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Diatomic Metasurface for Vectorial Holography Zi-Lan Deng, Junhong Deng, Xin Zhuang, Shuai Wang, Kingfai Li, Yao Wang, Yihui Chi, Xuan Ye, Jian Xu, Guo Ping Wang, Rongkuo Zhao, xiaolei wang, Yaoyu Cao, Xing Cheng, Guixin LI, and Xiangping Li Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b00047 • Publication Date (Web): 28 Mar 2018 Downloaded from http://pubs.acs.org on March 29, 2018
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Nano Letters
Diatomic Metasurface for Vectorial Holography Zi-Lan Deng1,†, Junhong Deng2,†, Xin Zhuang2, Shuai Wang1,6, Kingfai Li2, Yao Wang3, Yihui Chi2, Xuan Ye1, Jian Xu1, Guo Ping Wang4, Rongkuo Zhao5, Xiaolei Wang6, Yaoyu Cao1, Xing Cheng2, Guixin Li2,*, Xiangping Li1,* 1
Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Institute of
Photonics Technology, Jinan University, Guangzhou 510632, China. 2
Department of Materials Science and Engineering, Shenzhen Institute for Quantum Science and
Engineering, Southern University of Science and Technology, 518055, Shenzhen, China. 3
Materials Characterization and Preparation Center, Southern University of Science and Technology,
518055, Shenzhen, China. 4
College of Electronic Science and Technology, Shenzhen University, Shenzhen 518060, China.
5
NSF Nanoscale Science and Engineering Center, University of California, Berkeley, California 94720,
USA. 6
Institute of Modern Optics, Key Laboratory of Optical Information Science and Technology, Nankai
University, Tianjin 300350, China.
Abstract The emerging metasurfaces with the exceptional capability of manipulating an arbitrary wavefront have revived the holography with unprecedented prospects. However, most of the reported meta-holograms suffer from limited polarization controls for a restrained bandwidth, in addition to their complicated meta-atom designs with spatially-variant dimensions. Here, we demonstrate a new concept of vectorial holography based on diatomic metasurfaces consisting of meta-molecules formed by two orthogonal meta-atoms. Based on a simply linear relationship between phase and polarization modulations with displacements and orientations of identical meta-atoms, active diffraction of multiple polarization states and reconstruction of holographic images are simultaneously achieved, which is robust against both incident angles and wavelengths. Leveraging this appealing feature, broadband vectorial holographic images with spatially-varying polarization states and dual-way 1
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polarization switching functionalities have been demonstrated, suggesting a new route to
achromatic
diffractive
elements,
polarization
optics
and
ultra-secure
anti-counterfeiting. Keywords: Metasurfaces, Vectorial holography, Full phase and polarization control, dual-way polarization multiplexing †
These authors contributed equally to this work. E-mail:
[email protected],
[email protected] *
Two-dimensional metasurfaces,1-8 the ultrathin layers of spatially-varying meta-atoms, have been shown to control the wavefront of light wave with unprecedented abilities, leading to many novel planar optical components, such as meta-lenses,9-17 metasurface beam shapers,18-24 meta-polarizers25-31 and meta-holograms.32-35 The metasurface platform has revitalized the holography with high performances36 and extraordinary capabilities.37 Particularly, dispersionless and full control of both phase and polarization has motivated the research for meta-holograms based on novel meta-atoms, which is quite challenging for conventional holography. In this context, geometric plasmonic metasurfaces36-41 and Huygens all-dielectric metasurfaces42, 43 have been proposed. As far as the dispersionless phase control, geometric metasurface provides a nice solution, as the phases only depend on the in-plane orientation angles of the meta-atoms with identical geometries.36-41 However, the polarization state of the incident light for geometric metasurfaces is restricted to circular polarization.36 On the other hand, Huygens metasurfaces work for arbitrarily-polarized incident light, but
2
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can only control the phase of the wavefront without any polarization manipulation.42, 43
To circumvent this constraint, the combination of geometric phase with propagation
phase was proposed for complete control of the
phase and polarization,44, 45 leading
to unprecedented capability of multiplexing two independent phase profiles in arbitrary orthogonal polarization states,44,
45
and fascinating applications such as
