Abstract

Recent advances in metasurfaces, i.e., artificial arrays of engineered inclusions assembled over a thin surface, have opened promising venues to control electromagnetic waves in unique and unprecedented ways, by means of locally engineering their near-field wave–matter interactions. Gradient or locally nonperiodic metasurfaces are one of the most exciting recent advances in nano-optics, due to the promise of enabling ultimate light molding, in both the near-field and the far-field, with large efficiency and a minimal footprint. These artificial surfaces are characterized by a transverse variation of their surface properties and lack of local periodicity, distinguishing them from conventional frequency selective surfaces and optical gratings. In this paper, we review recent work in the area of gradient metasurfaces, aimed at arbitrary wave shaping. The significant recent progress and novel applications achieved through optical metasurfaces, including ultrathin invisibility cloaks and polarization-dependent light splitting, are discussed, outlining the typical challenges and their outstanding prospects in integrated nanophotonic devices. Following our discussion on metasurface design approaches, we then revisit the problem of controlling the distribution of energy between multiple diffraction orders by means of gradient metasurfaces. Our discussions reveal that Huygens-based designs hold the promise of overcoming the low conversion efficiency issues associated with other techniques.

© 2015 Optical Society of America

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2015 (8)

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]

N. Mohammadi Estakhri, C. Argyropoulos, and A. Alù, “Graded metascreens to enable a new degree of nanoscale light management,” Philos. Trans. R. Soc. A 373, 20140351 (2015).
[Crossref]

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).
[Crossref]

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15, 1615–1621 (2015).
[Crossref]

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347, 1342–1345 (2015).
[Crossref]

B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B 91, 195444 (2015).
[Crossref]

K. Jha, X. Ni, C. Wu, Y. Wang, and X. Zhang, “Metasurface-enabled remote quantum interference,” Phys. Rev. Lett. 115, 025501 (2015).
[Crossref]

B. Desiatov, N. Mazurski, Y. Fainman, and U. Levy, “Polarization selective beam shaping using nanoscale dielectric metasurfaces,” Opt. Express 23, 22611–22618 (2015).
[Crossref]

2014 (13)

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26, 5031–5036 (2014).
[Crossref]

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).
[Crossref]

P. R. West, J. L. Stewart, A. V. Kildishev, V. M. Shalaev, V. V. Shkunov, F. Strohkendl, Y. A. Zakharenkov, R. K. Dodds, and R. Byren, “All-dielectric subwavelength metasurface focusing lens,” Opt. Express 22, 26212–26221 (2014).
[Crossref]

M. Kim, A. M. Wong, and G. V. Eleftheriades, “Optical Huygens’ metasurfaces with independent control of the magnitude and phase of the local reflection coefficients,” Phys. Rev. X 4, 041042 (2014).

Y. Ra’di, V. S. Asadchy, and S. Tretyakov, “Tailoring reflections from thin composite metamirrors,” IEEE Trans. Antennas Propag. 62, 3749–3760 (2014).
[Crossref]

A. Epstein and G. Eleftheriades, “Passive lossless Huygens metasurfaces for conversion of arbitrary source field to directive radiation,” IEEE Trans. Antennas Propag. 62, 5680–5695 (2014).
[Crossref]

N. Mohammadi Estakhri and A. Alù, “Ultra-thin unidirectional carpet cloak and wavefront reconstruction with graded metasurfaces,” IEEE Antennas Wireless Propag. Lett. 13, 1775–1778 (2014).
[Crossref]

N. Mohammadi Estakhri and A. Alù, “Manipulating optical reflections using engineered nanoscale metasurfaces,” Phys. Rev. B 89, 235419 (2014).
[Crossref]

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

C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, “Efficient light bending with isotropic metamaterial Huygens’ surfaces,” Nano Lett. 14, 2491–2497 (2014).
[Crossref]

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

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).
[Crossref]

2013 (21)

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alù, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
[Crossref]

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

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, C. W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013).

