Abstract

This article reviews recent progress leading to the realization of planar optical components made of a single layer of phase shifting nanostructures. After introducing the principles of planar optics and discussing earlier works on subwavelength diffractive optics, we introduce a classification of metasurfaces based on their different phase mechanisms and profiles and a comparison between plasmonic and dielectric metasurfaces. We place particular emphasis on the recent developments on electric and magnetic field control of light with dielectric nanostructures and highlight the physical mechanisms and designs required for efficient all-dielectric metasurfaces. Practical devices of general interest such as metalenses, beam deflectors, holograms, and polarizing interfaces are discussed, including high-performance metalenses at visible wavelengths. Successful strategies to achieve achromatic response at selected wavelengths and near unity transmission/reflection efficiency are discussed. Dielectric metasurfaces and dispersion management at interfaces open up technology opportunities for applications including wavefront control, lightweight imaging systems, displays, electronic consumer products, and conformable and wearable optics.

© 2017 Optical Society of America

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2016 (13)

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: from microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
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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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R. C. Devlin, M. Khorasaninejad, W.-T. Chen, J. Oh, and F. Capasso, “Broadband high efficiency dielectric metasurfaces at visible wavelengths,” Proc. Natl. Acad. Sci. USA 113, 10473–10478 (2016).
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M. Khorasaninejad, A. 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, 7229–7234 (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 Photon. 3, 209–214 (2016).
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Y. Li, X. Li, M. Pu, Z. Zhao, X. Ma, Y. Wang, and X. Luo, “Achromatic flat optical components via compensation between structure and material dispersions,” Sci. Rep. 6, 19885 (2016).
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P. Wang, N. Mohammad, and R. Menon, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6, 21545 (2016).
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J. Y. H. Teo, L. J. Wong, C. Molardi, and P. Genevet, “Controlling electromagnetic fields at boundaries of arbitrary geometries,” Phys. Rev. A 94, 013824 (2016).
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S. M. Kamali, A. Arbabi, E. Arbabi, Y. Horie, and A. Faraon, ”Decoupling optical function and geometrical form using conformal flexible dielectric metasurfaces,” Nat. Commun. 7, 11618 (2016).
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N. M. Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6, 041008 (2016).
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M. Khorasaninejad, A. Ambrosio, P. Kanhaiya, and F. Capasso, “Broadband and chiral binary dielectric meta-holograms,” Sci. Adv. 2, e1501258 (2016).
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E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3, 628 (2016).
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S. Zhang, M.-H. Kim, F. Aieta, A. She, T. Mansuripur, I. Gabay, M. Khorasaninejad, D. Rousso, X. Wang, M. Troccoli, N. Yu, and F. Capasso, “High efficiency near diffraction-limited mid-infrared flat lenses based on metasurface reflectarrays,” Opt. Express 24, 18024–18034 (2016).
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2015 (18)

B. Desiatov, N. Mazurski, Y. Fainman, and U. Levy, “Polarization selective beam shaping using nanoscale dielectric metasurfaces,” Opt. Express 23, 22611–22618 (2015).
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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, 33310–33317 (2015).
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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, 5369–5374 (2015).
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U. Zywietz, M. K. Schmidt, A. B. Evlyukhin, C. Reinhardt, J. Aizpurua, and B. N. Chichkov, “Electromagnetic resonances of silicon nanoparticle dimers in the visible,” ACS Photon. 2, 913–920 (2015).
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M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
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N. Xi, Z. J. Wong, M. Mrejen, Y. Wang, and X. Zhang, “An ultrathin invisibility skin cloak for visible light,” Science 349, 1310–1314 (2015).
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D. Wen, F. Yue, G. Li, G. Zheng, K. Chan, S. Chen, M. Chen, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, S. Zhang, and X. Chen, “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6, 8241 (2015).
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M. Khorasaninejad and F. Capasso, “Broadband multifunctional efficient meta-gratings based on dielectric waveguide phase shifters,” Nano Lett. 15, 6709–6715 (2015).
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G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10, 308–312 (2015).
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F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347, 1342–1345 (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, 813–820 (2015).
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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, 937–943 (2015).
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P. Moitra, B. A. Slovick, W. Li, I. I. Kravchencko, D. P. Briggs, S. Krishnamurthy, and J. Valentine, “Large-scale all-dielectric metamaterial perfect reflectors,” ACS Photon. 2, 692–698 (2015).
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Y. F. Yu, A. Y. Zhu, R. Paniagua-Dominguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Adv. Opt. Mater. 3, 813–820 (2015).
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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, 7069 (2015).
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W. Luo, S. Xiao, Q. He, S. Sun, and L. Zhou, “Photonic spin Hall effect with nearly 100% efficiency,” Adv. Opt. Mater. 3, 1102–1108 (2015).
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X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light Sci. Appl. 4, E290 (2015).
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P. Genevet and F. Capasso, “Holographic optical metasurfaces: a review of current progress,” Rep. Prog. Phys. 78, 024401 (2015).
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2014 (15)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3, E167 (2014).
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Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14, 1394–1399 (2014).
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H. Liu, M. Q. Mehmood, K. Huang, L. Ke, H. Ye, P. Genevet, M. Zhang, A. Danner, S. P. Yeo, C.-W. Qiu, and J. Teng, “Twisted focusing of optical vortices with broadband flat spiral zone plates,” Adv. Opt. Mater. 2, 1193–1198 (2014).
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S. Collin, “Nanostructure arrays in free-space: optical properties and applications,” Rep. Prog. Phys. 77, 126402 (2014).
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A. B. Evlyukhin, R. L. Eriksen, W. Cheng, J. Beermann, C. Reinhardt, A. Petrov, S. Prorok, M. Eich, B. N. Chichkov, and S. I. Bozhevolnyi, “Optical spectroscopy of single Si nanocylinders with magnetic and electric resonances,” Sci. Rep. 4, 4126 (2014).
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P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104, 171102 (2014).
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D. Lin, P. Fan, E. Hasman, and M. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).

