Broadband achromatic optical metasurface devices. — TEI-tagged view

Shuming WangpersName, Pin Chieh WupersName, Vin-Cent SupersName, Yi-Chieh LaipersName, Cheng Hung ChupersName, Jia-Wern ChenpersName, Shen-Hung LupersName, Ji ChenpersName, Beibei XupersName, Chieh-Hsiung KuanpersName, Tao LipersName, Shining ZhupersName, Din Ping TsaipersName (2017date). “Broadband achromatic optical metasurface devices..” Nature Communicationstitle·j.

Object of study — achromaticterm·key metasurfaceterm·key lenses and deflectors in the near-infrared

Research question — how to eliminate the chromatic aberrationterm·dom of metasurfacesterm·key caused by their phase dispersion

Contribution — a design principle for achromaticterm·key metasurfacesterm·key working over continuous 1200-1680 nm

Full text — tagged

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Broadband achromaticterm·key optical metasurfaceterm·key devices.

Abstract Among various flat optical devices, metasurfacesterm·key have presented their great ability in efficient manipulation of light fields and have been proposed for variety of devices with specific functionalities. However, due to the high phase dispersion of their building blocks, metasurfacesterm·key significantly suffer from large chromatic aberrationterm·dom. Here we propose a design principle to realize achromaticterm·key metasurfaceterm·key devices which successfully eliminate the chromatic aberrationterm·dom over a continuous wavelength region from 1200 to 1680date nm for circularly-polarized incidences in a reflection scheme. For this proof-of-concept, we demonstrate broadband achromaticterm·key metalensesterm·dom (with the efficiency on the order of ∼12%) which are capable of focusing light with arbitrary wavelength at the same focal plane. A broadband achromaticterm·key gradient metasurfaceterm·key is also implemented, which is able to deflect wide-band light by the same angle. Through this approach, various flat achromaticterm·key devices that were previously impossible can be realized, which will allow innovation in full-color detection and imaging.

Introduction Wavelength dispersion is a key characteristic of optical materials, which always plays an important role in designing optical components and systems. In most dielectrics like glasses, the index of refraction decreases with the longer wavelength, which is called normal chromatic dispersionterm·dom 1 . Utilizing such materials, refractive lenses will perform larger focal lengthsterm·key and prisms will deflect at a smaller angle for longer wavelength. Such chromatic aberrationterm·dom significantly degrades the performance of full-color optical applications, such as in communication, detection, imaging, displaying etc. Taking the refractive lenses as an example, complete elimination of chromatic aberrationterm·dom at three and four wavelengths is accomplished by integrating several materials arranged into a single component to achieve the same focal lengthterm·key, which are termed as apochromatic and superachromatic lens 2 , respectively. Although successful, this strategy adds weight, complexity and cost to optical systems, which greatly limits their usage.

In contrast to the traditional bulk optical elements, metasurfacesterm·key 3 – 6 provide a new perspective on flexibly shaping the electromagnetic field 7 by manipulating its phase, amplitude as well as polarization at will via a compact and easy-of-fabrication system. Such promising approaches prove their great features and functionality in a variety of applications, such as nonlinear dynamics 8 , light beam shaping 9 – 11 , highly dimensional holographic images 12 – 15 , polarization control and analysis 16 – 18 , invisible cloak carpet 19 etc. In addition to the compact dimension, the main distinction between metalensesterm·dom (planar lenses based on metasurfacesterm·key) and traditional optical lensesterm·dom is the integrated functionality that allows the achievement of specific characteristics such as multispectral 20 , dual-functional 21 and off-axis focusing 22 . Recent works reported the dielectric metasurfacesterm·key for metalensterm·key with high numerical aperture (NA) and optical planar camera with monochromatic aberrations that are comparable with the commercial products, presenting their potential prospect in real applications 23 , 24 . However, these proposed metasurfaceterm·key devices still exhibit large chromatic aberrationterm·dom, which is mainly attributed to following fundamental properties: the resonant phase dispersion of the building blocks used in metasurfacesterm·key, the intrinsic dispersion in used materials, as well as the different phase accumulation through light propagation in free space with various wavelengths. Many works have shown that optical metasurfacesterm·key working in a relatively broad wavelength bandwidth can be achieved 25 – 30 . However, in these reports the optical performance of resonant elements in the metasurfacesterm·key is unchanged in a broad bandwidth and this is insufficient for the suppression of chromatic aberrationterm·dom.