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102, 231116 (2013).
[Crossref]

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

F. Monticone, N. Mohammadi Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3, 2155 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
[Crossref]

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2, e72 (2013).
[Crossref]

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).
[Crossref]

J. Zhang, Z. L. Mei, W. R. Zhang, F. Yang, and T. J. Cui, “An ultrathin directional carpet cloak based on generalized Snell’s law,” Appl. Phys. Lett. 103, 151115 (2013).
[Crossref]

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12, 25–28 (2013).
[Crossref]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref]

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 (2013).
[Crossref]

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, 1344–1352 (2013).
[Crossref]

M. Farmahini-Farahani and H. Mosallaei, “Birefringent reflectarray metasurface for beam engineering in infrared,” Opt. Lett. 38, 462–464 (2013).
[Crossref]

T. Roy, E. T. Rogers, and N. I. Zheludev, “Sub-wavelength focusing meta-lens,” Opt. Express 21, 7577–7582 (2013).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation,” Opt. Express 21, 14409–14429 (2013).
[Crossref]

A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21, 27438–27451 (2013).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Experimental demonstration of active electromagnetic cloaking,” Phys. Rev. X 3, 041011 (2013).

2012 (10)

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).
[Crossref]

M. Kang, J. Chen, X.-L. Wang, and H.-T. Wang, “Twisted vector field from an inhomogeneous and anisotropic metamaterial,” J. Opt. Soc. Am. B 29, 572–576 (2012).
[Crossref]

M. Kang, T. Feng, H.-T. Wang, and J. Li, “Wave front engineering from an array of thin aperture antennas,” Opt. Express 20, 15882–15890 (2012).
[Crossref]

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

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (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, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
[Crossref]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref]

P. Spinelli, M. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref]

C. L. Holloway, E. F. Kuester, J. Gordon, J. O. Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).
[Crossref]

Y. Zhao, M. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[Crossref]

2011 (6)

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]

P.-Y. Chen and A. Alù, “Subwavelength imaging using phase-conjugating nonlinear nanoantenna arrays,” Nano Lett. 11, 5514–5518 (2011).
[Crossref]

K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011).
[Crossref]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84, 075153 (2011).
[Crossref]

M. Al-Joumayly and N. Behdad, “Wideband planar microwave lenses using sub-wavelength spatial phase shifters,” IEEE Trans. Antennas Propag. 59, 4542–4552 (2011).
[Crossref]

2009 (2)

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: the two-dimensional equivalent of metamaterials,” Metamaterials 3, 100–112 (2009).
[Crossref]

A. Alù, “Mantle cloak: invisibility induced by a surface,” Phys. Rev. B 80, 245115 (2009).
[Crossref]

2007 (3)

A. Sihvola, “Metamaterials in electromagnetics,” Metamaterials 1, 2–11 (2007).
[Crossref]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
[Crossref]

A. Alù, A. Salandrino, and N. Engheta, “Coupling of optical lumped nanocircuit elements and effects of substrates,” Opt. Express 15, 13865–13876 (2007).
[Crossref]

2006 (1)

2005 (2)

U. Levy, H.-C. Kim, C.-H. Tsai, and Y. Fainman, “Near-infrared demonstration of computer-generated holograms implemented by using subwavelength gratings with space-variant orientation,” Opt. Lett. 30, 2089–2091 (2005).
[Crossref]

C. L. Holloway, M. Mohamed, E. F. Kuester, and A. Dienstfrey, “Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles,” IEEE Trans. Electromagn. Compat. 47, 853–865 (2005).
[Crossref]

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, 328–330 (2003).
[Crossref]

2001 (1)

J. Encinar, “Design of two-layer printed reflectarrays using patches of variable size,” IEEE Trans. Antennas Propag. 49, 1403–1410 (2001).
[Crossref]

1997 (1)

D. M. Pozar, S. D. Targonski, and H. Syrigos, “Design of millimeter wave microstrip reflectarrays,” IEEE Trans. Antennas Propag. 45, 287–296 (1997).
[Crossref]

1987 (1)

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[Crossref]

1976 (1)

A. Love, “Some highlights in reflector antenna development,” Radio Sci. 11, 671–684 (1976).
[Crossref]

Aieta, F.

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347, 1342–1345 (2015).
[Crossref]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref]

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

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]

Albrektsen, O.

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3, 2155 (2013).
[Crossref]

Al-Joumayly, M.

M. Al-Joumayly and N. Behdad, “Wideband planar microwave lenses using sub-wavelength spatial phase shifters,” IEEE Trans. Antennas Propag. 59, 4542–4552 (2011).
[Crossref]

Alù, A.