K. B. Crozier and M. Khorasaninejad, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
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X. H. Ling, X. X. Zhou, W. X. Shu, H. L. Luo, and S. C. Wen, “Realization of tunable photonic spin Hall effect by tailoring the Pancharatnam-Berry phase,” Sci. Rep. 4, 5557 (2014).
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W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization- controlled dual images,” Nano Lett. 14, 225–230 (2014).
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S. Vo, D. Fattal, W. V. Sorin, Z. Peng, T. Tran, M. Fiorentino, and R. G. Beausoleil, “Sub-wavelength grating lenses with a twist,” IEEE Photon. Technol. Lett. 26, 1375–1378 (2014).
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L. Xu and H. Chen, “Conformal transformation optics,” Nat. Photonics 9, 15–23 (2014).
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P. Rauter, J. Lin, P. Genevet, S. P. Khanna, M. Lachab, A. Giles Davies, E. H. Linfield, and F. Capasso, “Electrically pumped semiconductor laser with monolithic control of circular polarization,” Proc. Natl. Acad. Sci. USA 111, E5623–E5632 (2014).
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S. Liu, M. B. Sinclair, T. S. Mahony, Y. C. Jun, S. Campione, J. Ginn, D. A. Bender, J. R. Wendt, J. F. Ihlefeld, P. G. Clem, J. B. Wright, and I. Brener, “Optical magnetic mirrors without metals,” Optica 1, 250–256 (2014).
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2013 (13)

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
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N. I. Zheludev and T. F. Rogers, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15, 094008 (2013).
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S. Person, M. Jain, Z. Lapin, J. J. Sáenz, G. Wicks, and L. Novotny, “Demonstration of zero optical backscattering from single nanoparticles,” Nano Lett. 13, 1806–1809 (2013).
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J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13, 4269–4274 (2013).
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Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4, 1527 (2013).
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A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett. 13, 829–834 (2013).
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A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
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N. Yu, P. Genevet, F. Aieta, M. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
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A. Grbic and C. Pfeiffer, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
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X. J. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013).
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L. L. Huang, X. Z. Chen, H. Mühlenbernd, H. Zhang, and S. M. Chen, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
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N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340, 724–726 (2013).
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2012 (14)

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C.-W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
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X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
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S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient metasurfaces,” Nano Lett. 12, 6223–6229 (2012).
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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, 4932–4936 (2012).
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M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. USA 109, 12364–12368 (2012).
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F. Aieta, P. Genevet, N. F. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12, 1702–1706 (2012).
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P. Genevet, N. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012).
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A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, and S. I. Bozhevolnyi, “Chichkov demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749–3755 (2012).
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A. I. Kuznetsov, A. E. Miroshnichenko, Y. H. Fu, J. Zhang, and B. Luk’yanchuk, “Magnetic light,” Sci. Rep. 2, 492 (2012).
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J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclair, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108, 097402 (2012).
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J. M. Geffrin, B. García-Cámara, R. Gómez-Medina, P. Albella, L. Froufe-Pérez, C. Eyraud, A. Litman, R. Vaillon, F. González, and M. Nieto-Vesperinas, “Magnetic and electric coherence in forward-and back-scattered electromagnetic waves by a single dielectric subwavelength sphere,” Nat. Commun. 3, 1171 (2012).
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S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett. 37, 2391–2393 (2012).
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B. Rolly, B. Stout, and N. Bonod, “Boosting the directivity of optical antennas with magnetic and electric dipolar resonant particles,” Opt. Express 20, 20376–20386 (2012).
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C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photon. 4, 379–440 (2012).
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2011 (9)