Up to now, several pioneering works have realized multi-wavelength achromaticterm·key metalensesterm·dom that are capable of eliminating the chromatic aberrationterm·dom at several discrete wavelengths 31 – 37 . Very recently, there has been a successful demonstration of an achromaticterm·key metalensterm·key which is able to suppress the chromatic effect over a 60-nm bandwidth in the visible 38 . However, although continuous, the working bandwidth (about 11.4% of the central wavelength) is still not broad enough for practical purposes and there is still lack of an effective design rule for unit elements in achromaticterm·key metasurfaceterm·key devices. Therefore, much work remains to be done in order to accomplish a broadband achromaticterm·key flat optical component working over a continuous bandwidth because of the abrupt phase change from the resonant unit elements. In this work, we employ the integrated-resonantterm·key unit element in metasurfacesterm·key with smooth and linear phase dispersion combining with geometric phaseterm·dom to design broadband achromaticterm·key flat optical components. For the proof of concept, achromaticterm·key converging metalensesterm·dom and beam deflector with gradient metasurfacesterm·key are demonstrated that are valid at will within a broad infrared (IR) bandwidth from wavelength of 1200 to 1680date nm. The broadband achromaticterm·key metasurfaceterm·key devices based on our approach greatly innovate a complete class of designs in full-color light manipulation and imaging and push them forward to the practical applications.

Results Phase requirement of broadband achromaticterm·key metalensterm·key As the most basic and important functional element, converging lens plays a crucial role in various optical systems. The typical distribution of phase retardation for a metalensterm·key follows: 1 φ R , λ = - 2 π R 2 + f 2 - f 1 λ where R = x 0 2 + y 0 2 is the distance from arbitrary position ( x 0 , y 0 ) on the metalensterm·key to the center and f is the focal lengthterm·key. To realize a broadband achromaticterm·key metalensterm·key (BAMLterm·dom), which is schematically shown in the right side of Fig. 1a , such phase retardation with a fixed focal lengthterm·key is exactly required in a wide range of wavelength. Generally, for the case of working wavelength λ ∈ λ min , λ max , with λ min and λ max being the boundaries of the interested wavelength band, the phase in Eq. 1 can be re-written as: 2 φ Lens R , λ = φ R , λ max +Δ φ R , λ with 3 Δ φ R , λ = - 2 π R 2 + f 2 - f 1 λ - 1 λ max Fig. 1 Achromaticterm·key metalensterm·key. a Schematic for chromatic ( left ) and achromaticterm·key ( right ) metalensesterm·dom. In the case of chromatic metalensterm·dom, the focal lengthterm·key is changed as the incident wavelength is switched, resulting in a rainbow-like focal line when it is illuminated by a light source with continuously changed wavelength. The focal point will become a single spot for the case of BAMLterm·dom with optimized phase compensationterm·key. b Phase profile for a BAMLterm·dom at arbitrary wavelength of λ ∈ { λ min , λ max } The BAMLterm·dom can only be realized once these two key phase characteristics are exactly satisfied simultaneously; therefore, the designed phase of BAMLterm·dom can be accordingly divided into two components. The former part in Eq. 2 , φ ( R , λ max ), is considered as a basic phase profile, which is only related with λ max and is independent to the working wavelength λ . Such phase profile can be acquired by exploiting the geometric phaseterm·dom as the phase modulation in each metalensterm·key unit element. The geometric phaseterm·dom, also called Berry phaseterm·dom, is produced from the rotation of the resonant elements in metasurfaceterm·key with a circularly-polarized incidence 39 . The produced phase modulation only depends on the orientation of scattered elements, which can therefore work as the solution for the wavelength-independent phase modulation. In contrary, the latter part in Eq. 2 , Δ φ ( R , λ ), is a function of working wavelength and presents a linear relation with 1/ λ , which is considered as the phase difference between various incident wavelengths. Such phase difference can be obtained by suitably designing the phase response of each unit element of the metalensterm·key, which must also exhibit the phase dispersion owning a linear relation with 1/ λ , in consistent with Δ φ ( R , λ ). Since the mechanism of this resonant phase response is completely different from the geometric phaseterm·dom, these two parts of phase won’t disturb with each other, but can be simply merged together.

