lett. 17, 4297–4303 (2017).
[Crossref]

Capasso, F.

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, 1190–1194 (2016).
[Crossref]

R. C. Devlin, K. Mohammadreza, W. T. Chen, J. Oh, and F. Capasso, “Broadband high efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. USA 113, 10473–10478 (2016).
[Crossref]

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Y. Zhao, X.-X. Liu, and A. Alù, “Recent advances on optical metasurfaces,” J. Opt. 16, 035403 (2014).
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L. Zhang, J. Ding, H. Y. Zheng, S. S. An, H. T. Lin, B. W. Zheng, D. Y. Du, G. F. Yin, J. Michon, and Y. F. Zhang, “Ultra-thin high-efficiency mid-infrared transmissive Huygens meta-optics,” Nat. Commun. 9, 1481 (2018).
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L. Zhang, J. Ding, H. Y. Zheng, S. S. An, H. T. Lin, B. W. Zheng, D. Y. Du, G. F. Yin, J. Michon, and Y. F. Zhang, “Ultra-thin high-efficiency mid-infrared transmissive Huygens meta-optics,” Nat. Commun. 9, 1481 (2018).
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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, 1190–1194 (2016).
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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 wavelength,” Nano Lett. 16, 7229–7234 (2016).
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ACS Nano (1)

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Domingguez, 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, 7824–7832 (2013).
[Crossref]

ACS Photon. (1)

A. J. Ollanik, J. A. Smith, M. J. Belue, and M. D. Escarra, “High efficiency all-dielectric Huygens metasurfaces from the ultraviolet to the infrared,” ACS Photon. 5, 1351–1358 (2018).
[Crossref]

Adv. Mater. (1)

V. N. Gururaj, M. S. Vladimir, and B. Alexandra, “Alternative plasmonic materials: beyond gold and silver,” Adv. Mater. 25, 3264–3294 (2013).
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Adv. Opt. Mater. (2)

Z. Wang, X. Ding, K. Zhang, B. Ratni, S. N. Burokur, X. Gu, and Q. Wu, “Huygens metasurface holograms with the modulation of focal energy distribution,” Adv. Opt. Mater. 6, 1800121 (2018).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, P. Thomas, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

APL Photon. (1)

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

Appl. Phys. Lett. (2)

Y. Huang, Q. Zhao, S. K. Kalyoncu, R. Torun, Y. Lu, F. Capolino, and O. Boyraz, “Phase-gradient gap-plasmon metasurface based blazed grating for real time dispersive imaging,” Appl. Phys. Lett. 104, 161106 (2014).
[Crossref]

W. Y. Zhao, H. Jiang, B. Y. Liu, J. Song, and Y. Y. Jiang, “High-efficiency beam manipulation combining geometric phase with anisotropic Huygens surface,” Appl. Phys. Lett. 108, 181102 (2016).
[Crossref]

Europhys. Lett. (1)

Y. Z. Chen and J. Mei, “All-dielectric two-dimensional metasurfaces based on electric and magnetic dipolar Mie resonances,” Europhys. Lett. 122, 54002 (2018).
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J. Opt. (1)

Y. Zhao, X.-X. Liu, and A. Alù, “Recent advances on optical metasurfaces,” J. Opt. 16, 035403 (2014).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. Chem. Lett. (1)

E. Ringe, M. R. Langille, K. Sohn, J. Zhang, J. Huang, C. A. Mirkin, R. P. Van Duyne, and L. D. Marks, “Plasmon length: a universal parameter to describe size effects in gold nanoparticles,” J. Phys. Chem. Lett. 3, 1479–1483 (2012).
[Crossref]

J. Phys. D (1)

D. Arslan, K. E. Chong, A. Miroshnichenko, D. Y. Choi, D. N. Neshev, T. Pertsch, Y. S. Kivshar, and I. Staude, “Angle-selective all-dielectric Huygens’ metasurfaces,” J. Phys. D 50, 434002 (2017).
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Laser Photon. Rev. (3)

V. E. Babicheva and A. B. Evlyukhin, “Resonant lattice Kerker effect in metasurfaces with electric and magnetic optical responses,” Laser Photon. Rev. 11, 1700132 (2017).
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L. Philippe and C. Pierre, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

A. E. Minovich, A. E. Miroshnichenko, A. Y. Bykov, T. V. Murzina, D. N. Neshev, and Y. S. Kivshar, “Functional and nonlinear optical metasurfaces,” Laser Photon. Rev. 9, 195–213 (2015).
[Crossref]

Light Sci. Appl. (1)

E. Maguid, I. Yulevich, M. Yannai, V. Kleiner, M. L. Brongersma, and E. Hasman, “Multifunctional interleaved geometric-phase dielectric metasurfaces,” Light Sci. Appl. 6, e17027 (2017).
[Crossref]

Nano Lett. (4)

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 wavelength,” Nano Lett. 16, 7229–7234 (2016).
[Crossref]

S. Sun, K. Y. Yang, C. M. Wang, T. K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. T. Kung, and G. Y. Guo, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
[Crossref]

M. I. Shalaev, J. B. Sun, A. Tsukernik, A. Pandey, K. Nikolskly, and N. M. Litchinister, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15, 6261–6266 (2015).
[Crossref]

S. Liu, A. Vaskin, S. Campione, O. Wolf, M. B. Sinclair, J. L. Reno, G. A. Keeler, I. Staude, and I. Brener, “Huygens’ metasurfaces enabled by magnetic dipole resonance tuning in split dielectric nanoresonators,” Nano Lett. 17, 4297–4303 (2017).
[Crossref]

Nat. Commun. (2)

