Embed Size (px)
Citation preview
1
Nonlinear Vectorial Metasurface for Optical Encryption
Yutao Tang,1,2 Yuttana Intaravanne3, Junhong Deng,1,2 King Fai Li,1,2 Xianzhong Chen,3,* and Guixin Li1,2,†
1Department of Materials Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055 China.
2Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055 China.
3SUPA, Institute of Photonics and Quantum Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
The unprecedented capability of metasurface in manipulation of light propagation has
been extended to the nonlinear optical regime, enabling a plethora of applications for
nonlinear optical security and encryption. One of the key issues in this area is how to
arbitrarily control the vectorial polarization profile of nonlinear waves. Here we
propose and experimentally demonstrate a nonlinear photonic metasurface that can
generate a vectorial polarization profile for nonlinear imaging. The high-resolution
grayscale image can be read out through a second harmonic generation (SHG) beam
from an ultrathin nonlinear metasurface. The polarization of SHG waves can be locally
manipulated by simply changing the orientation angle of the plasmonic meta-atoms.
The grayscale image is revealed using a linear polarizer based on the Malus’s law. We
believe that the rich polarization information based on nonlinear metasurfaces has
significant potential for the applications in nonlinear optical image encryption, security,
anti-counterfeiting, and so on.
2
I. INTRODUCTION
Light, with its abundant degrees of freedom, has become the cornerstone of the
drastic development of information processing, optical communications, etc. The
degrees of freedom of light field that could be modulated include the amplitude, the
phase, the state of polarization and the orbital angular momentum (OAM), etc.
Recently, it was demonstrated that photonic metasurfaces, consisting of spatially
variant meta-atoms, provide unprecedented capability to tailor the various degrees of
freedom of light. To some extent, the metasurface based devices are more compact and
have more integrated functionalities than many conventional optical components [1,2].
Applications of metasurfaces such as planar lenses [3-5], retroreflector [6], metasurface
hologram [7-13], optical diffuser [14], polarimetry [15], augmented reality [16] and so
on have been successfully demonstrated. Among the family of working mechanisms,
phase control represents a powerful tool to manipulate the properties of light fields. In
the linear optical regime, both the propagation phase and the geometric Pancharatnam-
Berry phase (P-B phase) have been widely used for polarization encoded optical
holography [13] and generation of vectorial light beam via arbitrary spin-to-orbital
angular momentum conversion [17,18]. While the above phase control methods are
based on the elaborate engineering of the size and orientation of the meta-atoms, an
alternative way to manipulate the polarization of light can be achieved by controlling
both the displacements and orientations of two orthogonal identical meta-atoms [11].
Such diatomic metasurface can be utilized to implement vectorial optical
holography [11]. In addition to the applications in optical holography, phase control
metasurface can be also used for high-resolution grayscale and multicolor
imaging [19,20].
Recently, the study of light-matter interaction on nonlinear optical metasurfaces
has attracted extensive interests [21-28]. Nonlinear optical processes such as
second [29-34], third [35-37] and high [38] harmonic generation, broadband optical
frequency mixer [39] have been extensively investigated by using both plasmonic and
dielectric metasurfaces. It is reported that the nonlinear optical susceptibility of the
meta-atoms strongly depends on the orders of the nonlinear process, the spin states of
fundamental wave (FW) and the local symmetry of the meta-atom [40]. Ascribed to the
effect of the nonlinear P-B phase, the method to continuously and locally tailor the
phase of nonlinear optical susceptibility was established recently [41], facilitating
3
applications such as nonlinear holography [42,43], nonlinear spin-orbital interaction of
light [44], nonlinear metalens [45] and nonlinear image encryption [46] and so on.
Among all the above topics, the high-resolution nonlinear metasurface imaging has
great potential for information encoding and encryption. Previous effort has been
dedicated to the modulation of the intensity of nonlinear signal in real space by utilizing
the interference of SHG from two neighboring meta-atoms [46], however, the image
resolution is limited by the diatomic meta-molecule. Here we demonstrate a nonlinear
optical metasurface to locally manipulate the polarization states of the SHG wave and
encode a high-resolution image in the polarization profile accordingly [Fig. 1(a)]. Such
nonlinear image information could be revealed after filtering out the FW and converting
the vectorial polarization profile into intensity profile according to the Malus’s law. The
difference between the linear geometric metasurface and nonlinear geometric
metasurface provides a possible route to realize different polarization profiles for the
fundamental wave and the SHG wave, which can further improve the level of security
and encryption.