It should be mentioned that an additional phase shift φ shift ( λ ) can be introduced to optimize the phase compensationterm·key effect from the specially designed metalensterm·key, since such phase shift won’t affect the focusing property of the metalensterm·key 34 , as shown in Fig. 1b . Then, the phase profile of the achromaticterm·key metalensterm·key is changed to 4 φ Lens ′ R , λ = - 2 π R 2 + f 2 - f 1 λ + φ shift ( λ ) The phase difference consequently becomes Δ φ ′ R , λ = Δ φ R , λ + φ shift λ . To maintain the linear relation with 1/ λ , φ shift ( λ ) has to match the form as φ shift ( λ ) = α / λ + β , with α = χ λ max λ min λ max - λ min and β = - χ λ min λ max - λ min , where χ denotes the largest additional phase shift between λ min and λ max at the central position of the BAMLterm·dom. It is the key parameter in the design of BAMLterm·dom, especially for the determination of the diameter of BAMLterm·dom. How to design special unit elements to compensate the phase difference at corresponding position is subsequently the crucial issue. Here, for a proof-of-concept demonstration, the working wavelength is chosen in the commonly used telecom region, i.e., { λ min , λ max }→{1200, 1680date nm}.

Design of integrated-resonantterm·key unit elements In our design, the basic building blocks of the BAMLterm·dom are metallic nano-rods (MNRs) and their assemblies, coupled MNRs. The metal-dielectric-metal structural configuration (insets in Fig. 2 ) is implemented to access a cavity-like resonance so as to enhance the operating efficiency of metasurfacesterm·key 40 , 41 . Generally, a single MNR is able to support multiple plasmonic resonances, such as the fundamental dipolar mode and various high order modes. An abrupt phase shift usually occurs when these plasmonic resonances are excited, which does not fit the requirement of smooth and linear phase difference Δ φ ′( R , λ ) (Supplementary Fig. 1 ). In contrast, the phase distribution between these resonances exhibits a smooth trend with a nearly linear profile against 1/ λ . Since such state is fall in between the two strong resonant modes, it could be termed as an integrated-resonant stateterm·dom. In addition, such integrated-resonantterm·key features provide a promising method to slickly compensate the phase difference for BAMLterm·dom. Moreover, since the produced phase compensationterm·key owns a linear relation with of 1/ λ , the BAMLterm·dom will naturally be achieved at any wavelength within the working bandwidth as long as the largest phase difference Δ φ ′( R , λ min ) is exactly compensated by the designed unit elements. Fig. 2 Phase profile of integrated-resonantterm·key unit elements based on coupled nano-rods. a , c , e RCP-to-LCP polarization conversion efficiency ( red curves ), phase profile ( blue curves ) and ( b , d , f ) electric field distribution (color mapping) of integrated-resonantterm·key unit elements. Each unit element with 550 nm periods along x and y axes consists of one or several gold MNRs with fixed thickness 30 nm. The MNRs stand on a SiO 2 /Au substrate with varying gap size, length and width are optimized to achieve various phase compensationterm·key between λ min and λ max (Supplementary Tables 1 and 2 ). The thickness of dielectric spacer SiO 2 is 60 nm. Gray region and black arrows remark the range of working bandwidth of BAMLterm·dom and positions of resonant modes, respectively Due to linear relation of the phase distribution, the slope S in the phase spectrum can be directly obtained as S = C ∕ 1 λ R 1 - 1 λ R 2 , where λ R 1 and λ R 2 are the resonant wavelengths of the MNR, and C is a constant. This indicates that the slope of the phase profile can be tuned via tuning the wavelength distance between two resonances. Therefore, one can effectively steer the phase compensationterm·key δ ( λ ) provided by the integrated-resonantterm·key unit elements composed of MNRs or coupled MNRs, which obeys δ λ = S 1 λ - 1 λ max = C 1 λ - 1 λ max ∕ 1 λ R 1 - 1 λ R 2 . The largest phase compensationterm·key produced by these unit elements between λ min and λ max therefore becomes δ = C 1 λ min - 1 λ max ∕ 1 λ R 1 - 1 λ R 2 , which can be directly utilized to cover the largest phase difference Δ φ ′( R , λ min ) required at any position in BAMLterm·dom.

For the case of slight slope S corresponding to the small phase compensationterm·key, a single MNR with large aspect ratio is utilized, in which the fundamental dipole mode and high order mode are excited. When the wavelengths of these two plasmonic modes are tuned far away from each other, the small phase compensationterm·key is realized. The detail information of the single MNR structure with large aspect ratio can be found in Supplementary Fig. 2 . To improve the operating efficiency, multiple MNRs are integrated within an integrated-resonantterm·key unit element. Following this approach, the smallest phase compensationterm·key, also a key parameter for determining the size of BAMLterm·dom, can be achieved at around 30˚, as shown in Fig. 2a . The electric field distributions at the wavelengths corresponding to the dipole mode and second order plasmonic mode are respectively plotted in Fig. 2b .