L. Zhang, J. Ding, H. Y. Zheng, S. S. An, H. T. Lin, B. W. Zheng, D. Y. Du, G. F. Yin, J. Michon, and Y. F. Zhang, “Ultra-thin high-efficiency mid-infrared transmissive Huygens meta-optics,” Nat. Commun. 9, 1481 (2018).
[Crossref]

A. Amir, H. Yu, J. B. Alexander, B. Mahmood, and F. Andrei, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
[Crossref]

Nat. Mater. (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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Figures (9)

Fig. 1.
Fig. 1. (a) Sketch of an isolated cross-shaped silicon structure. Fixed parameters include ly=700  nm, wy=150  nm, h=400  nm, and wx=140  nm. (b) Simulation unit cell of a periodical cross-shaped structure array, consisting of a cross-shaped particle, substrate, and coating layer. The thicknesses of the substrate and coating layer are 200 and 500 nm, respectively, and Px=Py=1  μm. (c) Sketch of the dipolar moments induced in the two arms of the cross-shaped particle. The gray-colored area depicts the top view of the particle. (d) Sketch of the proposed refracting metasurface. The three cross-shaped elements in the structure are marked as C1, C2, and C3, respectively. Fixed parameters are the same as in (a). The refractive index of the substrate is set as 1.45, while the refractive index of the coating layer is set as 1.4. The refractive index of the silicon is set as 3.5. The ordinate origin is set as the center of the cross particle for (a) and (b), while it is set as the center of the cross particle C2 for the structure in (d).
Fig. 2.
Fig. 2. (a) Scattering cross sections of ED and MD components varying with x arm length lx. (b) ED and MD resonant wavelengths as a function of lx for an isolated cross-shaped particle.
Fig. 3.
Fig. 3. (a) Spectral reflection and (b) spectral phase as a function of the structure parameter lx in Fig. 1(b).
Fig. 4.
Fig. 4. Electric field magnitude distributions |E|2 at the (a) first reflection peak and (b) second reflection peak in Fig. 3(a). Electric field vector distribution at the (c) first reflection peak and (b) second reflection peak in Fig. 3(a). The incident electric field is along the negative x direction. The variable lx is set as 0.27 μm. (a)–(d) are the electric field distributions at the y=0 plane.
Fig. 5.
Fig. 5. (a)–(c) Electric field distributions of the periodically arranged cross-shaped structures E1, E2, and E3, respectively, at 1.507 μm. (d) Electric field distribution of one unit cell of the metasurface configuration 1, consisting of three elements, namely E1, E2, and E3. (a)–(d) depict the electric field distributions at the y=0 plane. (e) Phase distribution of the metasurface configuration 1 at 1.493 μm. Three unit cells (UCs), marked as UC1, UC2, and UC3, are plotted to have a comfortable aspect ratio for the figure. (f) Spectral transmission for the proposed three configurations.
Fig. 6.
Fig. 6. (a) Top view of the metasurface configuration 1. (b) Top view of the metasurface configuration 2. The parameters of each element stay unchanged, while only the spaces d1 and d2 between three elements change from 1 to 0.86 μm. (c) Top view of the metasurface configuration 3. Element parameters lx are optimized. The optimized parameters lx of the three elements are 0.3, 0.4, and 0.56 μm, respectively. (d) Calculated phase distribution of the second configuration of the metasurface; the operating wavelength is 1.495 μm. (e) Calculated phase distribution of the third configuration of the metasurface; the incident wavelength is 1.521 μm.
Fig. 7.
Fig. 7. (a) Transmissive response of the metasurface varying with the element spacing d. Black dotted line marks the applied working wavelength. (b) Phase response along the x direction inside a metasurface unit cell varying with the element spacing d at working wavelength. The parameters lx of the three elements are 0.3, 0.4, and 0.56 μm, respectively.
Fig. 8.
Fig. 8. Far-field transmitting intensity (T.I.) for the three configurations at different diffraction angles. The transmitting intensity is normalized to the total transmission intensity.
Fig. 9.
Fig. 9. Phase distribution of the Huygens’ metasurfaces consisting of different element numbers. (a) Four-element Huygens’ metasurface. (b) Five-element Huygens’ metasurface. (c) Six-element Huygens’ metasurface. Each figure consists of two unit cells to better show the anomalous deflection effect. The spacing between neighboring elements in these three configurations is set as 0.86 μm for simplicity. Other parameters are listed in Table 2.

Tables (2)

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Table 1. First Configuration of the Phase Gradient Metasurfacea

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Table 2. Crucial Parameters of the Huygens’ Metasurfaces Consisting of Different Numbers of Huygens’ Elementsa

Equations (6)

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aE(l,m)=(i)(l1)k2ηOlmE0[π(2l+1)]1/2exp(imϕ){[Ψl(kr)+Ψl(kr)]·Plm(cosθ)r^·JS,j(r)+Ψl(kr)kr[τlm(θ)θ^·JS,j(r)iπlm(θ)ϕ^·JS,j(r)]}d3raM(l,m)=(i)(l1)k2ηOlmE0[π(2l+1)]1/2exp(imϕ)jl(k,r)[τlm(θ)ϕ^·JS,j(r)+iπlm(θ)θ^·JS,j(r)]}d3r,
Cs=πk2l=1m=ll(2l+1)[|aE(l,m)|2+|aM(l,m)|2].
σED=3πk2m=11|aE(1,m)|2,σMD=3πk2m=11|aM(1,m)|2,
ε0/αeffED=ε0/αEDks2Gxx0/2,1/αeffMD=1/αMDks2Gyy0/2,
r=iks2DL(αeffEDαeffMD),t=1iks2DL(αeffEDαeffMD),
θt=arcsin{1nt[λ0P+(sinθi)ni]},