M. Nieto-Vesperinas, R. Gomez-Medina, and J. J. Saenz, “Angle-suppressed scattering and optical forces on submicrometer dielectric particles,” J. Opt. Soc. Am. A 28, 54–60 (2011).
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E. H. Khoo, E. P. Li, and K. B. Crozier, “Plasmonic wave plate based on subwavelength nanoslits,” Opt. Lett. 36, 2498–2500 (2011).
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B. Memarzadeh and H. Mosallaei, “Array of planar plasmonic scatterers functioning as light concentrator,” Opt. Lett. 36, 2569–2571 (2011).
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M. A. Kats, N. Yu, P. Genevet, Z. Gaburro, and F. Capasso, “Effect of radiation damping on the spectral response of plasmonic components,” Opt. Express 19, 21748–21753 (2011).
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J. Li, D. Fattal, M. Fiorentino, and R. G. Beausoleil, “Strong optical confinement between nonperiodic flat dielectric gratings,” Phys. Rev. Lett. 106, 193901 (2011).
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P.-Y. Chen and A. Alù, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84, 205110 (2011).
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R. Gomez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, and J. José Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophotonics 5, 053512 (2011).
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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, 333–337 (2011).
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Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
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2010 (7)

C. G. M. Ryan, M. Z. Chaharmir, J. Shaker, J. R. Bray, Y. M. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Trans. Antennas Propag. 58, 1486–1493 (2010).
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P. Padilla, A. Muñoz-Acevedo, M. Sierra-Castaner, and M. Sierra-Perez, “Electronically reconfigurable transmitarray at Ku band for microwave applications,” IEEE Trans. Antennas Propag. 58, 2571–2579 (2010).
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N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
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C. Ryan, M. Chaharmir, J. Shaker, J. Bray, Y. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Trans. Antennas Propag. 58, 1486–1493 (2010).
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2009 (3)

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D. Lin, P. Fan, E. Hasman, and M. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).

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C. Huygens, Traite De La Lumiere (Van Der Aa, 1690).

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Figures (10)

Fig. 1.
Fig. 1.

(a) According to Huygens’ construction, each element of a wavefront may be regarded as the center of a secondary disturbance that gives rise to spherical wavelets; the position of the wavefront at any later time is given by the envelope of all such wavelets [51]. (b) Through the introduction of phase shifts for each spherical wavelet by means of subwavelength spaced and thick optical elements, the wavefront at any time later can be designed to have any desired profile. In our schematic, the retardations vary in a form of a linear gradient along the plane of incidence in the z direction (meaning that φ x = 0 ) to refract light at user-defined angles in the plane of incidence. Note that in this schematic, we have assumed that there is no reflected light. This is correct if the metasurface is impedance matched. Such interfaces are dubbed Huygens metasurfaces and have been proposed and realized in [52].

Fig. 2.
Fig. 2.

This table summarizes different solutions proposed to address wavefront control with metasurfaces. In the top panel from (a)–(c), the optical response of the nanostructures is tailored by changing the geometry of each individual resonator forming the metasurface. Metasurfaces based on resonance tuning of dielectrics can achieve a phase coverage up to 2 π using TE and TM modes, while resonant tuning metasurfaces based on thin plasmonic rod antennas cannot cover the entire 2 π phase range. From (d)–(g), metasurfaces based on the PB phase present very high scattering efficiencies, both in reflection and in transmission. PB metasurfaces must, however, be addressed with circularly or elliptically polarized light. (h)–(k) Metasurfaces that work by using both resonant tuning and PB phase tuning have also been demonstrated. (a) is adapted from [31], (b) is adapted from [57], (c) is adapted from [58], (d) is adapted from [18], (e) is adapted from [59], (f) is adapted from [60], (g) is adapted from [27], (h) is adapted from [13], (i) is adapted from [19], (j) is adapted from [61], and (k) is adapted from [33].

Fig. 3.
Fig. 3.

