Tailoring light properties using metasurfaces made of optically thin and subwavelength structure arrays has led to a variety of innovative optical components with intriguing functionalities. Transmitted/reflected light field distribution with exquisite nanoscale resolution achievable with metasurfaces has been utilized to encode holographic complex amplitude, leading to arbitrary holographic intensity profile in the plane of interest. Vectorial metasurface holography, which not only controls the intensity profile, but also modifies the polarization distributions of the light field, has recently attracted enormous attention due to their promising applications in photonics and optics. Here, we review the recent progresses of the vectorial metasurface holography, from the basic concept to the practical implementation. Moreover, vectorial metasurfaces can also be multiplexed with other degrees of freedom, such as wavelength and nonlinearity, enriching and broadening its applications in both civil and military field.
References
1.
J. B.
Pendry
, A. J.
Holden
, W. J.
Stewart
, and I.
Youngs
, “Extremely low frequency plasmons in metallic mesostructures
,” Phys. Rev. Lett.
76
(25
), 4773
–4776
(1996
).2.
J. B.
Pendry
, A. J.
Holden
, D. J.
Robbins
, and W. J.
Stewart
, “Magnetism from conductors and enhanced nonlinear phenomena
,” IEEE Trans. Microwave Theory Tech.
47
(11
), 2075
–2084
(1999
).3.
J. B.
Pendry
, “Negative refraction makes a perfect lens
,” Phys. Rev. Lett.
85
(18
), 3966
–3969
(2000
).4.
J. B.
Pendry
, “Controlling electromagnetic fields
,” Science
312
(5781
), 1780
–1782
(2006
).5.
D. R.
Smith
, W. J.
Padilla
, D. C.
Vier
, S. C.
Nemat-Nasser
, and S.
Schultz
, “Composite medium with simultaneously negative permeability and permittivity
,” Phys. Rev. Lett.
84
(18
), 4184
–4187
(2000
).6.
D.
Schurig
, J. J.
Mock
, B. J.
Justice
, S. A.
Cummer
, J. B.
Pendry
, A. F.
Starr
, and D. R.
Smith
, “Metamaterial electromagnetic cloak at microwave frequencies
,” Science
314
(5801
), 977
–980
(2006
).7.
R.
Liu
, C.
Ji
, J.
Mock
, J.
Chin
, T.
Cui
, and D.
Smith
, “Broadband ground-plane cloak
,” Science (New York, NY)
323
, 366
–369
(2009
).8.
D. R.
Smith
, “Metamaterials and negative refractive index
,” Science
305
(5685
), 788
–792
(2004
).9.
I.
Liberal
and N.
Engheta
, “Near-zero refractive index photonics
,” Nat. Photonics
11
(3
), 149
–158
(2017
).10.
N. I.
Zheludev
and Y. S.
Kivshar
, “From metamaterials to metadevices
,” Nat. Mater.
11
(11
), 917
–924
(2012
).11.
A.
Poddubny
, I.
Iorsh
, P.
Belov
, and Y.
Kivshar
, “Hyperbolic metamaterials
,” Nat. Photonics
7
(12
), 948
–957
(2013
).12.
B.
Luk’yanchuk
, N. I.
Zheludev
, S. A.
Maier
, N. J.
Halas
, P.
Nordlander
, H.
Giessen
, and C. T.
Chong
, “The Fano resonance in plasmonic nanostructures and metamaterials
,” Nat. Mater.
9
(9
), 707
–715
(2010
).13.
Y.
Shi
, T.
Zhu
, T.
Zhang
, A.
Mazzulla
, D. P.
Tsai
, W.
Ding
, A. Q.
Liu
, G.
Cipparrone
, J. J.
Sáenz
, and C.-W.
Qiu
, “Chirality-assisted lateral momentum transfer for bidirectional enantioselective separation
,” Light Sci. Appl.
9
(1
), 62
(2020
).14.
S. A.
Cummer
, J.
Christensen
, and A.
Alù
, “Controlling sound with acoustic metamaterials
,” Nat. Rev. Mater.
1
(3
), 16001
(2016
).15.
J.
Li
and C. T.
Chan
, “Double-negative acoustic metamaterial
,” Phys. Rev. E
70
(5
), 055602
(2004
).16.
T.
Brunet
, A.
Merlin
, B.
Mascaro
, K.
Zimny
, J.
Leng
, O.
Poncelet
, C.
Aristégui
, and O.
Mondain-Monval
, “Soft 3D acoustic metamaterial with negative index
,” Nat. Mater.
14
(4
), 384
–388
(2015
).17.
M.
Molerón
and C.
Daraio
, “Acoustic metamaterial for subwavelength edge detection
,” Nat. Commun.
6
(1
), 8037
(2015
).18.
V.
Peri
, Z.-D.
Song
, M.
Serra-Garcia
, P.
Engeler
, R.
Queiroz
, X.
Huang
, W.
Deng
, Z.
Liu
, B. A.
Bernevig
, and S. D.
Huber
, “Experimental characterization of fragile topology in an acoustic metamaterial
,” Science
367
(6479
), 797
–800
(2020
).19.
S.
Brûlé
, E. H.
Javelaud
, S.
Enoch
, and S.
Guenneau
, “Experiments on seismic metamaterials: molding surface waves
,” Phys. Rev. Lett.
112
(13
), 133901
(2014
).20.
M.
Miniaci
, A.
Krushynska
, F.
Bosia
, and N. M.
Pugno
, “Large scale mechanical metamaterials as seismic shields
,” New J. Phys.
18
(8
), 083041
(2016
).21.
Y.
Zeng
, Y.
Xu
, K.
Deng
, P.
Peng
, H.
Yang
, M.
Muzamil
, and Q.
Du
, “A broadband seismic metamaterial plate with simple structure and easy realization
,” J. Appl. Phys.
125
(22
), 224901
(2019
).22.
A.
Colombi
, P.
Roux
, S.
Guenneau
, P.
Gueguen
, and R. V.
Craster
, “Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances
,” Sci. Rep.
6
(1
), 19238
(2016
). 23.
S.-H.
Kim
and M. P.
Das
, “Seismic waveguide of metamaterials
,” Mod. Phys. Lett. B
26
(17
), 1250105
(2012
).24.
N.
Yu
, P.
Genevet
, M. A.
Kats
, F.
Aieta
, J.-P.
Tetienne
, F.
Capasso
, and Z.
Gaburro
, “Light propagation with phase discontinuities: Generalized laws of reflection and refraction
,” Science
334
(6054
), 333
–337
(2011
).25.
N.
Yu
and F.
Capasso
, “Flat optics with designer metasurfaces
,” Nat. Mater.
13
(2
), 139
–150
(2014
).26.
Y.
Yang
, I. I.
Kravchenko
, D. P.
Briggs
, and J.
Valentine
, “All-dielectric metasurface analogue of electromagnetically induced transparency
,” Nat. Commun.
5
(1
), 5753
(2014
).27.
C.
Yan
, K.-Y.
Yang
, and O. J. F.
Martin
, “Fano-resonance-assisted metasurface for color routing
,” Light
6
(7
), e17017
(2017
).28.
Q. H.
Song
, P. C.
Wu
, W. M.
Zhu
, W.
Zhang
, Z. X.
Shen
, P. H. J.
Chong
, Q. X.
Liang
, D. P.
Tsai
, T.
Bourouina
, Y.
Leprince-Wang
, and A. Q.
Liu
, “Split Archimedean spiral metasurface for controllable GHz asymmetric transmission
,” Appl. Phys. Lett.
114
(15
), 151105
(2019
).29.
Q.
Song
, W.
Zhang
, P. C.
Wu
, W.
Zhu
, Z. X.
Shen
, P. H. J.
Chong
, Q. X.
Liang
, Z. C.
Yang
, Y. L.
Hao
, and H.
Cai
, “Water-resonator-based metasurface: an ultrabroadband and near-unity absorption
,” Adv. Opt. Mater.
5
(8
), 1601103
(2017
).30.