The larger phase compensationterm·key can be acquired by decreasing the difference between two resonant wavelengths of the MNR. With the aspect ratio of the MNR decreasing, the dipole mode along its short axis can be excited instead of the second order plasmonic modes, being the nearest resonant mode from the dipole mode along the long axis. With the wavelength distance between these two modes shrinking, larger phase compensationterm·key is obtained. As shown in Fig. 2c , two dipole modes can be evidently observed in the operation efficiency spectrum, in which 120˚ phase compensationterm·key is realized. The electric field distributions at these two resonant wavelengths are shown in Fig. 2d , which obviously indicates their identities.

It will turn into another issue when the phase compensationterm·key is larger than 150˚ in such integrated-resonantterm·key MNRs, in that case steering the relation between two resonances is insufficient, and one more resonance is necessary to be introduced into the working wavelength region. However, it is quite challenging to exhibit three resonances within the concerning wavelength band using single MNR. Therefore, a compound structure composed of two perpendicularly aligned MNRs with different lengths and widths is utilized to introduce the third plasmonic resonant mode. Assuming that the second resonant wavelength λ R 2 located near the middle of resonant wavelength region { λ R 1 , λ R 3 }, the slopes of phase spectrum of two wavelength regions { λ R 1 , λ R 2 } and { λ R 2 , λ R 3 } can be close to S 21 = C 21 ∕ 1 λ R 1 - 1 λ R 2 ~ S 32 = C 32 ∕ 1 λ R 2 - 1 λ R 3 , assuming C 21 ∼ C 32 = C . Thus, the entire phase slope S can be expressed as S ~ 2 C ∕ 1 λ R 1 - 1 λ R 3 , which can theoretically be two times larger than the single MNR case. Figure 2e presents the case of 210˚ phase compensationterm·key between λ min and λ max after structural optimization with three resonances. The corresponding electric field distributions are also provided to recognize which individual MNR these resonances belonging to, as shown in Fig. 2f . Based on this approach, the largest phase compensationterm·key can reach to even 360°, with a fairly good efficiency at most wavelengths (Supplementary Fig. 3 ). In fact, the phase compensationterm·key can be further increased by introducing more resonances to the integrated-resonantterm·key unit element, which will enable a BAMLterm·dom with larger size (Supplementary Fig. 10 ).