4
FIG. 1. Nonlinear vectorial metasurface for optical encryption. (a) Schematic illustration of a nonlinear optical process to generate a polarization profile of the second harmonic generation (SHG) wave, by using a nonlinear photonic metasurface. A linear polarizer acts as an analyzer to convert the polarization profile into a grayscale image. (b) Metasurface unit cells with nonlinear gold meta-atoms. The unit cell is 500 nm × 500 nm and the length (L) and width (w) of each rectangular petal. The orientation parameter θ is varied to locally manipulate the polarization states of the SHG wave. (c) The generated SHG intensity is a squared cosine function of θ when the transmission axes of polarizer and analyzer are aligned horizontally. (d) The SHG intensities of θ = 0° and 30° meta-atoms behind a rotated analyzer, where α is the angle between the transmission axes of the analyzer and the horizontally aligned polarizer.
II. DESIGN PRINCIPLE OF THE NONLINEAR ENCRYPTION
METASURFACES
To encrypt image information into nonlinear optical devices, we utilize the
nonlinear plasmonic meta-atoms with three-fold rotational (C3) symmetry to construct
the nonlinear metasurface [Fig. 1(b)]. For a meta-atom with m-fold rotational
symmetry, when illuminated along its rotational axis by circularly polarized
fundamental waves, the allowed orders of the nonlinear harmonic generation are
restricted by the selection rule as 1n lm= ± . where l is an integer and the ‘+’ and ‘−’
signs indicate that the harmonic waves and the FWs possess the same and opposite spin
states [40,41]. Therefore, the C3 meta-atom can selectively produce SHG with opposite
handedness to that of the incident circularly polarized FW. More significantly, the
nonlinear polarizability of the meta-atoms can be continuously manipulated by varying
their orientations [Fig. 1(b), right panel]. As a result, a nonlinear geometric phase −3σθ
is simultaneously imparted to the SHG wave, where is the handedness of the
incident FW and θ is the angle by which the C3 meta-atom is rotated with respect to
the laboratory frame [40]. By using this characteristic we can encrypt an image
information into a polarization profile of the SHG waves.
Consider a horizontally polarized FW, its polarization state can be represented by
components as , where
and denote the components of the FW with left- and right-
circular polarizations, respectively, and ω is the angular frequency of the FW. After
passing through a nonlinear meta-atom, the polarization state of the SHG wave is given
by , the subscript 2ω
1σ = ±
FW LCP / 2 RCP / 2ω ω ω
= + TLCP [1 i] / 2ω
=
TRCP [1 i] / 2ω
= −
2 2 2SHG LCP exp(3i ) / 2 RCP exp( 3i ) / 2
ω ω ωθ θ= + −
5
denotes the double frequency of the SHG wave, in other words, a phase difference
equals to 6θ is introduced between the two opposite spin components of the SHG wave,
corresponding to a 6θ rotation of the polarization vector in the equator of the Poincaré
sphere. Due to the two-to-one homomorphism between the physical SU(2) space of the
light beam and the topological SO(3) space of Poincaré sphere [47], such an equatorial
rotation corresponds to a 3θ rotation of the orientation angle of the linearly polarized
light. A linearly polarized FW along the horizontal direction can produce a transmitted
SHG wave with its polarization angle manipulated locally by the in-plane rotation of
nonlinear meta-atoms θ(x,y), and therefore encrypt a polarization profile.
To reveal the hidden information, we can filter out the FW by using a color filter
and then use a polarization analyzer to convert the polarization profile into an intensity
profile. According to the Malus’s law, when a polarized light beam passes through a
polarizer, the transmitted light intensity is , where α is the angle
between the polarization direction of light and the transmission axis of the polarizer.
The polarization direction of the SHG wave is rotated 3θ with respect to the horizontal
direction, and the insertion of a polarizer with horizontally aligned transmission axis
will lead to the intensity modulation, which is , as shown in
[Fig. 1(c)]. Therefore, the spatial intensity modulation I(x,y) after the linear analyzer
can reveal the distribution of the orientations of the meta-atoms θ(x,y), hence the
encoded image.