K. T. P.
Lim
, H.
Liu
, Y.
Liu
, and J. K. W.
Yang
, “Holographic colour prints for enhanced optical security by combined phase and amplitude control
,” Nat. Commun.
10
(1
), 25
(2019
).31.
K.
Kumar
, H.
Duan
, R. S.
Hegde
, S. C. W.
Koh
, J. N.
Wei
, and J. K. W.
Yang
, “Printing colour at the optical diffraction limit
,” Nat. Nanotechnol.
7
(9
), 557
–561
(2012
).32.
L.
Li
, Z.
Liu
, X.
Ren
, S.
Wang
, V.-C.
Su
, M.-K.
Chen
, C. H.
Chu
, H. Y.
Kuo
, B.
Liu
, W.
Zang
, G.
Guo
, L.
Zhang
, Z.
Wang
, S.
Zhu
, and D. P.
Tsai
, “Metalens-array–based high-dimensional and multiphoton quantum source
,” Science
368
(6498
), 1487
–1490
(2020
).33.
S.
Wang
, P. C.
Wu
, V.-C.
Su
, Y.-C.
Lai
, M.-K.
Chen
, H. Y.
Kuo
, B. H.
Chen
, Y. H.
Chen
, T.-T.
Huang
, J.-H.
Wang
, R.-M.
Lin
, C.-H.
Kuan
, T.
Li
, Z.
Wang
, S.
Zhu
, and D. P.
Tsai
, “A broadband achromatic metalens in the visible
,” Nat. Nanotechnol.
13
(3
), 227
–232
(2018
).34.
W. T.
Chen
, A. Y.
Zhu
, V.
Sanjeev
, M.
Khorasaninejad
, Z.
Shi
, E.
Lee
, and F.
Capasso
, “A broadband achromatic metalens for focusing and imaging in the visible
,” Nat. Nanotechnol.
13
(3
), 220
–226
(2018
).35.
R. J.
Lin
, V.-C.
Su
, S.
Wang
, M. K.
Chen
, T. L.
Chung
, Y. H.
Chen
, H. Y.
Kuo
, J.-W.
Chen
, J.
Chen
, Y.-T.
Huang
, J.-H.
Wang
, C. H.
Chu
, P. C.
Wu
, T.
Li
, Z.
Wang
, S.
Zhu
, and D. P.
Tsai
, “Achromatic metalens array for full-colour light-field imaging
,” Nat. Nanotechnol.
14
(3
), 227
–231
(2019
).36.
W.
Zhu
, Q.
Song
, L.
Yan
, W.
Zhang
, P.-C.
Wu
, L. K.
Chin
, H.
Cai
, D. P.
Tsai
, Z. X.
Shen
, T. W.
Deng
, S. K.
Ting
, Y.
Gu
, G. Q.
Lo
, D. L.
Kwong
, Z. C.
Yang
, R.
Huang
, A.-Q.
Liu
, and N.
Zheludev
, “A flat lens with tunable phase gradient by using random access reconfigurable metamaterial
,” Adv. Mater.
27
(32
), 4739
–4743
(2015
).37.
L.
Cong
, N.
Xu
, W.
Zhang
, and R.
Singh
, “Polarization control in terahertz metasurfaces with the lowest order rotational symmetry
,” Adv. Opt. Mater.
3
(9
), 1176
–1183
(2015
).38.
F.
Ding
, B.
Chang
, Q.
Wei
, L.
Huang
, X.
Guan
, and S. I.
Bozhevolnyi
, “Versatile polarization generation and manipulation using dielectric metasurfaces
,” Laser Photonics Rev.
14
(11
), 2000116
(2020
).39.
L.
Yan
, W.
Zhu
, M. F.
Karim
, H.
Cai
, A. Y.
Gu
, Z.
Shen
, P. H. J.
Chong
, D.-L.
Kwong
, C.-W.
Qiu
, and A. Q.
Liu
, “0.2 λ 0 thick adaptive retroreflector made of spin-locked metasurface
,” Adv. Mater.
30
(39
), 1802721
(2018
).40.
P. C.
Wu
, W.
Zhu
, Z. X.
Shen
, P. H. J.
Chong
, W.
Ser
, D. P.
Tsai
, and A.-Q.
Liu
, “Broadband wide-angle multifunctional polarization converter via liquid-metal-based metasurface
,” Adv. Opt. Mater.
5
(7
), 1600938
(2017
).41.
X.
Yu
, X.
Gao
, W.
Qiao
, L.
Wen
, and W.
Yang
, “Broadband tunable polarization converter realized by graphene-based metamaterial
,” IEEE Photonics Technol. Lett.
28
(21
), 2399
–2402
(2016
).42.
S.
Teng
, Q.
Zhang
, H.
Wang
, L.
Liu
, and H.
Lv
, “Conversion between polarization states based on a metasurface
,” Photonics Res.
7
(3
), 246
(2019
).43.
G.
Li
, S.
Chen
, N.
Pholchai
, B.
Reineke
, P. W. H.
Wong
, E. Y. B.
Pun
, K. W.
Cheah
, T.
Zentgraf
, and S.
Zhang
, “Continuous control of the nonlinearity phase for harmonic generations
,” Nat. Mater.
14
(6
), 607
–612
(2015
).44.
B.
Liu
, B.
Sain
, B.
Reineke
, R.
Zhao
, C.
Meier
, L.
Huang
, Y.
Jiang
, and T.
Zentgraf
, “Nonlinear wavefront control by geometric‐phase dielectric metasurfaces: influence of mode field and rotational symmetry
,” Adv. Opt. Mater.
8
(9
), 1902050
(2020
). 45.
K.
O’Brien
, H.
Suchowski
, J.
Rho
, A.
Salandrino
, B.
Kante
, X.
Yin
, and X.
Zhang
, “Predicting nonlinear properties of metamaterials from the linear response
,” Nat. Mater
14
(4
), 379
–383
(2015
).46.
G.
Li
, S.
Zhang
, and T.
Zentgraf
, “Nonlinear photonic metasurfaces
,” Nat. Rev. Mater.
2
(5
), 17010
(2017
).47.
M.
Tymchenko
, J. S.
Gomez-Diaz
, J.
Lee
, N.
Nookala
, M. A.
Belkin
, and A.
Alù
, “Gradient nonlinear Pancharatnam-Berry metasurfaces
,” Phys. Rev. Lett.
115
(20
), 207403
(2015
).48.
R. C.
Devlin
, A.
Ambrosio
, N. A.
Rubin
, J. P. B.
Mueller
, and F.
Capasso
, “Arbitrary spin-to-orbital angular momentum conversion of light
,” Sci.
358
(6365
), 896
–901
(2017
).49.
Y.
Guo
, S.
Zhang
, M.
Pu
, Q.
He
, J.
Jin
, M.
Xu
, Y.
Zhang
, P.
Gao
, and X.
Luo
, “Spin-decoupled metasurface for simultaneous detection of spin and orbital angular momenta via momentum transformation
,” Light Sci. Appl.
10
(1
), 63
(2021
).50.
M.
Chen
, L.
Jiang
, and W.
Sha
, “Orbital angular momentum generation and detection by geometric-phase based metasurfaces
,” Appl. Sci.
8
(3
), 362
(2018
).51.
P.
Genevet
, J.
Lin
, M. A.
Kats
, and F.
Capasso
, “Holographic detection of the orbital angular momentum of light with plasmonic photodiodes
,” Nat. Commun.
3
(1
), 1278
(2012
).52.
R. C.
Devlin
, A.
Ambrosio
, D.
Wintz
, S. L.
Oscurato
, A. Y.
Zhu
, M.
Khorasaninejad
, J.
Oh
, P.
Maddalena
, and F.
Capasso
, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces
,” Opt. Exp.
25
(1
), 377
(2017
).53.
Y.-W.
Huang
, N. A.
Rubin
, A.
Ambrosio
, Z.
Shi
, R. C.
Devlin
, C.-W.
Qiu
, and F.