arbitrary spin to orbital conversion46. Nevertheless, in all the previous metasurface holograms, the output polarization states of holographic images are not freely controllable, which only exhibit limited polarization states determined by the incident light. In this Letter, we propose the concept of vectorial meta-holography based on diatomic metasurfaces that can diffract holographic images with multiple arbitrary polarization states. The building block of the metasurface follows a diatomic meta-molecule design consisting of two orthogonal meta-atoms (Figure 1a). Without varying the dimension of meta-atoms, the diatomic metasurface modulates both the spatial displacement and orientation angle of constituent meta-atoms in each meta-molecule for full and dispersionless phase and polarization control. Compared with the previous schemes for full phase and polarization control by varying both dimensions and orientations of meta-atoms,44-46 the displacement-targeted phase47 introduced by the diatomic meta-molecule can be continuously manipulated, which is inherently robust against both wavelengths and incident angles. The polarization states of the diatomic meta-holograms in this work are freely controllable by 3
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meticulously tuning the geometrical parameters of the meta-molecules, enabling the realization of broadband vectorial holographic images with arbitrary polarization distributions at visible-near infrared wavelengths, which is superior to traditional vectorial holography that can only passively diffract and reconstruct two orthogonal polarization states.48, 49 Leveraging this feature, a new functionality, the dual-way polarization-switchable
meta-holograms that can simultaneously switch the
holographic images at both input and output beam paths, were also experimentally demonstrated. We believe that, the proposed diatomic vectorial meta-holograms provide a powerful platform for various applications such as bio-imaging, optical data storage, information encryption and anti-counterfeiting.50, 51 As shown in Figure 1a, the meta-molecule of the diatomic metasurface consists of two identical plasmonic meta-atoms with the directions of their long arms perpendicular to each other. To obtain the near-unity diffraction efficiency, we adopt the metal-dielectric-metal tri-layer design of plasmonic meta-atoms.52, 53 At its -1st diffraction direction in the far field, the phase and polarization of scattered light from each meta-molecule can be independently manipulated in a linear form through finely tuning the global displacement of the meta-molecules, the local displacement between constituent meta-atoms, as well as the in-plane orientation angle of the meta-molecules, respectively (Figure 1a). From the powerful ability of simultaneously controlling both phase and polarization with the meta-molecules, holographic images with pre-designed arbitrary polarization distributions can be obtained under 4
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illumination of a linearly polarized light (Figure 1b). Considering only the 0th and -1st diffraction channels of the metasurface consisting of meta-molecules, the momentum conservation along the metasurface interface gives that,
2π
λ
sin θ0 +
2π
λ
sin θ−1 =
2π , p0
(1)
where λ is the wavelength of the incident light, p0 is the periodicity of the meta-molecule in the x direction, θ0 and θ-1 represent the incident angle and diffraction angle, respectively. The displacement-targeted phase due to the light path differences in both input and output sides of the metasurface can be written as (Supplementary sections 1, 2), 2π
p ( sin θ 0 + sin θ −1 ) = 2π p / p0 , λ 2π s ( sin θ 0 + sin θ −1 ) = 2π s / p0 , δ= λ
ϕ=
(2) (3)
where p is the global displacement from the unit cell boundary to the centroid of the meta-molecule, and s is the local displacement between the two constituent meta-atoms in each meta-molecule. Considering the meta-atom with strong anisotropy that only responds to light with polarization along its longitudinal axis, then φ and δ will represent the overall wavefront phase and relative phase between two perpendicular field components, respectively. As a result, the meta-molecule simultaneously enables both phase and polarization modulation in the -1st diffraction order with the form,
5
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E1 iϕ cos Ψ = e iδ , e sin Ψ E2
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(4)
where Ψ regulates the amplitude ratio of the output field which is equal to the orientation angle of the meta-atom with respect to the x-axis denoted as ψ (see Supplementary section 1),
Ψ=ψ.