B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B 91, 195444 (2015).
[Crossref]

N. Mohammadi Estakhri, C. Argyropoulos, and A. Alù, “Graded metascreens to enable a new degree of nanoscale light management,” Philos. Trans. R. Soc. A 373, 20140351 (2015).
[Crossref]

N. Mohammadi Estakhri and A. Alù, “Manipulating optical reflections using engineered nanoscale metasurfaces,” Phys. Rev. B 89, 235419 (2014).
[Crossref]

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

N. Mohammadi Estakhri and A. Alù, “Ultra-thin unidirectional carpet cloak and wavefront reconstruction with graded metasurfaces,” IEEE Antennas Wireless Propag. Lett. 13, 1775–1778 (2014).
[Crossref]

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alù, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
[Crossref]

F. Monticone, N. Mohammadi Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
[Crossref]

Y. Zhao, M. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[Crossref]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).
[Crossref]

P.-Y. Chen and A. Alù, “Subwavelength imaging using phase-conjugating nonlinear nanoantenna arrays,” Nano Lett. 11, 5514–5518 (2011).
[Crossref]

A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84, 075153 (2011).
[Crossref]

A. Alù, “Mantle cloak: invisibility induced by a surface,” Phys. Rev. B 80, 245115 (2009).
[Crossref]

A. Alù, A. Salandrino, and N. Engheta, “Coupling of optical lumped nanocircuit elements and effects of substrates,” Opt. Express 15, 13865–13876 (2007).
[Crossref]

N. Mohammadi Estakhri and A. Alù, under review, to be called “Wavefront transformation with gradient metasurfaces.”

Argyropoulos, C.

N. Mohammadi Estakhri, C. Argyropoulos, and A. Alù, “Graded metascreens to enable a new degree of nanoscale light management,” Philos. Trans. R. Soc. A 373, 20140351 (2015).
[Crossref]

Asadchy, V. S.

Y. Ra’di, V. S. Asadchy, and S. Tretyakov, “Tailoring reflections from thin composite metamirrors,” IEEE Trans. Antennas Propag. 62, 3749–3760 (2014).
[Crossref]

Atwater, H. A.

K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011).
[Crossref]

Aydin, K.

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15, 1615–1621 (2015).
[Crossref]

K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011).
[Crossref]

Azad, A. K.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: the two-dimensional equivalent of metamaterials,” Metamaterials 3, 100–112 (2009).
[Crossref]

Bai, B.

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, C. W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

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).
[Crossref]

Behdad, N.

M. Al-Joumayly and N. Behdad, “Wideband planar microwave lenses using sub-wavelength spatial phase shifters,” IEEE Trans. Antennas Propag. 59, 4542–4552 (2011).
[Crossref]

Belkin, M.

Y. Zhao, M. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[Crossref]

Berry, M. V.

M. V. Berry, “The adiabatic phase and Pancharatnam’s phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[Crossref]

Beruete, M.

B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B 91, 195444 (2015).
[Crossref]

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, 328–330 (2003).
[Crossref]

Blanchard, R.

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

Boltasseva, A.

C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, “Efficient light bending with isotropic metamaterial Huygens’ surfaces,” Nano Lett. 14, 2491–2497 (2014).
[Crossref]

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

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Booth, J.

C. L. Holloway, E. F. Kuester, J. Gordon, J. O. Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).
[Crossref]

Boyd, R. W.

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).
[Crossref]

Bozhevolnyi, S. I.

A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21, 27438–27451 (2013).
[Crossref]

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3, 2155 (2013).
[Crossref]

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).
[Crossref]

Brener, I.

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).
[Crossref]

Briggs, D. P.

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).
[Crossref]

Briggs, R. M.

K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011).
[Crossref]

Brongersma, M. L.

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

Butun, S.

Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15, 1615–1621 (2015).
[Crossref]

Byren, R.

Capasso, F.

F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347, 1342–1345 (2015).
[Crossref]

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

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
[Crossref]

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

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]

Castaldi, G.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

Cheah, K. W.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, C. W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

Chen, J.

Chen, P. Y.

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alù, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
[Crossref]

Chen, P.-Y.

P.-Y. Chen and A. Alù, “Subwavelength imaging using phase-conjugating nonlinear nanoantenna arrays,” Nano Lett. 11, 5514–5518 (2011).
[Crossref]

Chen, S.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, C. W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

Chen, W. T.