Capasso
, “Versatile total angular momentum generation using cascaded J-plates
,” Opt. Exp.
27
(5
), 7469
(2019
).54.
L.
Marrucci
, C.
Manzo
, and D.
Paparo
, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media
,” Phys. Rev. Lett.
96
(16
), 163905
(2006
).55.
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
(1
), 013101
(2012
).56.
L.
Feng
, Y.-L.
Xu
, W. S.
Fegadolli
, M.-H.
Lu
, J. E. B.
Oliveira
, V. R.
Almeida
, Y.-F.
Chen
, and A.
Scherer
, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies
,” Nat. Mater.
12
(2
), 108
–113
(2013
).57.
N.
Papasimakis
, V. A.
Fedotov
, V.
Savinov
, T. A.
Raybould
, and N. I.
Zheludev
, “Electromagnetic toroidal excitations in matter and free space
,” Nat. Mater.
15
(3
), 263
–271
(2016
).58.
W. M.
Zhu
, A. Q.
Liu
, T.
Bourouina
, D. P.
Tsai
, J. H.
Teng
, X. H.
Zhang
, G. Q.
Lo
, D. L.
Kwong
, and N. I.
Zheludev
, “Microelectromechanical Maltese-cross metamaterial with tunable terahertz anisotropy
,” Nat. Commun.
3
, 1274
(2012
).59.
J.
Deng
, Y.
Yang
, J.
Tao
, L.
Deng
, D.
Liu
, Z.
Guan
, G.
Li
, Z.
Li
, S.
Yu
, G.
Zheng
, Z.
Li
, and S.
Zhang
, “Spatial frequency multiplexed meta-holography and meta-nanoprinting
,” ACS Nano
13
(8
), 9237
–9246
(2019
).60.
P.
Gutruf
, C.
Zou
, W.
Withayachumnankul
, M.
Bhaskaran
, S.
Sriram
, and C.
Fumeaux
, “Mechanically tunable dielectric resonator metasurfaces at visible frequencies
,” ACS Nano
10
(1
), 133
–141
(2016
).61.
P.
Genevet
, D.
Wintz
, A.
Ambrosio
, A.
She
, R.
Blanchard
, and F.
Capasso
, “Controlled steering of Cherenkov surface plasmon wakes with a one-dimensional metamaterial
,” Nat. Nanotechnol.
10
(9
), 804
–809
(2015
).62.
P.
Genevet
, F.
Capasso
, F.
Aieta
, M.
Khorasaninejad
, and R.
Devlin
, “Recent advances in planar optics: From plasmonic to dielectric metasurfaces
,” Optica
4
(1
), 139
(2017
).63.
Q.
Song
, Z.
Shen
, and J.
Lu
, “Log-periodic monopole array with uniform spacing and uniform height
,” IEEE Trans. Antennas Propag.
66
(9
), 4687
–4694
(2018
).64.
W.
Zhang
, Q.
Song
, W.
Zhu
, Z.
Shen
, P.
Chong
, D. P.
Tsai
, C.
Qiu
, and A. Q.
Liu
, “Metafluidic metamaterial: A review
,” Adv. Phys.
3
(1
), 1417055
(2018
).65.
M. A.
Gorlach
, X.
Ni
, D. A.
Smirnova
, D.
Korobkin
, D.
Zhirihin
, A. P.
Slobozhanyuk
, P. A.
Belov
, A.
Alù
, and A. B.
Khanikaev
, “Far-field probing of leaky topological states in all-dielectric metasurfaces
,” Nat. Commun.
9
(1
), 909
(2018
).66.
Y.
Shi
, S.
Xiong
, L. K.
Chin
, J.
Zhang
, W.
Ser
, J.
Wu
, T.
Chen
, Z.
Yang
, Y.
Hao
, B.
Liedberg
, P. H.
Yap
, D. P.
Tsai
, C.-W.
Qiu
, and A. Q.
Liu
, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers
,” Sci. Adv.
4
(1
), eaao0773
(2018
).67.
Y. Z.
Shi
, S.
Xiong
, Y.
Zhang
, L. K.
Chin
, Y.-Y.
Chen
, J. B.
Zhang
, T. H.
Zhang
, W.
Ser
, A.
Larrson
, S. H.
Lim
, J. H.
Wu
, T. N.
Chen
, Z. C.
Yang
, Y. L.
Hao
, B.
Liedberg
, P. H.
Yap
, K.
Wang
, D. P.
Tsai
, C.-W.
Qiu
, and A. Q.
Liu
, “Sculpting nanoparticle dynamics for single-bacteria-level screening and direct binding-efficiency measurement
,” Nat. Commun.
9
(1
), 815
(2018
).68.
S.
Sun
, Q.
He
, S.
Xiao
, Q.
Xu
, X.
Li
, and L.
Zhou
, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves
,” Nat. Mater
11
(5
), 426
–431
(2012
).69.
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
(1
), 225
–230
(2014
).70.
Y.-W.
Huang
, W. T.
Chen
, W.-Y.
Tsai
, P. C.
Wu
, C.-M.
Wang
, G.
Sun
, and D. P.
Tsai
, “aluminum plasmonic multicolor meta-hologram
,” Nano Lett.
15
(5
), 3122
–3127
(2015
).71.
P.
Spinelli
, M. A.
Verschuuren
, and A.
Polman
, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators
,” Nat. Commun.
3
(1
), 692
(2012
).72.
M.
Khorasaninejad
, A. Y.
Zhu
, C.
Roques-Carmes
, W. T.
Chen
, J.
Oh
, I.
Mishra
, R. C.
Devlin
, and F.
Capasso
, “Polarization-insensitive metalenses at visible wavelengths
,” Nano Lett.
16
(11
), 7229
–7234
(2016
).73.
H.
Ren
, G.
Briere
, X.
Fang
, P.
Ni
, R.
Sawant
, S.
Héron
, S.
Chenot
, S.
Vézian
, B.
Damilano
, V.
Brändli
, S. A.
Maier
, and P.
Genevet
, “Metasurface orbital angular momentum holography
,” Nat. Commun.
10
(1
), 2986
(2019
).74.
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 transmit arrays
,” Nat. Commun.
6
(1
), 7069
(2015
).75.
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
(6
), 628
(2016
).76.
A.
Arbabi
, R. M.
Briggs
, Y.
Horie
, M.
Bagheri
, and A.
Faraon
, “Efficient dielectric metasurface collimating lenses for mid-infrared quantum cascade lasers
,” Opt. Exp.
23
(26
), 33310
(2015
).77.
D.
Lin
, P.
Fan
, E.
Hasman
, and M. L.
Brongersma
, “Dielectric gradient metasurface optical elements
,” Science
345
(6194
), 298
–302
(2014
).78.
G.
Zheng
, H.
Mühlenbernd
, M.
Kenney
, G.
Li
, T.
Zentgraf
, and S.
Zhang
, “Metasurface holograms reaching 80% efficiency
,” Nat. Nanotechnol.
10
(4
), 308
–312
(2015
).79.
B.
Reineke
, B.
Sain
, R.
Zhao
, L.
Carletti
, B.
Liu
, L.
Huang
, C.
De Angelis
, and T.
Zentgraf
, “Silicon metasurfaces for third harmonic geometric phase manipulation and multiplexed holography
,” Nano Lett.
19
(9
), 6585
–6591
(2019
).80.
Q.
Song
, M.
Odeh
, J.
Zúñiga-Pérez
, B.
Kanté
, and P.
Genevet
, “Plasmonic topological metasurface by encircling an exceptional point
,” Science
373
(6559
), 1133
–1137
(2021
).81.
Q.
Song
, “Novel metasurface phase-modulation mechanism
,” Light Sci. Appl.
10
(1
), 184
(2021
).82.
Z.
Xie
, T.
Lei
, G.
Si
, X.
Wang
, J.
Lin
, C.
Min
, and X.
Yuan
, “Meta-holograms with full parameter control of wavefront over a 1000 nm bandwidth
,” ACS Photonics
4
(9
), 2158
–2164
(2017
).83.