III. RESULTS AND DISCUSSION
Here we fabricate two nonlinear metasurfaces for polarization manipulation by
using standard electron beam lithography followed by a lift-off process (see
Supplemental Material [48] for details). The C3 gold meta-atoms sit on an indium tin
oxide (ITO) glass, with ITO thickness of ~20 nm. The width and the length of each arm
of the C3 meta-atom are 80 nm and 180 nm, respectively [Fig. 1(b)]. Each pixel is a
500 × 500 nm square cell with the C3 meta-atom at center. Two images comprising 201
× 201 pixels are eventually embedded into two small metasurfaces of 100 × 100μm
squares. One image is a grayscale bar which consisting 101 grayscale levels with a
linear intensity increase from the darkest to the brightest, while the other is an image of
a grayscale flower. The SEM and optical images of the fabricated metasurfaces are
shown in Figs. 2(a)-2(d).
2) (0)cos(I Iα α=
20) 3( cosI Iθ θ=
6
We first measured the linear transmittances of the fabricated samples, as are shown
in Fig. 2(e). The transmittances are measured as the transmission axes of the polarizer
and the analyzer are parallel to each other, both horizontally aligned. The transmission
spectra of the two distinct samples are virtually identical to each other, proved that the
meta-atoms are isotropic when working in the linear mode. We also measured the
transmittance when the analyzer was perpendicular to the polarizer. The near to zero
transmittance clearly shows there is no polarization conversion for the incident light
(see Fig. S2 in Supplemental Material [48]). When working in the nonlinear mode, as
expected from the theoretical analysis, the metasurfaces exhibit strong dependencies on
the spin of the FW signal. As shown in Figs. 2(f)-2(g), under the illumination of a
circularly polarized (LCP or RCP) FW, the measured intensity of SHG wave with
opposite handedness are much larger than the same one. The measured SHG responses
of the grayscale bar sample also show maximum efficiency at fundamental wavelength
of 1225 nm, where we also measured the power dependence of the SHG signal, which
is presented in Fig. 2(h). The fitted slopes for both conversions of cross polarization
combination (LCP-RCP and RCP-LCP) are close to 2.0, which is the characteristic of
the nonlinear SHG process.
FIG. 2. Vectorial metasurfaces and the measured optical properties. Scanning electron microscopy (SEM) images of the metasurfaces for encoding (a) a grayscale bar and (b) an image of a flower. (c) and (d) are corresponding optical microscope images of the bar and flower metasurfaces. (e) Measured linear transmission spectra of the two samples in the near infrared regime. The transmission axes of the polarizer and the analyzer are parallel to each other, both horizontally aligned. (f) Measured nonlinear SHG intensity of the grayscale bar sample as the fundamental wavelength varies. Four spin polarization combinations are recorded to reveal the cross-polarization conversion property of the metasurface. The maximum SHG intensity is observed at 1225 nm. (g)
7
Nonlinear response of the metasurface for the encoded flower. Strongest SHG response is found at 1250 nm. (h) Power dependencies of the SHG intensity of the flower metasurface.
To reveal the image hiding in the SHG signal of the nonlinear metasurface, we use
a pair of linear polarizers as polarizer and analyzer to retrieve the image encoded in the
SHG waves, in addition to a color filter to filter out the FW. The experimental setup is
shown in Fig. 3(a). We observe the SHG polarization profile at the pumping wavelength
of 1225 nm, under the pumping power of 15 mW. Fig. 3(b) shows the measured images
collected with varied orientations of the transmission axis of the analyzer while fixing
the polarizer with horizontally aligned transmission axis. The figure also includes the
simulated results of the corresponding scenarios (see simulation method in
Supplemental Material [48]). While the simulation results assume homogeneous
illumination of the fundamental wave, the laser beam illuminated at the metasurface in
experiments possesses a Gaussian intensity profile. As a result, the intensity variations
are most obvious at the center of each measured images when the analyzer is rotated,
while in the marginal parts of the images (especially in the four corners), only slight
variations are observed. In all measured images, we can consistently observe a range of
brightness from the brightest to the darkest, and the positions of the brightest and the
darkest lines are changing as expected in the simulated results. Such a position shift is
most pronounced when the transmission axes of the polarizer and the analyzer are
changed from mutually parallel to orthogonal configurations [α＝ 0° and 90° in
Fig. 3(b), respectively], as the brightest line in the center changes to the darkest line,
although the FW is the strongest at center. Therefore, our observation successfully
proved the encoding capability of the nonlinear metasurface, indicating that the
predesigned local orientation profile of the nonlinear meta-atoms can effectively impart
a polarization profile into the SHG wave.