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 (2013).
[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, G. Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
[Crossref]

Chen, X.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, C. W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
[Crossref]

L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2, e70 (2013).
[Crossref]

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).
[Crossref]

Chiang, I. D.

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 (2013).
[Crossref]

Cui, T. J.

J. Zhang, Z. L. Mei, W. R. Zhang, F. Yang, and T. J. Cui, “An ultrathin directional carpet cloak based on generalized Snell’s law,” Appl. Phys. Lett. 103, 151115 (2013).
[Crossref]

De Leon, I.

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).
[Crossref]

Decker, 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, 813–820 (2015).
[Crossref]

Desiatov, B.

Dienstfrey, A.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: the two-dimensional equivalent of metamaterials,” Metamaterials 3, 100–112 (2009).
[Crossref]

C. L. Holloway, M. Mohamed, E. F. Kuester, and A. Dienstfrey, “Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles,” IEEE Trans. Electromagn. Compat. 47, 853–865 (2005).
[Crossref]

Dodds, R. K.

Dominguez, J.

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).
[Crossref]

Eleftheriades, G.

A. Epstein and G. Eleftheriades, “Passive lossless Huygens metasurfaces for conversion of arbitrary source field to directive radiation,” IEEE Trans. Antennas Propag. 62, 5680–5695 (2014).
[Crossref]

Eleftheriades, G. V.

M. Kim, A. M. Wong, and G. V. Eleftheriades, “Optical Huygens’ metasurfaces with independent control of the magnitude and phase of the local reflection coefficients,” Phys. Rev. X 4, 041042 (2014).

M. Selvanayagam and G. V. Eleftheriades, “Experimental demonstration of active electromagnetic cloaking,” Phys. Rev. X 3, 041011 (2013).

M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation,” Opt. Express 21, 14409–14429 (2013).
[Crossref]

Emani, N. K.

C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, “Efficient light bending with isotropic metamaterial Huygens’ surfaces,” Nano Lett. 14, 2491–2497 (2014).
[Crossref]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335, 427 (2012).
[Crossref]

Encinar, J.

J. Encinar, “Design of two-layer printed reflectarrays using patches of variable size,” IEEE Trans. Antennas Propag. 49, 1403–1410 (2001).
[Crossref]

Engheta, N.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
[Crossref]

A. Alù, A. Salandrino, and N. Engheta, “Coupling of optical lumped nanocircuit elements and effects of substrates,” Opt. Express 15, 13865–13876 (2007).
[Crossref]

N. Engheta, “Thin absorbing screens using metamaterial surfaces,” in Antennas and Propagation Society International Symposium 2002 (IEEE, 2002), Vol. 2, pp. 392–395.

N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations (Wiley, 2006).

Epstein, A.

A. Epstein and G. Eleftheriades, “Passive lossless Huygens metasurfaces for conversion of arbitrary source field to directive radiation,” IEEE Trans. Antennas Propag. 62, 5680–5695 (2014).
[Crossref]

Eriksen, R. L.

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).
[Crossref]

Fainman, Y.

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, 813–820 (2015).
[Crossref]

Fan, P.

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

Farmahini-Farahani, M.

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P.-Y. Chen and A. Alù, “Subwavelength imaging using phase-conjugating nonlinear nanoantenna arrays,” Nano Lett. 11, 5514–5518 (2011).
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N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012).
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C. Pfeiffer, N. K. Emani, A. M. Shaltout, A. Boltasseva, V. M. Shalaev, and A. Grbic, “Efficient light bending with isotropic metamaterial Huygens’ surfaces,” Nano Lett. 14, 2491–2497 (2014).
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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 meta-surfaces,” Nano Lett. 12, 6223–6229 (2012).
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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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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 (2013).
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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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Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15, 1615–1621 (2015).
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Nat. Commun. (6)

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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L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, C. W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).
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X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013).