S.
Sinzinger
and V.
Arrizón
, “High-efficiency detour-phase holograms
,” Opt. Lett.
22
(12
), 928
(1997
).84.
M.
Khorasaninejad
, A.
Ambrosio
, P.
Kanhaiya
, and F.
Capasso
, “Broadband and chiral binary dielectric meta-holograms
,” Sci. Adv.
2
(5
), e1501258
(2016
).85.
A.
Tittl
, A.-K. U.
Michel
, M.
Schäferling
, X.
Yin
, B.
Gholipour
, L.
Cui
, M.
Wuttig
, T.
Taubner
, F.
Neubrech
, and H.
Giessen
, “A switchable mid-infrared plasmonic perfect absorber with multispectral thermal imaging capability
,” Adv. Mater.
27
(31
), 4597
–4603
(2015
).86.
G. M.
Akselrod
, J.
Huang
, T. B.
Hoang
, P. T.
Bowen
, L.
Su
, D. R.
Smith
, and M. H.
Mikkelsen
, “Large-area metasurface perfect absorbers from visible to near-infrared
,” Adv. Mater.
27
(48
), 8028
–8034
(2015
).87.
N. I.
Landy
, S.
Sajuyigbe
, J. J.
Mock
, D. R.
Smith
, and W. J.
Padilla
, “Perfect metamaterial absorber
,” Phys. Rev. Lett.
100
(20
), 207402
(2008
).88.
Y.
Yao
, R.
Shankar
, M. A.
Kats
, Y.
Song
, J.
Kong
, M.
Loncar
, and F.
Capasso
, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators
,” Nano Lett.
14
(11
), 6526
–6532
(2014
).89.
J.
Jang
, H.
Jeong
, G.
Hu
, C.-W.
Qiu
, K. T.
Nam
, and J.
Rho
, “Kerker-conditioned dynamic cryptographic nanoprints
,” Adv. Opt. Mater.
7
(4
), 1801070
(2019
).90.
Y.
Gao
, C.
Huang
, C.
Hao
, S.
Sun
, L.
Zhang
, C.
Zhang
, Z.
Duan
, K.
Wang
, Z.
Jin
, N.
Zhang
, A. V.
Kildishev
, C.-W.
Qiu
, Q.
Song
, and S.
Xiao
, “Lead halide perovskite nanostructures for dynamic color display
,” ACS Nano
12
(9
), 8847
–8854
(2018
).91.
Q.
Wei
, B.
Sain
, Y.
Wang
, B.
Reineke
, X.
Li
, L.
Huang
, and T.
Zentgraf
, “Simultaneous spectral and spatial modulation for color printing and holography using all-dielectric metasurfaces
,” Nano Lett.
19
(12
), 8964
–8971
(2019
).92.
H.
Liu
, J.
Xu
, H.
Wang
, Y.
Liu
, Q.
Ruan
, Y.
Wu
, X.
Liu
, and J. K. W.
Yang
, “Tunable resonator‐upconverted emission (TRUE) color printing and applications in optical security
,” Adv. Mater.
31
(15
), 1807900
(2019
).93.
X.
Duan
, S.
Kamin
, and N.
Liu
, “Dynamic plasmonic colour display
,” Nat. Commun.
8
(1
), 14606
(2017
).94.
W.
Yang
, S.
Xiao
, Q.
Song
, Y.
Liu
, Y.
Wu
, S.
Wang
, J.
Yu
, J.
Han
, and D.-P.
Tsai
, “All-dielectric metasurface for high-performance structural color
,” Nat. Commun.
11
(1
), 1864
(2020
).95.
A.
Overvig
, N.
Yu
, and A.
Alù
, “Chiral quasi-bound states in the continuum
,” Phys. Rev. Lett.
126
(7
), 073001
(2021
).96.
K.
Koshelev
, S.
Lepeshov
, M.
Liu
, A.
Bogdanov
, and Y.
Kivshar
, “Asymmetric metasurfaces with high- Q resonances governed by bound states in the continuum
,” Phys. Rev. Lett.
121
(19
), 193903
(2018
).97.
M.
Liu
and D.-Y.
Choi
, “Extreme Huygens’ metasurfaces based on quasi-bound states in the continuum
,” Nano Lett.
18
(12
), 8062
–8069
(2018
).98.
M. V.
Gorkunov
, A. A.
Antonov
, and Y. S.
Kivshar
, “Metasurfaces with maximum chirality empowered by bound states in the continuum
,” Phys. Rev. Lett.
125
(9
), 093903
(2020
).99.
L.
Cong
and R.
Singh
, “Symmetry‐protected dual bound states in the continuum in metamaterials
,” Adv. Opt. Mater.
7
(13
), 1900383
(2019
).100.
Y. D.
Chong
, L.
Ge
, and A. D.
Stone
, “P T -symmetry breaking and laser-absorber modes in optical scattering systems
,” Phys. Rev. Lett.
106
(9
), 093902
(2011
).101.
W. R.
Sweeney
, C. W.
Hsu
, S.
Rotter
, and A. D.
Stone
, “Perfectly absorbing exceptional points and chiral absorbers
,” Phys. Rev. Lett.
122
(9
), 093901
(2019
).102.
M.
Li
, Z.
Wang
, W.
Yin
, E.
Li
, and H.
Chen
, “Controlling asymmetric absorption of metasurfaces via non-Hermitian doping
,” arXiv:2012.12601.103.
S. H.
Park
, S.-G.
Lee
, S.
Baek
, T.
Ha
, S.
Lee
, B.
Min
, S.
Zhang
, M.
Lawrence
, and T.-T.
Kim
, “Observation of an exceptional point in a non-Hermitian metasurface
,” Nanophotonics
9
(5
), 1031
–1039
(2020
).104.
D.
Gabor
, “A new microscopic principle
,” Nature
161
(4098
), 777
–778
(1948
).105.
E. N.
Leith
and J.
Upatnieks
, “Reconstructed wavefronts and communication theory*
,” J. Opt. Soc. Am., JOSA
52
(10
), 1123
–1130
(1962
).106.
B. R.
Brown
and A. W.
Lohmann
, “Complex spatial filtering with binary masks
,” Appl. Opt., AO
5
(6
), 967
–969
(1966
).107.
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.
Yue Bun Pun
, S.
Zhang
, and X.
Chen
, “Helicity multiplexed broadband metasurface holograms
,” Nat. Commun.
6
(1
), 8241
(2015
).108.
Y.
Gao
, Y.
Fan
, Y.
Wang
, W.
Yang
, Q.
Song
, and S.
Xiao
, “Nonlinear holographic all-dielectric metasurfaces
,” Nano Lett.
18
(12
), 8054
–8061
(2018
).109.
S. C.
Malek
, H.-S.
Ee
, and R.
Agarwal
, “Strain multiplexed metasurface holograms on a stretchable substrate
,” Nano Lett.
17
(6
), 3641
–3645
(2017
).110.
Y.-W.
Huang
, H. W. H.
Lee
, R.
Sokhoyan
, R. A.
Pala
, K.
Thyagarajan
, S.
Han
, D. P.
Tsai
, and H. A.
Atwater
, “Gate-tunable conducting oxide metasurfaces
,” Nano Lett.
16
(9
), 5319
–5325
(2016
).111.
R.
Zhao
, B.
Sain
, Q.
Wei
, C.
Tang
, X.
Li
, T.
Weiss
, L.
Huang
, Y.
Wang
, and T.
Zentgraf
, “Multichannel vectorial holographic display and encryption
,” Light
7
(1
), 95
(2018
).112.
G.
Makey
, Ö.
Yavuz
, D. K.
Kesim
, A.
Turnalı
, P.
Elahi
, S.
Ilday
, O.
Tokel
, and F. Ö.
Ilday
, “Breaking crosstalk limits to dynamic holography using orthogonality of high-dimensional random vectors
,” Nat. Photonics
13
(4
), 251
–256
(2019
).113.