8
FIG. 3. Schematic of experimental setup and nonlinear optical results of the grayscale bar metasurface. a) Optical setup. P: linear polarizer; L: lens; Obj: objective lens; CF: color filter (short pass filter); CCD: camera. b) Simulated and experimental results for the SHG intensity profiles of the grayscale bar metasurface. Pumping wavelength is at 1225 nm. The analyzer is rotated counterclockwise while the transmission axis of the polarizer is fixed along the horizontal direction. α is the angle between the transmission axes of the polarizer and the analyzer.
To demonstrate the polarization encoding capability of the nonlinear metasurface
more vividly, we designed the second metasurface and encoded an image of a flower
into it. We also measured the revealed intensity profile converted from the vectorial
polarization profile of the SHG wave. The experimental setup is the same as the one
used to measure the grayscale bar sample, but the pumping wavelength is set as 1250
nm for the maximum nonlinear response [as indicated in Fig. 2(e)]. The simulated and
measured results are presented in Fig. 4, where varied analyzer orientations are set to
reflect the polarization profile of the SHG beam. The image revealed by transmission
axes parallel aligned setup (α＝ 0°) shows clearly view of a flower, with exact
configuration of five petals as the design target, and fine grayscale change from the
flower petal centers to the corners. Although the small water droplet on one of the
flower petals can’t be clearly distinguished from the measured image, the overall
9
display quality of the image is quite impressive. The slight difference should be
attributed to the fabrication imperfection. On the other side, the measured images under
different configurations of the analyzer varied in a way consistent with the simulated
results. When the transmission axis of the analyzer is rotated from the parallel direction
of the polarizer to the orthogonal direction, the bright pixels of the image become dark
and vice versa, therefore an operation of image reversion can be easily achieved by
changing the orientation of the transmission axis of the analyzer. Actually, any pair of
images obtained after orthogonally orientated analyzer are complementary to each
other. For example, images obtained in α＝0° and α＝90°, or α＝30° and α＝
120° configurations, are mutually inverted from each other. This complementary
characteristic of the image pairs also indicates the superior polarization encoding
capability of the nonlinear metasurface. As the complementary characteristic of the
nonlinear image indicate, the summed image intensity should be homogenous, i.e. no
intensity modulation of SHG waves from the nonlinear metasurface. The measured
SHG image without an analyzer is shown in the last column of Fig. 4, from which we
can find that only slight intensity variation as predicted by the theory.
FIG. 4. Nonlinear vectorial metasurface for encoding a flower into the polarization profile of the SHG wave. The measurement setup is same as that in Fig. 3(a). The pumping wavelength is at 1250 nm. The last column shows the results when the analyzer [P2 in Fig. 3(a)] is absent in the experimental setup.
IV. CONCLUSION
To realize nonlinear responses, the complex phase-matching process and optically
large samples are typically required due to the inherent weak nonlinear response in
natural materials. Nonlinear metasurfaces have provided unprecedented capability to
produce similar effects with much smaller footprints, which can keep pace with
continued miniaturization of nonlinear devices and the daunting increase in the volume
10
of the integrated nonlinear systems. Nonlinear metasurface paradigm is very promising
and can efficiently generate nonlinear polarization topology by engineering artificial
materials with predesigned polarization profile. The manipulation of light polarization
at subwavelength resolution via metasurfaces has been extended to the nonlinear optical
regime, enabling the applications of this technique for nonlinear optical security and
encryption, which are impossible or very difficult to realize with conventional methods.
Such nonlinear image information could be revealed after filtering out the FW and
converting the vectorial polarization profile into the intensity profile according to an
elegant rule (Malus’s law).
In this work, we utilized the spin-dependent nonlinear phase control metasurface
to manipulate the polarization profile of the second harmonic generation wave. A one-
to-one correspondence between the desired relative phase difference of the two spin
components of the SHG signal wave and the local orientation configuration of the
nonlinear meta-atoms can be built. With such an encoding process, one can effectively
control the polarization states of the SHG wave in the transverse plane. Using a linear
polarizer we can simply convert the polarization profile into an intensity profile, which
is easier for people to observe. Our demonstration of the polarization controlled
nonlinear metasurface provide a novel way for image encryption in nonlinear optical
process, which may have important applications for security of optical information.
ACKNOWLEDGEMENTS
G. L. is supported by the National Natural Science Foundation of China
(11774145), the Guangdong Provincial Innovation and Entrepreneurship Project
(2017ZT07C071), the Applied Science and Technology Project of Guangdong Science
and Technology Department (2017B090918001) and the Natural Science Foundation
of Shenzhen Municipal Science and Technology Innovation Commission
(JCYJ20170412153113701). X. C. acknowledge the support from Engineering and
Physical Sciences Research Council of the United Kingdom (Grant Ref:
EP/P029892/1). Y.T., Y.I. and J.D. contributed equally to this work.