K. Aydin, V. E. Ferry, R. M. Briggs, and H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Commun. 2, 517 (2011).
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P. Spinelli, M. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
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Y. Zhao, M. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
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Nat. Mater. (2)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. Mater. 12, 25–28 (2013).
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New J. Phys. (1)

J. C. Soric, P. Y. Chen, A. Kerkhoff, D. Rainwater, K. Melin, and A. Alù, “Demonstration of an ultralow profile cloak for scattering suppression of a finite-length rod in free space,” New J. Phys. 15, 033037 (2013).
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Opt. Express (9)

D. A. Miller, “On perfect cloaking,” Opt. Express 14, 1245712466 (2006).
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A. Alù, A. Salandrino, and N. Engheta, “Coupling of optical lumped nanocircuit elements and effects of substrates,” Opt. Express 15, 13865–13876 (2007).
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M. Kang, T. Feng, H.-T. Wang, and J. Li, “Wave front engineering from an array of thin aperture antennas,” Opt. Express 20, 15882–15890 (2012).
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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, 1344–1352 (2013).
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T. Roy, E. T. Rogers, and N. I. Zheludev, “Sub-wavelength focusing meta-lens,” Opt. Express 21, 7577–7582 (2013).
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M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation,” Opt. Express 21, 14409–14429 (2013).
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A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21, 27438–27451 (2013).
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P. R. West, J. L. Stewart, A. V. Kildishev, V. M. Shalaev, V. V. Shkunov, F. Strohkendl, Y. A. Zakharenkov, R. K. Dodds, and R. Byren, “All-dielectric subwavelength metasurface focusing lens,” Opt. Express 22, 26212–26221 (2014).
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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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Opt. Lett. (2)

Philos. Trans. R. Soc. A (1)

N. Mohammadi Estakhri, C. Argyropoulos, and A. Alù, “Graded metascreens to enable a new degree of nanoscale light management,” Philos. Trans. R. Soc. A 373, 20140351 (2015).
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Phys. Rev. B (5)

A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84, 075153 (2011).
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N. Mohammadi Estakhri and A. Alù, “Manipulating optical reflections using engineered nanoscale metasurfaces,” Phys. Rev. B 89, 235419 (2014).
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A. Alù, “Mantle cloak: invisibility induced by a surface,” Phys. Rev. B 80, 245115 (2009).
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B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B 91, 195444 (2015).
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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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Phys. Rev. Lett. (3)

K. Jha, X. Ni, C. Wu, Y. Wang, and X. Zhang, “Metasurface-enabled remote quantum interference,” Phys. Rev. Lett. 115, 025501 (2015).
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F. Monticone, N. Mohammadi Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110, 203903 (2013).
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C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110, 197401 (2013).
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Phys. Rev. X (2)

M. Selvanayagam and G. V. Eleftheriades, “Experimental demonstration of active electromagnetic cloaking,” Phys. Rev. X 3, 041011 (2013).

M. Kim, A. M. Wong, and G. V. Eleftheriades, “Optical Huygens’ metasurfaces with independent control of the magnitude and phase of the local reflection coefficients,” Phys. Rev. X 4, 041042 (2014).

Radio Sci. (1)

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Sci. Rep. (1)

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3, 2155 (2013).
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Science (9)

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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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
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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, 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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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).
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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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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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A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
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Figures (9)

Fig. 1.
Fig. 1.

Generalized Snell’s law of refraction. (a) An ultrathin plasmonic array of nanoantennas is designed to provide a linear scattering phase response to the cross-polarized beam. Full-wave simulations of individual array elements indicate the beam-steering properties of the metasurface. A schematic of one supercell of the metasurface is shown in the upper panel. (b) Demonstration of the presence of anomalously refracted and reflected beams for cross-polarized scattered beams. [Figures adapted from Ref. [5] with permission from AAAS: Figs. 2(f), 2(g), and 3(b).]

Fig. 2.
Fig. 2.

With proper arrangement of surface electric and magnetic currents, determined from the equivalence principle, desired field distributions satisfying the Helmholtz equation can be independently supported in regions I and II. (Figure adapted from Ref. [29] with permission from the American Physical Society: Fig. 1.)

Fig. 3.
Fig. 3.

(a) Basic building blocks tailored for optical gradient metasurfaces based on transverse resonances sustained by nanocapacitors (dielectric nanoblocks) and nanoinductors (plasmonic nanoblocks). The right panel shows circular plasmonic posts suitable for polarization-independent metasurfaces, while the nanoresonator model in the left panel is polarization selective. (b) Gradient metasurfaces implemented in reflective setups. (c) Multilayer metasurfaces operating in transmission mode. Each panel corresponds to one of the blocks proposed in (a). [Figs. 3(a) and 3(b) adapted from Ref. [31]: Fig. 1(c).]