J.
Kim
, Y.
Yang
, T.
Badloe
, I.
Kim
, G.
Yoon
, and J.
Rho
, “Geometric and physical configurations of meta‐atoms for advanced metasurface holography
,” InfoMat
3
(7
), 739
–754
(2021
).114.
W.
Wan
, J.
Gao
, and X.
Yang
, “Metasurface holograms for holographic imaging
,” Adv. Opt. Mater.
5
(21
), 1700541
(2017
).115.
R.
Izumi
, S.
Ikezawa
, and K.
Iwami
, “Metasurface holographic movie: A cinematographic approach
,” Opt. Exp.
28
(16
), 23761
(2020
).116.
Q.
Wang
, E.
Plum
, Q.
Yang
, X.
Zhang
, Q.
Xu
, Y.
Xu
, J.
Han
, and W.
Zhang
, “Reflective chiral meta-holography: Multiplexing holograms for circularly polarized waves
,” Light
7
(1
), 25
(2018
).117.
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
(1
), 2808
(2013
).118.
Y.
Yuan
, K.
Zhang
, B.
Ratni
, Q.
Song
, X.
Ding
, Q.
Wu
, S. N.
Burokur
, and P.
Genevet
, “Independent phase modulation for quadruplex polarization channels enabled by chirality-assisted geometric-phase metasurfaces
,” Nat. Commun.
11
(1
), 4186
(2020
).119.
120.
R. W.
Gerchberg
and W. O.
Saxton
, “A practical algorithm for the determination of phase from image and diffraction plane pictures
,” Optics (Jena)
35
, 237
(1972
).121.
J.
Yan
, X.
Yang
, C.-W.
Qiu
, and B.
Li
, “Point-source geometric metasurface holography
,” Nano Lett.
21
(5
), 2332
–2338
(2021
).122.
M.
Lehmann
, “Determination and correction of the coherent wave aberration from a single off-axis electron hologram by means of a genetic algorithm
,” Ultramicroscopy
85
(3
), 165
–182
(2000
).123.
K.
Matsushima
, Y.
Arima
, and S.
Nakahara
, “Digitized holography: Modern holography for 3D imaging of virtual and real objects
,” Appl. Opt., AO
50
(34
), H278
–H284
(2011
).124.
L.
Ahrenberg
, P.
Benzie
, M.
Magnor
, and J.
Watson
, “Computer generated holograms from three dimensional meshes using an analytic light transport model
,” Appl. Opt., AO
47
(10
), 1567
–1574
(2008
).125.
D.
Im
, J.
Cho
, J.
Hahn
, B.
Lee
, and H.
Kim
, “Accelerated synthesis algorithm of polygon computer-generated holograms
,” Opt. Express
23
(3
), 2863
(2015
).126.
L. G.
Valiant
, “Holographic Algorithms
,” SIAM J. Comput.
37
(5
), 1565
–1594
(2008
).127.
P.
Hariharan
, Basics of Holography
(Cambridge university Press
, 2002
).128.
T.
Shimobaba
, T.
Kakue
, and T.
Ito
, “Review of fast algorithms and hardware implementations on computer holography
,” IEEE Trans. Ind. Inf.
12
(4
), 1611
–1622
(2015
).129.
Q.
Song
, A.
Baroni
, P. C.
Wu
, S.
Chenot
, V.
Brandli
, S.
Vézian
, B.
Damilano
, P.
de Mierry
, S.
Khadir
, P.
Ferrand
, and P.
Genevet
, “Broadband decoupling of intensity and polarization with vectorial Fourier metasurfaces
,” Nat. Commun.
12
(1
), 3631
(2021
).130.
E.
Arbabi
, S. M.
Kamali
, A.
Arbabi
, and A.
Faraon
, “Vectorial holograms with a dielectric metasurface: Ultimate polarization pattern generation
,” ACS Photonics
6
(11
), 2712
–2718
(2019
).131.
G.
Cao
, H.-X.
Xu
, L.-M.
Zhou
, Y.
Deng
, Y.
Zeng
, S.
Dong
, Q.
Zhang
, Y.
Li
, H.
Yang
, Q.
Song
, X.
Liu
, Y.
Li
, and C.-W.
Qiu
, “Infrared metasurface-enabled compact polarization nanodevices
,” Mater. Today
50
, 499
–515
(2021
).132.
Y.
Hu
, X.
Wang
, X.
Luo
, X.
Ou
, L.
Li
, Y.
Chen
, P.
Yang
, S.
Wang
, and H.
Duan
, “All-dielectric metasurfaces for polarization manipulation: Principles and emerging applications
,” Nanophotonics
9
(12
), 3755
–3780
(2020
).133.
B.
Schaefer
, E.
Collett
, R.
Smyth
, D.
Barrett
, and B.
Fraher
, “Measuring the Stokes polarization parameters
,” Am. J. Phys.
75
(2
), 163
–168
(2007
).134.
N. A.
Rubin
, G.
D’Aversa
, P.
Chevalier
, Z.
Shi
, W. T.
Chen
, and F.
Capasso
, “Matrix Fourier optics enables a compact full-Stokes polarization camera
,” Science
365
(6448
), eaax1839
(2019
).135.
P.
Ferrand
, A.
Baroni
, M.
Allain
, and V.
Chamard
, “Quantitative imaging of anisotropic material properties with vectorial ptychography
,” Opt. Lett.
43
(4
), 763
(2018
).136.
P.
Ferrand
, M.
Allain
, and V.
Chamard
, “Ptychography in anisotropic media
,” Opt. Lett.
40
(22
), 5144
(2015
).137.
A.
Baroni
, M.
Allain
, P.
Li
, V.
Chamard
, and P.
Ferrand
, “Joint estimation of object and probes in vectorial ptychography
,” Opt. Exp.
27
(6
), 8143
(2019
).138.
H. M. L.
Faulkner
and J. M.
Rodenburg
, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm
,” Phys. Rev. Lett.
93
(2
), 023903
(2004
).139.
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
(12
), 6328
–6333
(2012
).140.
S.
Khadir
, D.
Andrén
, R.
Verre
, Q.
Song
, S.
Monneret
, P.
Genevet
, M.
Käll
, and G.
Baffou
, “Metasurface optical characterization using quadriwave lateral shearing interferometry
,” ACS Photonics
8
(2
), 603
–613
(2021
).141.
P.
Bon
, G.
Maucort
, B.
Wattellier
, and S.
Monneret
, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells
,” Opt. Exp.
17
(15
), 13080
(2009
).142.
Q.
Song
, S.
Khadir
, S.
Vézian
, B.
Damilano
, P.
de Mierry
, S.
Chenot
, V.
Brandli
, R.
Laberdesque
, B.
Wattellier
, and P.
Genevet
, “Printing polarization and phase at the optical diffraction limit: Near- and far-field optical encryption
,” Nanophotonics
10
(1
), 697
–704
(2020
).143.
S.
Khadir
, D.
Andrén
, P. C.
Chaumet
, S.
Monneret
, N.
Bonod
, M.
Käll
, A.
Sentenac
, and G.
Baffou
, “Full optical characterization of single nanoparticles using quantitative phase imaging
,” Optica
7
(3
), 243
(2020
).144.
X.
Chang
, L.
Bian
, and J.
Zhang
, “Large-scale phase retrieval
,” eLight
1
(1
), 4
(2021
).145.
J.
Babocký
, A.
Křížová
, L.
Štrbková
, L.
Kejík
, F.
Ligmajer
, M.
Hrtoň
, P.
Dvořák
, M.
Týč
, J.
Čolláková
, V.
Křápek
, R.
Kalousek
, R.
Chmelík
, and T.
Šikola
, “Quantitative 3D phase imaging of plasmonic metasurfaces
,” ACS Photonics
4
(6
), 1389
–1397
(2017
).146.
A.
Azari
, E.
Mohajerani
, Z.
Abedi
, and A.