Schematic representations of the electric fields in (a, b) plasmonic resonators and in (c) a dielectric sphere. Plasmonic rod antennas support only electric resonances with negligible magnetic contribution. Strong magnetic dipole resonance can be achieved in plasmonic particles by shaping the metallic rod in the form of a split ring resonator [71]. (d) Rectangular dielectric nanoparticles also exhibit electric and magnetic polarizabilities. Shown are the electric dipole (ED), magnetic dipole (MD), and total scattering cross sections (arbitrary units) associated with the corresponding modes shown in (e) and (f) [72].

Fig. 4.
Fig. 4.

(a) Schematic representations of forward and backward scattering properties of a submicrometer dielectric particle. (b) Scattering diagrams for a 240 nm germanium sphere; the refractive index n s p = 4 is constant and real in this wavelength range. Both polarizations, with the incident electric field parallel (TM or p polarization) or normal (TE or s polarization) to the plane of incidence are considered. (c) The total extinction cross section Q ext (black solid line) versus wavelength depends on the contribution of each term in the Mie expansion. The red line corresponds to the magnetic dipole contribution, the blue curve to the electric dipole contribution, and the pink around 1.4 μm is attributed to the magnetic quadrupole. Forward/backward scattering is obtained when the electric and magnetic dipole resonances overlap in-phase/phase-opposition as denoted by the pink/orange highlighted region in the diagram around 1.8 μm/2.2 μm. The scattering diagrams presented in (b) correspond to these regions. (d) Amplitude and phase of the scattered field as functions of the wavelength of an idealized subwavelength array of loss-less nanodisks with electric and magnetic dipole resonances of equal strength and width under plane-wave illumination. (e) Numerically calculated transmittance intensity (red solid line) and phase (blue line) for an array of silicon nanoposts ( radius = 242    nm , height = 220    nm ) embedded in a homogeneous medium with optimized refractive index ( n = 1.66 ). Resonance occurs at a design wavelength of 1340    nm . Note the 2 π phase coverage. (f) Schematic illustration superimposed with the finite elements simulation results of near-field distribution of light scattered by a single 715 nm tall circular amorphous silicon nanopost with a diameter of 150 nm in air. (b, c) are adapted from [73]; (d, e) are adapted from [74]; and (f) is adapted from [75].

Fig. 5.
Fig. 5.

(a) Schematic diagram of a transmissive planar lens. (b) Side view of TiO 2 nanofin on a glass substrate, showing its height. (c) Top view of the lens building block with dimensions S × S depicting nanofin width W and length L . (d) Simulation results showing the nanofin conversion efficiency that peaks at three design wavelengths of 405, 532, and 660 nm. (e) Measured focusing efficiency of the fabricated planar lenses designed at wavelengths of 660 and 532 nm. A scanning electron microscopy (SEM) image showing fabricated TiO 2 metasurfaces based on array of nanofins of 60 × 170    nm dimensions is presented in Fig 2(f). Figures are adapted from [60].

Fig. 6.
Fig. 6.

Measured focal spot profiles of the planar lenses designed at wavelengths of (a) 405 nm, (b) 532 nm, and (c) 660 nm. (d) Imaging with a metalens designed at λ = 532    nm with diameter D = 2    mm and focal length f = 0.725    mm . Image of the 1951 USAF resolution test chart formed by the metalens. The laser wavelength is set at 530 nm. Scale bar, 40 μm. Figures are adapted from [60].

Fig. 7.
Fig. 7.

(a) False color SEM image of four pixels of the chiral transmission dielectric hologram made of Si nanofins on glass. Each pixel consists of two parts: in purple, a meta-grating that imparts the required phase map for letter “L” and, in green, that for the phase map for letter “R.” Nanofins have width W = 85    nm , length L = 350    nm , height H = 1000    nm , and center-to-center distance of 500 nm. Scale bar is 1 μm. (b) Side-view SEM image of a portion of the chiral hologram. Scale bar is 1 μm. (c)–(e) Holographic images formed in the first diffraction order (false colored) under different incident polarizations at wavelength λ = 1350    nm . The chiral hologram was illuminated by (c) right-circularly, (d) left-circularly, and (e) linearly polarized light, which result in the appearance of the letters “R,” “L,” and “RL,” respectively. (f) Schematic of the nanorod distribution for the merged metasurface reflective hologram made of silver nanorods on glass with a silver back plane. The phase levels are denoted by the different colors of the nanorods. The nanorods in the columns with odd numbers and even numbers, starting from the left, contribute to the reconstruction of “bee” and “flower,” respectively. (g) Experimentally obtained images for the incident light with left-circular (top) and right-circular (bottom) polarization. The wavelength of the incident light is 524 nm. Figures (a)–(e) are adapted from [116] and (f)–(h) from [105].

Fig. 8.
Fig. 8.