Fig. 4.
Fig. 4.

(a) Power splitting from a carefully designed birefringent metasurface. The TE portion of the incident beam redirects light toward 50 deg, while the TM portion experiences specular reflection. The metasurface is based on nanoresonators, as shown in Fig. 3(a) (left), also illustrated in the inset. (b) Tunable directional surface plasmon coupling: the ellipticity of the excitation beam (x-axis) determines the direction of surface plasmon propagation and can be continuously controlled in opposite directions. Blue and red curves indicate the portion of power coupled into the right and left ports of the surface coupler, respectively. (Figures adapted from Ref. [31]: Fig. 4(b) and from Ref. [24] with permission from Macmillan Publishers Ltd: Fig. 5.)

Fig. 5.
Fig. 5.

(a) Active cloaking based on spatially inhomogeneous arrays of electric and magnetic dipoles. The weight of each dipole is determined based on the distribution of the incident wave and the geometrical shape of the object. (b) Snapshot of the electric field distribution around an aluminum cylinder when illuminated by a monopole antenna and 12 magnetic dipoles enclose the cylinder (left); the case of bare cylinder (right). The active cloak restores the initial radiation pattern of the monopole antenna. (c) Concept of carpet cloaking based on gradient metasurfaces: field distribution around the obstacle is reconstructed through proper arrangement of scattering elements over its surface. (d) Snapshot of the electric field distribution around a bare PEC cylindrical dome (upper panel); the case of dome covered with properly designed nonperiodic metasurface (lower panel). Metasurface elements are similar to those shown in Fig. 3(a) (right). [Figures adapted from Ref. [65] with permission: Figs. 1, 8(a), and 8(b) and from Ref. [11]: Figs. 1, 3(c), and 3(d)].

Fig. 6.
Fig. 6.

(a) Time snapshot of the scattered magnetic field Hz, in a power splitter designed for θ1=45° and θ2=45°. Fields are normalized to the amplitude of the incident magnetic field, and the distribution of the local reflection phase along the metasurface is shown in the lower panel. (b) Distribution of the scattered power into different Floquet harmonics. Each of the desired modes carries 49% of the incident power.

Fig. 7.
Fig. 7.

Similar to Fig. 6 for θ1=75° and θ2=75°.

Fig. 8.
Fig. 8.

Metasurface local reflection coefficient R(x)=r(x)ejϕr(x) required to convert a normally incident wave into two refracted waves at θ1=17° and θ2=61.3°. The two waves carry same power toward normal direction. Solid lines show the exact solution and dashed lines correspond to the ray optics approximation, Rapprox.. The yellow region highlights one period of the metasurfaces.

Fig. 9.
Fig. 9.

Distribution of the reflected power from the metasurface into all excited diffraction orders. Metasurface beam splitter is designed to couple the incident energy into n=1 and n=3 diffraction orders. Green and red lines indicate the first and third Floquet harmonics corresponding to θ1=17° and θ2=61.3°, respectively. (a) Exact surface phase and (b) ray optics approximation.

Equations (9)

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ntsin(θt)nisin(θi)=λ02πdΦdx,nisin(θr)nisin(θi)=λ02πdΦdx,
J⃗s=n^×(H⃗2H⃗1),M⃗s=n^×(E⃗2E⃗1),
J⃗s=Ye·E⃗t,av,M⃗s=Zm·H⃗t,av.
Yeg=Ye2+jnscot(ksds)η0,
J⃗s=n^×H⃗s,M⃗s=n^×E⃗s,
(E⃗i,H⃗i)=(y^,x^η0)E0ejk0z.
(E⃗s,H⃗s)=A1(y^,x^cosθ1+z^sinθ1η0)E0ejsinθ1k0xejcosθ1k0z+A2(y^,x^cosθ2+z^sinθ2η0)E0ejsinθ2k0xejcosθ2k0z,
Ye=22A1ejk0xsinθ1cosθ12A2ejk0xsinθ2cosθ2η0+A1ejk0xsinθ1η0+A2ejk0xsinθ2η0;Zm=4Ye,
Rapprox.=y^·E⃗sy^·E⃗i=A1ejsinθ1k0x+A2ejsinθ2k0x.

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