Shams
, “Interferometry technique to eliminate noise in interference data based on a Mach–Zehnder interferometer
,” Appl. Opt., AO
53
(9
), 1734
–1738
(2014
).147.
A. J.
Ollanik
, G. Z.
Hartfield
, Y.
Ji
, J. T.
Robertson
, K.
Islam
, and M. D.
Escarra
, “Characterization of dynamic and nanoscale materials and metamaterials with continuously referenced interferometry
,” Adv. Opt. Mater.
7
(24
), 1901128
(2019
).148.
M.
Zhao
, M. K.
Chen
, Z.-P.
Zhuang
, Y.
Zhang
, A.
Chen
, Q.
Chen
, W.
Liu
, J.
Wang
, Z.-M.
Chen
, B.
Wang
, X.
Liu
, H.
Yin
, S.
Xiao
, L.
Shi
, J.-W.
Dong
, J.
Zi
, and D. P.
Tsai
, “Phase characterisation of metalenses
,” Light Sci Appl
10
(1
), 52
(2021
).149.
B. J.
Bohn
, M.
Schnell
, M. A.
Kats
, F.
Aieta
, R.
Hillenbrand
, and F.
Capasso
, “Near-field imaging of phased array metasurfaces
,” Nano Lett.
15
(6
), 3851
–3858
(2015
).150.
T.
Neuman
, P.
Alonso-González
, A.
Garcia-Etxarri
, M.
Schnell
, R.
Hillenbrand
, and J.
Aizpurua
, “Mapping the near fields of plasmonic nanoantennas by scattering-type scanning near-field optical microscopy
,” Laser Photonics Rev.
9
(6
), 637
–649
(2015
).151.
P.
Bouchal
, P.
Dvořák
, J.
Babocky
, Z.
Bouchal
, F.
Ligmajer
, M.
Hrton
, V.
Křápek
, A.
Faßbender
, S.
Linden
, and R.
Chmelík
, “High-resolution quantitative phase imaging of plasmonic metasurfaces with sensitivity down to a single nanoantenna
,” Nano letters
19
(2
), 1242
–1250
(2019
).152.
Z.-L.
Deng
and G.
Li
, “Metasurface optical holography
,” Mater. Today Phys.
3
, 16
–32
(2017
).153.
L.
Huang
, S.
Zhang
, and T.
Zentgraf
, “Metasurface holography: From fundamentals to applications
,” Nanophotonics
7
(6
), 1169
–1190
(2018
).154.
E.
Maguid
, I.
Yulevich
, D.
Veksler
, V.
Kleiner
, M. L.
Brongersma
, and E.
Hasman
, “Photonic spin-controlled multifunctional shared-aperture antenna array
,” Science
352
(6290
), 1202
–1206
(2016
).155.
P. C.
Wu
, J.-W.
Chen
, C.-W.
Yin
, Y.-C.
Lai
, T. L.
Chung
, C. Y.
Liao
, B. H.
Chen
, K.-W.
Lee
, C.-J.
Chuang
, C.-M.
Wang
, and D. P.
Tsai
, “Visible metasurfaces for on-chip polarimetry
,” ACS Photonics
5
(7
), 2568
–2573
(2018
).156.
Y.-Y.
Xie
, P.-N.
Ni
, Q.-H.
Wang
, Q.
Kan
, G.
Briere
, P.-P.
Chen
, Z.-Z.
Zhao
, A.
Delga
, H.-R.
Ren
, H.-D.
Chen
, C.
Xu
, and P.
Genevet
, “Metasurface-integrated vertical cavity surface-emitting lasers for programmable directional lasing emissions
,” Nat. Nanotechnol.
15
(2
), 125
–130
(2020
).157.
H.
Gao
, Y.
Wang
, X.
Fan
, B.
Jiao
, T.
Li
, C.
Shang
, C.
Zeng
, L.
Deng
, W.
Xiong
, J.
Xia
, and M.
Hong
, “Dynamic 3D meta-holography in visible range with large frame number and high frame rate
,” Sci. Adv.
6
(28
), eaba8595
(2020
).158.
P.
Rauter
, J.
Lin
, P.
Genevet
, S. P.
Khanna
, M.
Lachab
, A. G.
Davies
, E. H.
Linfield
, and F.
Capasso
, “Electrically pumped semiconductor laser with monolithic control of circular polarization
,” Proc Natl Acad Sci U. S. A.
111
(52
), E5623
–E5632
(2014
).159.
P. C.
Wu
, W.-Y.
Tsai
, W. T.
Chen
, Y.-W.
Huang
, T.-Y.
Chen
, J.-W.
Chen
, C. Y.
Liao
, C. H.
Chu
, G.
Sun
, and D. P.
Tsai
, “Versatile polarization generation with an aluminum plasmonic metasurface
,” Nano Lett.
17
(1
), 445
–452
(2017
).160.
D.
Wen
, J. J.
Cadusch
, J.
Meng
, and K. B.
Crozier
, “Vectorial holograms with spatially continuous polarization distributions
,” Nano Lett.
21
(4
), 1735
–1741
(2021
).161.
A.
Shaltout
, J.
Liu
, V. M.
Shalaev
, and A. V.
Kildishev
, “Optically active metasurface with non-chiral plasmonic nanoantennas
,” Nano Lett.
14
(8
), 4426
–4431
(2014
).162.
Q.
Guo
, C.
Schlickriede
, D.
Wang
, H.
Liu
, Y.
Xiang
, T.
Zentgraf
, and S.
Zhang
, “Manipulation of vector beam polarization with geometric metasurfaces
,” Opt. Exp.
25
(13
), 14300
(2017
).163.
X.
Zang
, F.
Dong
, F.
Yue
, C.
Zhang
, L.
Xu
, Z.
Song
, M.
Chen
, P.-Y.
Chen
, G. S.
Buller
, Y.
Zhu
, S.
Zhuang
, W.
Chu
, S.
Zhang
, and X.
Chen
, “Polarization encoded color image embedded in a dielectric metasurface
,” Adv. Mater.
30
(21
), 1707499
(2018
).164.
Q.
Song
, A.
Baroni
, R.
Sawant
, P.
Ni
, V.
Brandli
, S.
Chenot
, S.
Vézian
, B.
Damilano
, P.
de Mierry
, S.
Khadir
, P.
Ferrand
, and P.
Genevet
, “Ptychography retrieval of fully polarized holograms from geometric-phase metasurfaces
,” Nat. Commun.
11
(1
), 2651
(2020
).165.
Q.
Song
, S.
Khadir
, S.
Vézian
, B.
Damilano
, P. D.
Mierry
, S.
Chenot
, V.
Brandli
, and P.
Genevet
, “Bandwidth-unlimited polarization-maintaining metasurfaces
,” Sci. Adv.
7
(5
), eabe1112
(2021
).166.
Z.-L.
Deng
, J.
Deng
, X.
Zhuang
, S.
Wang
, T.
Shi
, G. P.
Wang
, Y.
Wang
, J.
Xu
, Y.
Cao
, X.
Wang
, X.
Cheng
, G.
Li
, and X.
Li
, “Facile metagrating holograms with broadband and extreme angle tolerance
,” Light: Sci. Appl.
7
(1
), 78
(2018
).167.
Y.
Yu
, S.
Sun
, Y.
Chen
, Q.-H.
Xu
, and C.-W.
Qiu
, “Dielectric metasurface for independent complex-amplitude control of arbitrary two orthogonal states of polarization
,” arXiv:2105.13640.168.
J. P.
Balthasar Mueller
, N. A.
Rubin
, R. C.
Devlin
, B.
Groever
, and F.
Capasso
, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization
,” Phys. Rev. Lett.
118
(11
), 113901
(2017
).169.
A.
Arbabi
, Y.
Horie
, M.
Bagheri
, and A.
Faraon
, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission
,” Nat. Nanotechnol.
10
(11
), 937
–943
(2015
).170.
Z.-L.
Deng
, J.
Deng
, X.
Zhuang
, S.
Wang
, K.
Li
, Y.
Wang
, Y.