(a) Refractive and diffractive optics are inherently dispersive, while metasurfaces can be designed to have an achromatic response. In the first two cases, the angles of deflection change as a function of wavelength. The achromatic metasurface consisting of subwavelength spaced resonators is designed to preserve its operation for multiple wavelengths. (b) Side view of the metasurface made of 240 unit cells, each consisting of a slot of the same width s , comprising two coupled rectangular dielectric resonators of fixed height t and varying widths w 1 and w 2 (inset). The metasurface is designed to diffract normally incident plane waves at three wavelengths ( λ 1 = 1300    nm , λ 2 = 1550    nm , and    λ 3 = 1800    nm ) by the same angle ( θ 0 = 17 ° ) by implementing a wavelength-dependent linear phase profile φ m that compensates the wavelength-dependent propagation phase in air. (c) and (d) Numerical simulation and the experimental data of the far-field intensity distribution (normalized to the maximum value for each of the three wavelengths) as a function of the angle θ from the normal to the interface. (e) SEM images of Si nanoparticle dimer structures on a glass substrate. (f) Energy-level diagram describing the hybridization of electric (red arrows) and magnetic (green arrows) dipolar resonances of single scatterers. (g) Calculated scattering intensities of dimer structures (solid red line) for separations of d = 320 , 100, 50, and 5 nm (top to bottom) compared to the experimental results (black line). The spectra are decomposed according to the hybridization scheme of electric and magnetic modes. Each single scatterer is an oblate ellipsoidal core(c-Si)–shell( SiO 2 ) structure with major and minor external radii of 95 and 78 nm, respectively, and a 4 nm oxide layer. Panels (a)–(d) are adapted from [72] and panels (e)–(g) are adapted from [118].

Fig. 9.
Fig. 9.

(a) Photograph of four chromatic-aberration-corrected diffractive lenses (CACDLs) patterned on a glass substrate. (b) 1D CACDL is comprised of linear grooves with a designed height, hi by a single step lithography on SC1827 photoresist. (c) SEM images of the cross sections of two CACDLs (scale bars: 5 μm). (d) Simulated (black) and measured (red) optical efficiency as a function of wavelength. Insets: photographs of the focus on a white observation screen at various wavelengths. The figure is adapted with permission from [122].

Fig. 10.
Fig. 10.

(a) 2D planar metasurface of subwavelength thickness. For planar interfaces, generalized sheet boundary conditions readily apply, and the surface susceptibility tensors can be calculated. (b) The local coordinate system of the surface follows its local curvature, changing with the position along the interface. Boundary conditions of the fields are obtained in the coordinate system of the interface and are therefore position dependent. To produce an effect equivalent to that in (a), the surface susceptibilities of the optical interface have to be engineered to account for the effect of the physical distortion. The dashed blue lines denote the equiphase fronts of the electromagnetic fields. The figure is adapted with permission from [130].

Equations (10)

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{ cos θ t sin ϕ t = λ 0 2 π · n t φ x , n t sin θ t n i sin θ i = λ 0 2 π φ z ,
{ cos θ r sin ϕ r = λ 0 2 π · n i φ x , sin θ r sin θ i = λ 0 2 π · n i φ z ,
d 2 x d t 2 + γ m d x d t + k m x = q m E 0 e i ω t + 2 q 2 3 m c 3 d 3 x d t 3 .
x ( t ) = A E 0 ( ω 0 2 ω 2 ) + i ( ω Γ a + ω 3 Γ s ) e i ω t ,
T ( 0 ) = 1 2 ( t u u + t v v ) I ^ + i 2 ( t u v t v u ) σ ^ 3 + 1 2 ( t u u t v v ) σ ^ 1 + 1 2 ( t u v + t v u ) σ ^ 2 .
T ( φ ) = 1 2 ( t u u + t v v ) I ^ + i 2 ( t u v t v u ) σ ^ 3 + 1 2 ( t u u t v v ) ( e i 2 φ σ ^ + + e i 2 φ σ ^ ) + 1 2 ( t u v + t v u ) ( e i 2 φ σ ^ + + e i 2 φ σ ^ )
α e = 3 i ϵ 2    k 3 a 1 and α m = 3 i 2    μ k 3 b 1 ,
σ s ( π ) = 4 π k 4 ( | ϵ 1 α e | 2 + | μ α m | 2 ) [ 1 + cos ( π Δ φ α ) ] ,
ϕ ( x , y ) = 2 π λ ( x 2 + y 2 + f 2 f ) ,
φ tot ( r , λ ) = φ m ( r , λ ) + φ p ( r , λ ) ,

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