[1] A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, Planar photonics with
metasurfaces, Science 339, 1232009 (2013).
11
[2] 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 (2016).
[3] X. Chen, L. Huang, H. Muhlenbernd, 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).
[4] M. Khorasaninejad and F. Capasso, Metalenses: Versatile multifunctional
photonic components, Science 358, 1146 (2017).
[5] 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, 227 (2018).
[6] A. Arbabi, E. Arbabi, Y. Horie, S. M. Kamali, and A. Faraon, Planar
metasurface retroreflector, Nat. Photon. 11, 415 (2017).
[7] 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).
[8] G. Zheng, H. Muhlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang,
Metasurface holograms reaching 80% efficiency, Nat. Nanotechnol. 10, 308
(2015).
[9] 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).
[10] Z. L. Deng and G. Li, Metasurface optical holography, Mater. Today Phys. 3,
16 (2017).
[11] 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, 2885 (2018).
[12] 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 Sci.
Appl. 7, 95 (2018).
[13] 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, 113901 (2017).
12
[14] A. E. Minovich, M. Peter, F. Bleckmann, M. Becker, S. Linden, and A. V.
Zayats, Reflective Metasurfaces for Incoherent Light To Bring Computer
Graphics Tricks to Optical Systems, Nano Lett. 17, 4189 (2017).
[15] A. Martínez, Polarimetry enabled by nanophotonics, Science 362, 750 (2018).
[16] G.-Y. Lee, J.-Y. Hong, S. Hwang, S. Moon, H. Kang, S. Jeon, H. Kim, J.-H.
Jeong, and B. Lee, Metasurface eyepiece for augmented reality, Nat. Commun.
9, 4562 (2018).
[17] R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso,
Arbitrary spin-to-orbital angular momentum conversion of light, Science 358,
896 (2017).
[18] F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, and X. Chen, Vector Vortex Beam
Generation with a Single Plasmonic Metasurface, ACS Photon. 3, 1558 (2016).
[19] F. Yue, C. Zhang, X.-F. Zang, D. Wen, B. D. Gerardot, S. Zhang, and X. Chen,
High-resolution grayscale image hidden in a laser beam, Light Sci. Appl. 7,
17129 (2018).
[20] 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,
1707499 (2018).
[21] M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, Colloquium: Nonlinear
metamaterials, Rev. Mod. Phys. 86, 1093 (2014).
[22] M. Kauranen and A. V. Zayats, Nonlinear plasmonics, Nat. Photon. 6, 737-748
(2012).
[23] A. Krasnok, M. Tymchenko, and A. Alù, Nonlinear metasurfaces: a paradigm
shift in nonlinear optics, Mater. Today 21, 8 (2018).
[24] Y. Kivshar, All-dielectric meta-optics and non-linear nanophotonics, Natl. Sci.
Rev. 5, 144 (2018).
[25] H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, and X. Zhang,
Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,
Science 342, 1223 (2013).
[26] N. Segal, S. Keren-Zur, N. Hendler, and T. Ellenbogen, Controlling light with
metamaterial-based nonlinear photonic crystals, Nat. Photon. 9, 180 (2015).
13
[27] E. Almeida, G. Shalem, and Y. Prior, Subwavelength nonlinear phase control
and anomalous phase matching in plasmonic metasurfaces, Nat. Commun. 7,
10367 (2016).
[28] J. Lee, M. Tymchenko, C. Argyropoulos, P.-Y. Chen, F. Lu, F. Demmerle, G.
Boehm, M.-C. Amann, A. Alù, and M. A. Belkin, Giant nonlinear response from
plasmonic metasurfaces coupled to intersubband transitions, Nature 511, 65
(2014).
[29] M. Celebrano, X. Wu, M. Baselli, S. Großmann, P. Biagioni, A. Locatelli, C.
De Angelis, G. Cerullo, R. Osellame, B. Hecht, L. Duò, F. Ciccacci, and M.
Finazzi, Mode matching in multiresonant plasmonic nanoantennas for enhanced
second harmonic generation, Nat. Nanotechnol. 10, 412 (2015).
[30] M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, Second-harmonic
generation from magnetic metamaterials, Science 313, 502 (2006).