Chi
, X.
Ye
, J.
Xu
, G. P.
Wang
, R.
Zhao
, X.
Wang
, Y.
Cao
, X.
Cheng
, G.
Li
, and X.
Li
, “Diatomic metasurface for vectorial holography
,” Nano Lett.
18
(5
), 2885
–2892
(2018
).171.
Y.
Bao
, J.
Ni
, and C.
Qiu
, “A minimalist single‐layer metasurface for arbitrary and full control of vector vortex beams
,” Adv. Mater.
32
(6
), 1905659
(2020
).172.
Y.
Bao
, L.
Wen
, Q.
Chen
, C.-W.
Qiu
, and B.
Li
, “Toward the capacity limit of 2D planar Jones matrix with a single-layer metasurface
,” Sci. Adv.
7
(25
), eabh0365
(2021
).173.
J. W.
Wu
, Z. X.
Wang
, Z. Q.
Fang
, J. C.
Liang
, X.
Fu
, J. F.
Liu
, H. T.
Wu
, D.
Bao
, L.
Miao
, X. Y.
Zhou
, Q.
Cheng
, and T. J.
Cui
, “Full-state synthesis of electromagnetic fields using high efficiency phase-only metasurfaces
,” Adv. Funct. Mater.
30
(39
), 2004144
(2020
).174.
D.
Wang
, F.
Liu
, T.
Liu
, S.
Sun
, Q.
He
, and L.
Zhou
, “Efficient generation of complex vectorial optical fields with metasurfaces
,” Light Sci Appl
10
(1
), 67
(2021
).175.
D.
Wang
, T.
Liu
, Y.
Zhou
, X.
Zheng
, S.
Sun
, Q.
He
, and L.
Zhou
, “High-efficiency metadevices for bifunctional generations of vectorial optical fields
,” Nanophotonics
10
(1
), 685
–695
(2021
).176.
Z. H.
Jiang
, L.
Kang
, T.
Yue
, H.
Xu
, Y.
Yang
, Z.
Jin
, C.
Yu
, W.
Hong
, D. H.
Werner
, and C.
Qiu
, “A single noninterleaved metasurface for high‐capacity and flexible mode multiplexing of higher‐order Poincaré sphere beams
,” Adv. Mater.
32
(6
), 1903983
(2020
).177.
W.
Wan
, W.
Yang
, H.
Feng
, Y.
Liu
, Q.
Gong
, S.
Xiao
, and Y.
Li
, “Multiplexing vectorial holographic images with arbitrary metaholograms
,” Adv. Opt. Mater.
9
(20
), 2100626
(2021
).178.
Y.
Hu
, L.
Li
, Y.
Wang
, M.
Meng
, L.
Jin
, X.
Luo
, Y.
Chen
, X.
Li
, S.
Xiao
, H.
Wang
, Y.
Luo
, C.-W.
Qiu
, and H.
Duan
, “Trichromatic and tripolarization-channel holography with noninterleaved dielectric metasurface
,” Nano Lett.
20
(2
), 994
–1002
(2020
).179.
S.
Cueff
, A.
Taute
, A.
Bourgade
, J.
Lumeau
, S.
Monfray
, Q.
Song
, P.
Genevet
, B.
Devif
, X.
Letartre
, and L.
Berguiga
, “Reconfigurable flat optics with programmable reflection amplitude using lithography‐free phase‐change material ultra‐thin films
,” Adv. Opt. Mater.
9
, 2001291
(2020
).180.
W. M.
Zhu
, A. Q.
Liu
, X. M.
Zhang
, D. P.
Tsai
, T.
Bourouina
, J. H.
Teng
, X. H.
Zhang
, H. C.
Guo
, H.
Tanoto
, T.
Mei
, G. Q.
Lo
, and D. L.
Kwong
, “Switchable magnetic metamaterials using micromachining processes
,” Adv. Mater.
23
(15
), 1792
–1796
(2011
).181.
W.
Zhang
, A. Q.
Liu
, W. M.
Zhu
, E. P.
Li
, H.
Tanoto
, Q. Y.
Wu
, J. H.
Teng
, X. H.
Zhang
, M. L. J.
Tsai
, G. Q.
Lo
, and D. L.
Kwong
, “Micromachined switchable metamaterial with dual resonance
,” Appl. Phys. Lett.
101
(15
), 151902
(2012
).182.
Q. H.
Song
, W. M.
Zhu
, P. C.
Wu
, W.
Zhang
, Q. Y. S.
Wu
, J. H.
Teng
, Z. X.
Shen
, P. H. J.
Chong
, Q. X.
Liang
, Z. C.
Yang
, D. P.
Tsai
, T.
Bourouina
, Y.
Leprince-Wang
, and A. Q.
Liu
, “Liquid-metal-based metasurface for terahertz absorption material: Frequency-agile and wide-angle
,” APL Mater.
5
(6
), 066103
(2017
).183.
L.
Yan
, W.
Zhu
, M. F.
Karim
, H.
Cai
, Y.
Gu
, Z.
Shen
, P. H. J.
Chong
, D. P.
Tsai
, D.-L.
Kwong
, C.-W.
Qiu
, and A. Q.
Liu
, “Arbitrary and independent polarization control in situ via a single metasurface
,” Adv. Opt. Mater.
6
(21
), 1800728
(2018
).184.
K.
Chen
, Y.
Feng
, F.
Monticone
, J.
Zhao
, B.
Zhu
, T.
Jiang
, L.
Zhang
, Y.
Kim
, X.
Ding
, S.
Zhang
, A.
Alù
, and C.-W.
Qiu
, “A reconfigurable active Huygens’ metalens
,” Adv. Mater.
29
(17
), 1606422
(2017
).185.
Y. C.
Jun
, E.
Gonzales
, J. L.
Reno
, E. A.
Shaner
, A.
Gabbay
, and I.
Brener
, “Active tuning of mid-infrared metamaterials by electrical control of carrier densities
,” Opt. Exp.
20
(2
), 1903
–1911
(2012
).186.
K.
Fan
, H. Y.
Hwang
, M.
Liu
, A. C.
Strikwerda
, A.
Sternbach
, J.
Zhang
, X.
Zhao
, X.
Zhang
, K. A.
Nelson
, and R. D.
Averitt
, “Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs
,” Phys. Rev. Lett.
110
(21
), 217404
(2013
).187.
H.
Tao
, A. C.
Strikwerda
, K.
Fan
, W. J.
Padilla
, X.
Zhang
, and R. D.
Averitt
, “Reconfigurable terahertz metamaterials
,” Phys. Rev. Lett.
103
(14
), 147401
(2009
).188.
H.-S.
Ee
and R.
Agarwal
, “Tunable metasurface and flat optical zoom lens on a stretchable substrate
,” Nano Lett.
16
(4
), 2818
–2823
(2016
).189.
T.
Lewi
, P. P.
Iyer
, N. A.
Butakov
, A. A.
Mikhailovsky
, and J. A.
Schuller
, “Widely tunable infrared antennas using free carrier refraction
,” Nano letters
15
(12
), 8188
–8193
(2015
).190.
A. D.
Boardman
, V. V.
Grimalsky
, Y. S.
Kivshar
, S. V.
Koshevaya
, M.
Lapine
, N. M.
Litchinitser
, V. N.
Malnev
, M.
Noginov
, Y. G.
Rapoport
, and V. M.
Shalaev
, “Active and tunable metamaterials
,” Laser Photonics Rev.
5
(2
), 287
–307
(2011
).191.
I.
Kim
, J.
Jang
, G.
Kim
, J.
Lee
, T.
Badloe
, J.
Mun
, and J.
Rho
, “Pixelated bifunctional metasurface-driven dynamic vectorial holographic color prints for photonic security platform
,” Nat. Commun.
12
(1
), 3614
(2021
).192.
J.
Xiong
and S.-T.
Wu
, “Planar liquid crystal polarization optics for augmented reality and virtual reality: From fundamentals to applications
,” eLight
1
(1
), 3
(2021
).193.