(5)
As it can be seen, all the three parameters (φ, δ, Ψ) that determines the overall phase and polarization states of light are simply linear functions of parameters (p, s, ψ), which are independent of both incident angles and wavelengths. Therefore, such diatomic metasurfaces exhibit intrinsically dispersionless phase and polarization modulations in their corresponding diffraction directions. Note that, the diffracted holographic image will locate at different angles when the incident wavelength are different, because when P0 is fixed, θ −1 will vary with the wavelength λ . Nevertheless, the appearance of the holographic image sustains robust at its corresponding diffraction direction. In theory, such full phase and polarization control is inherently dispersionless and enables broadband performances without considering any specific constituent materials. Without loss of generality, by taking nanorods made of real metals exhibiting dispersive permittivities into consideration, the optimized geometry still promises the dispersionless phase and polarization modulation in a broadband spectral range. Figure 2a-c show diffraction efficiencies of a periodic plasmonic nanorod array made of silver, with a length L=130 nm, a width w=50 nm, a thickness t=30 nm, a 6
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periodicity p0=500 nm, and a dielectric spacer thickness h=130 nm, respectively. Note that, the periodicity in the x direction p0 is meticulously chosen to make sure that only the 0th and -1st diffraction order channels are allowed to propagate 52. The transverse electric- (TE-) polarized light whose electric field is parallel to the nanorod can be high-efficiently diffracted into the -1st diffraction order (red solid curve in Figure 2b) with the near-complete suppression of the specular reflection (red dashed curve in Figure 2b), while the diffraction of transverse magnetic- (TM-) polarized light (electric field perpendicular to nanorod) is negligible (Supplementary section 3). Such polarization-selective diffraction enhancement does not rely on conventional phase-gradient metasurfaces that mimic a blazed grating, but stems from the plasmonic resonance of single unit cell, which largely simplifies the metasurface design.52, 54, 55 The enhanced diffraction spans for a wide wavelength range from 650 nm to 850 nm and an incident angle from 35o to 85o (Figure 2c), which is confined by the bandwidth of the plasmonic resonance and the Wood’s anomaly (WA) curves (white dashed curves in Figure 2c). For full phase and polarization control, one can replace the single nanorod with an orthogonally-aligned nanorod pair in each meta-molecule with the same periodicity as shown in Figure 2d (Supplementary section 4). Then, the diffracted light will have two orthogonal field components E1 and E2 parallel to each of the two nanorods, respectively. By varying the local displacement s from 0 to p0/2 (Figure 2e), the relative phase difference δ between E1 and E2 increases linearly with s, while the 7
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amplitude ratio Ψ = atan (| E1 / E2 |) stays almost unchanged for a broadband spectral range from 650 nm to 850 nm. The variation of δ from –π to 0 can be obtained by interchanging the individual positions of the two nanorods, which is equivalent to spanning s from 0 to -p0/2. The linear dependence of the parameter Ψ on the orientation angle ψ of the nanorods without the variation of δ is also shown in Figure 2f. As a result, when s varies from -p0/2 to p0/2, and ψ varies from 0o to 90o, arbitrary polarization states can be obtained in a broadband spectral range from 650 nm to 850 nm. The total diffraction efficiency will vary for different incident angles and wavelengths due to the scattering properties of the individual meta-atoms, nevertheless, the modulated phase and polarization parameters are applicable for a broad wavelength and angle range. It should be noted that, to avoid the influence of near-field coupling at variant local displacements, the two orthogonally-aligned nanorods were designed at a certain displacement (Sy=225 nm) in the y-direction (Figure S6). The total unit cell size of the meta-molecule in the y-direction Py=2Sy=450 nm is kept in the subwavelength scale so that there are no higher order diffraction in the y-direction. To verify the versatile polarization and phase controlling capability of the diatomic metasurfaces. We designed and fabricated 12 meta-holograms with different emoji images, where the unit cells have different orientation angles ψ and local displacements s, and experimentally characterize their vectorial features with the experimental setup as shown in Figure 3a. Both the reconstructed holographic images 8
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and the corresponding polarization states are shown in Figure 3b-m. The measurement of the polarization state of each holographic images is conducted by measuring the Stokes parameters (Supplementary section 5). According to the Stokes parameters, polarization
ellipse
(red
curves)
defined
by
the
equation
E12 E22 E E cos δ + −2 1 2 = sin 2 δ of each meta-hologram is plotted in the 2 2 sin Ψ cos Ψ sin Ψ cos Ψ right panel of each sub-figure in Figure 3, which is reasonably consistent with the simulated polarization states as shown in blue curves. Indeed, different holographic images with versatile polarization states can be obtained, with the measured efficiencies of 30%. The discrepancy between measured efficiencies and theoretical predictions can be largely ascribed to the oxidation effects of silver, which leads to the fabricated nanorod dimension deviated from the optimal design. For s=p0/2 (Figure 3b-d), the phase differences between the two orthogonal components E1 and E2 are δ=π, each unit cell of the metasurface performs as a half-wave plate, different orientation angles ψ of the meta-atom means rotating the half-wave plate with the angle ψ, which will rotate the linear polarization of the incident light by 2ψ. For s=p0/4 (Figure 3h-j), the phase differences between E1 and E2 are δ=π/2, each unit cell performs as a quarter-wave plate, when the angle between the equivalent quarter-wave plate and the linear incident light is π/4 (Figure 3i), circularly polarized light can be expected. The slight discrepancy between the experiment and the simulation can be attributed to the imperfection of the fabrication (Figure S8). When s takes other parameters, arbitrary phase differences between E1 and E2 can be 9
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obtained, which enables the arbitrarily-phased waveplate. By rotating the arbitrarily-phased waveplate, arbitrary polarization state conversion from a linear incident polarization can be realized. Note that, Figure 3 only shows the s>0 (0