[31] S. Linden, F. Niesler, J. Förstner, Y. Grynko, T. Meier, and M. Wegener,
Collective effects in second-harmonic generation from split-ring-resonator
arrays, Phys. Rev. Lett. 109, 015502 (2012).
[32] K. Konishi, T. Higuchi, J. Li, J. Larsson, S. Ishii, and M. Kuwata-Gonokami,
Polarization-controlled circular second-harmonic generation from metal hole
arrays with threefold rotational symmetry, Phys. Rev. Lett. 112, 135502 (2014).
[33] S. Liu, M. B. Sinclair, S. Saravi, G. A. Keeler, Y. Yang, J. Reno, G. M. Peake,
F. Setzpfandt, I. Staude, and T. Pertsch, Resonantly enhanced second-harmonic
generation using III–V semiconductor all-dielectric metasurfaces, Nano Lett.
16, 5426 (2016).
[34] L. Kang, Y. Cui, S. Lan, S. P. Rodrigues, M. L. Brongersma, and W. Cai,
Electrifying photonic metamaterials for tunable nonlinear optics, Nat. Commun.
5, 4680 (2014).
[35] A. S. Shorokhov, E. V. Melik-Gaykazyan, D. A. Smirnova, B. Hopkins, K. E.
Chong, D.-Y. Choi, M. R. Shcherbakov, A. E. Miroshnichenko, D. N. Neshev,
and A. A. Fedyanin, Multifold enhancement of third-harmonic generation in
dielectric nanoparticles driven by magnetic Fano resonances, Nano Lett. 16,
4857 (2016).
[36] A. Ahmadivand, M. Semmlinger, L. Dong, B. Gerislioglu, P. Nordlander, and
N. J. Halas, Toroidal Dipole-Enhanced Third Harmonic Generation of Deep
Ultraviolet Light Using Plasmonic Meta-atoms, Nano Lett. 19, 605 (2019).
14
[37] S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A.
Shorokhov, I. Kravchenko, B. Luther-Davies, and Y. Kivshar, Nonlinear light
generation in topological nanostructures, Nat. Nanotechnol. 14, 126 (2019).
[38] 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, 1006 (2018).
[39] S. Liu, P. P. Vabishchevich, A. Vaskin, J. L. Reno, G. A. Keeler, M. B. Sinclair,
I. Staude, and I. Brener, An all-dielectric metasurface as a broadband optical
frequency mixer, Nat. Commun. 9, 2507 (2018).
[40] G. Li, S. Zhang, and T. Zentgraf, Nonlinear photonic metasurfaces, Nat. Rev.
Mater. 2, 17010 (2017).
[41] 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, 607 (2015).
[42] E. Almeida, O. Bitton, and Y. Prior, Nonlinear metamaterials for holography,
Nat. Commun. 7, 12533 (2016).
[43] W. Ye, F. Zeuner, X. Li, B. Reineke, S. He, C.-W. Qiu, J. Liu, Y. Wang, S.
Zhang, and T. Zentgraf, Spin and wavelength multiplexed nonlinear
metasurface holography, Nat. Commun. 7, 11930 (2016).
[44] G. Li, L. Wu, K. F. Li, S. Chen, C. Schlickriede, Z. Xu, S. Huang, W. Li, Y.
Liu, E. Y. B. Pun, T. Zentgraf, K. W. Cheah, Y. Luo, and S. Zhang, Nonlinear
Metasurface for Simultaneous Control of Spin and Orbital Angular Momentum
in Second Harmonic Generation, Nano Lett. 17, 7974 (2017).
[45] C. Schlickriede, N. Waterman, B. Reineke, P. Georgi, G. Li, S. Zhang, and T.
Zentgraf, Imaging through Nonlinear Metalens Using Second Harmonic
Generation, Adv. Mater. 30, 1703843 (2018).
[46] F. Walter, G. Li, C. Meier, S. Zhang, and T. Zentgraf, Ultrathin Nonlinear
Metasurface for Optical Image Encoding, Nano Lett. 17, 3171-3175 (2017).
[47] G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Higher-Order Poincaré
Sphere, Stokes Parameters, and the Angular Momentum of Light, Phys. Rev.
Lett. 107, 053601 (2011).
[48] See Supplemental Material for details of the fabrication of the nonlinear
plasmonic metasurfaces, the experimental setup for the measurement of the
15
linear transmittances, and the simulation method of the SHG intensity profiles
under varies experimental configurations.