S.
Zhang
, L.
Huang
, X.
Li
, R.
Zhao
, Q.
Wei
, H.
Zhou
, Q.
Jiang
, G.
Geng
, J.
Li
, X.
Li
, and Y.
Wang
, “Dynamic display of full-stokes vectorial holography based on metasurfaces
,” ACS Photonics
8
(6
), 1746
–1753
(2021
).194.
W.
Wan
, J.
Gao
, and X.
Yang
, “Full-color plasmonic metasurface holograms
,” ACS Nano
10
(12
), 10671
–10680
(2016
).195.
H.
Feng
, Q.
Li
, W.
Wan
, J.-H.
Song
, Q.
Gong
, M. L.
Brongersma
, and Y.
Li
, “Spin-switched three-dimensional full-color scenes based on a dielectric meta-hologram
,” ACS Photonics
6
(11
), 2910
–2916
(2019
).196.
Z.
Deng
, M.
Jin
, X.
Ye
, S.
Wang
, T.
Shi
, J.
Deng
, N.
Mao
, Y.
Cao
, B.
Guan
, A.
Alù
, G.
Li
, and X.
Li
, “Full‐color complex‐amplitude vectorial holograms based on multi‐freedom metasurfaces
,” Adv. Funct. Mater.
30
(21
), 1910610
(2020
).197.
X.
Guo
, J.
Zhong
, B.
Li
, S.
Qi
, Y.
Li
, P.
Li
, D.
Wen
, S.
Liu
, B.
Wei
, and J.
Zhao
, “Full-color holographic display and encryption with full-polarization degree of freedom
,” Adv. Mater.
34
, 2103192
(2021
).198.
C.
Wang
, Z.
Li
, M.-H.
Kim
, X.
Xiong
, X.-F.
Ren
, G.-C.
Guo
, N.
Yu
, and M.
Lončar
, “Metasurface-assisted phase-matching-free second harmonic generation in lithium niobate waveguides
,” Nat. Commun.
8
(1
), 2098
(2017
).199.
T.
Stolt
, J.
Kim
, S.
Héron
, A.
Vesala
, Y.
Yang
, J.
Mun
, M.
Kim
, M. J.
Huttunen
, R.
Czaplicki
, M.
Kauranen
, J.
Rho
, and P.
Genevet
, “Backward phase-matched second-harmonic generation from stacked metasurfaces
,” Phys. Rev. Lett.
126
(3
), 033901
(2021
).200.
M.
Semmlinger
, M.
Zhang
, M. L.
Tseng
, T.-T.
Huang
, J.
Yang
, D. P.
Tsai
, P.
Nordlander
, and N. J.
Halas
, “Generating third harmonic vacuum ultraviolet light with a TiO2 metasurface
,” Nano Lett.
19
(12
), 8972
–8978
(2019
).201.
H.
Liu
, C.
Guo
, G.
Vampa
, J. L.
Zhang
, T.
Sarmiento
, M.
Xiao
, P. H.
Bucksbaum
, J.
Vučković
, S.
Fan
, and D. A.
Reis
, “Enhanced high-harmonic generation from an all-dielectric metasurface
,” Nat. Phys
14
(10
), 1006
–1010
(2018
).202.
Y.
Tang
, Y.
Intaravanne
, J.
Deng
, K. F.
Li
, X.
Chen
, and G.
Li
, “Nonlinear vectorial metasurface for optical encryption
,” Phys. Rev. Appl.
12
(2
), 024028
(2019
).203.
H.
Ren
, X.
Fang
, J.
Jang
, J.
Bürger
, J.
Rho
, and S. A.
Maier
, “Complex-amplitude metasurface-based orbital angular momentum holography in momentum space
,” Nat. Nanotechnol.
15
, 948
–955
(2020
).204.
X.
Fang
, H.
Ren
, and M.
Gu
, “Orbital angular momentum holography for high-security encryption
,” Nat. Photonics
14
(2
), 102
–108
(2020
).205.
H.
Zhou
, B.
Sain
, Y.
Wang
, C.
Schlickriede
, R.
Zhao
, X.
Zhang
, Q.
Wei
, X.
Li
, L.
Huang
, and T.
Zentgraf
, “Polarization-encrypted orbital angular momentum multiplexed metasurface holography
,” ACS Nano
14
(5
), 5553
–5559
(2020
).206.
A. H.
Dorrah
, N. A.
Rubin
, A.
Zaidi
, M.
Tamagnone
, and F.
Capasso
, “Metasurface optics for on-demand polarization transformations along the optical path
,” Nat. Photonics
15
(4
), 287
–296
(2021
).207.
H.
Ren
, W.
Shao
, Y.
Li
, F.
Salim
, and M.
Gu
, “Three-dimensional vectorial holography based on machine learning inverse design
,” Sci. Adv.
6
(16
), eaaz4261
(2020
).208.
Y.
Hu
, X.
Luo
, Y.
Chen
, Q.
Liu
, X.
Li
, Y.
Wang
, N.
Liu
, and H.
Duan
, “3D-Integrated metasurfaces for full-colour holography
,” Light Sci. Appl.
8
(1
), 86
(2019
).209.
R. T.
Marler
and J. S.
Arora
, “Survey of multi-objective optimization methods for engineering
,” Struct. Multidiscip. Optim.
26
(6
), 369
–395
(2004
).210.
M. M. R.
Elsawy
, A.
Gourdin
, M.
Binois
, R.
Duvigneau
, D.
Felbacq
, S.
Khadir
, P.
Genevet
, and S.
Lanteri
, “Multiobjective statistical learning optimization of RGB metalens
,” ACS Photonics
8
(8
), 2498
–2508
(2021
).211.
M. M. R.
Elsawy
, M.
Binois
, R.
Duvigneau
, S.
Lanteri
, and P.
Genevet
, “Optimization of metasurfaces under geometrical uncertainty using statistical learning
,” Opt. Exp.
29
(19
), 29887
(2021
).212.
C.-H.
Lin
, Y.-S.
Chen
, J.-T.
Lin
, H. C.
Wu
, H.-T.
Kuo
, C.-F.
Lin
, P.
Chen
, and P. C.
Wu
, “Automatic inverse design of high-performance beam-steering metasurfaces via genetic-type tree optimization
,” Nano Lett.
21
(12
), 4981
–4989
(2021
).213.
I.
Sajedian
, H.
Lee
, and J.
Rho
, “Double-deep Q-learning to increase the efficiency of metasurface holograms
,” Sci Rep
9
(1
), 10899
(2019
).214.
M.
Meier
, V.
Romano
, and T.
Feurer
, “Material processing with pulsed radially and azimuthally polarized laser radiation
,” Appl. Phys. A
86
(3
), 329
–334
(2007
).215.
K.
Toyoda
, F.
Takahashi
, S.
Takizawa
, Y.
Tokizane
, K.
Miyamoto
, R.
Morita
, and T.
Omatsu
, “Transfer of light helicity to nanostructures
,” Phys. Rev. Lett.
110
(14
), 143603
(2013
).216.
J. T.
Barreiro
, T.-C.
Wei
, and P. G.
Kwiat
, “Remote preparation of single-photon ‘hybrid’ entangled and vector-polarization states
,” Phys. Rev. Lett.
105
(3
), 030407
(2010
).217.
V.
Parigi
, V.
D’Ambrosio
, C.
Arnold
, L.
Marrucci
, F.
Sciarrino
, and J.
Laurat
, “Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory
,” Nat. Commun.
6
(1
), 7706
(2015
).218.
F.
Lu
, W.
Zheng
, and Z.
Huang
, “Coherent anti-Stokes Raman scattering microscopy using tightly focused radially polarized light
,” Opt. Lett.
34
(12
), 1870
(2009
).219.
L.
Novotny
, M. R.
Beversluis
, K. S.
Youngworth
, and T. G.
Brown
, “Longitudinal field modes probed by single molecules
,” Phys. Rev. Lett.
86
(23
), 5251
–5254
(2001
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.