Characterizations of the BAMLterm·dom Employing the proposed policy, a broadband achromaticterm·key converging metalensterm·key with numerical aperture (NA) = 0.268 is designed and demonstrated. Figure 3a shows the optical image of the fabricated metalensterm·key, which has a diameter of 55.55 μm and designed focal lengthterm·key of 100 μm. This metalensterm·key was fabricated using standard electron beam lithography (see Methods section for details). The measured focal spots show the highly symmetric profiles, performing a good ability on light convergence in designed BAMLterm·dom. The focal spot at the middle of the working wavelength range, 1500 nm, is presented as an example in Fig. 3b . Figure 3c presents the zoom-in scanning electron microscope (SEM) image, in which a set of integrated-resonantterm·key MNRs with accurate gap sizes are observed. To capture the light intensity distribution, a couple of optical components including an IR objective and an IR coupled charge device (CCD) are moved together along the propagation direction of reflected light at different x–y planes (see Supplementary Fig. 7 for details of measurement setup). The right-hand circular polarization (RCP) to left-hand circular polarization (LCP) light intensity profiles on x – z plane is subsequently obtained from stitching all captured images together. Figure 3d shows that the measured and simulated light intensity profiles along the cross section plane are in a good agreement with each other. As theoretical predication, the focal lengthterm·key keeps almost unchanged while incident wavelength varies, indicating the realization of a broadband achromaticterm·key converging property in near-IRterm·key region. Fig. 3 Verification of achromaticterm·key converging metalensterm·key. a Optical image of fabricated metalensterm·key with NA = 0.268. b Measured light intensity of focal spot at incident wavelength λ = 1500 nm. c Zoom-in scanning electron microscope (SEM) image of fabricated metalensterm·key. More images and design details can be found in the Supplementary Note 3 . d Experimental ( top row ) and numerical ( bottom row ) intensity profiles of BAMLterm·dom along axial planes at various incident wavelengths For optical characteristics of the designed metalensterm·key, the focal lengthsterm·key vs. incident wavelength of both achromaticterm·key and chromatic metalensesterm·dom are measured. Figure 4a shows the results of three achromaticterm·key metalensesterm·dom with different NA values, which exhibits unchanged focal lengthterm·key with varied incident wavelength. These results confirmed again that the designed BAMLterm·dom is able to focus the incident light at the same focal plane in a continuous and wide range of wavelength (~33.3% of the central wavelength). Such perfect achromaticterm·key property can be realized from metalensterm·key with various NA values. To the best of our knowledge, this is the state-of-the-art demonstration of an achromaticterm·key metalensterm·key, which is able to completely eliminate the chromatic effect over the broadest wavelength range at continuously changed steps. In contrast to the BAMLterm·dom, the focal lengthterm·key of chromatic metalensesterm·dom (which is designed and fabricated using Berry phaseterm·dom based metasurfacesterm·key) strongly depends on the incident wavelength. For comparison, the phase distributions of chromatic metalensesterm·dom are designed for similar NA values with the achromaticterm·key ones at the longest wavelength in the interested wavelength range (Supplementary Note 4 ). The obvious chromatic aberrationterm·dom can be observed with evident focal lengthterm·key enlarging as the wavelength decreasing in all three metalensesterm·dom, shown in Fig. 4b . Fig. 4 Performance of broadband achromaticterm·key metalensterm·key. Measured and simulated focal lengthterm·key of a BAMLterm·dom with various NA values and b chromatic metalensesterm·dom. Measured c FWHM and d operation efficiency at corresponding focal plane as a function of wavelength. The efficiency is defined as the ratio of light intensity from the focal spot at corresponding focal plane to the light intensity reflected by a metallic mirror with the same pixel sizes. The error bars present the length of distance from the focal plane where the intensity of focal spot remains the maximum value in measurements To further examine the working performance of designed BAMLterm·dom, full-width at half-maximum (FWHM) and operating efficiency are measured at near-IRterm·key region, as shown in Figs. 4c and 4d . The FWHM, which is defined as the beam waist of the normalized light intensity at 0.5, is estimated by fitting the measured light intensity along the focal line with Gaussian function. All measured FWHM are located at the range of 1.5 λ ~2 λ that are nearly diffraction-limited. The maximum focusing efficiency of 8.4, 12.44 and 8.56% were measured for BAMLterm·dom with NA = 0.217, 0.268 and 0.324, respectively. The focusing efficiency drops at the boundaries of measured wavelength region is due to the lower polarization conversion efficiency of utilized unit elements at λ min and λ max . Though the efficiency spectrum shows some fluctuations in the operating wavelength range, which is the inevitable corollary from the introduction of the integrated-resonantterm·key unit elements, the average working efficiency can be further increased by replacing the material components with dielectrics or further optimizing the structural configuration 42 , 43 .

Design and characterizations of the broadband achromaticterm·key gradient metasurfaceterm·key Generally, our design principle can be used to realize various flat optical components without chromatic effect like the broadband achromaticterm·key gradient metasurfaceterm·key (BAGMS). The design of a BAGMS to deflect a normally incident light by the same angle in a broad wavelength range is demonstrated (Fig. 5a ). The building blocks are the same as those used in the above achromaticterm·key metalensterm·key, and the orientation of each unit element is designed to obey the required phase distribution: 5 φ x , λ = - 2 π λ x sin θ d where x is the spatial coordinate and θ d is the reflected angle of anomalous beam, namely the LCP light beam reflection with RCP incidence. To realize the phase requirement for deflecting light with the same θ d at different incident wavelengths, the specially designed unit elements with proper orientation are implemented to compensate the phase difference Δ φ ( x , λ ), as shown in Fig. 5b . The detailed information of design is shown in Supplementary Note 5 . As predicted, all the LCP light reflected angles are kept almost unchanged when the incident wavelength is changed from 1200 to 1650 nm, showing a broadband achromaticterm·key performance in anomalous beam deflection (see Fig. 5c ). It is further experimentally verified by capturing the scattering light through a slight focus (see Supplementary Fig. 8 for the optical measurement). Figure 5d presents the SEM image of the fabricated sample. As shown in Fig. 5e , the beam spot keeps in the center of CCD while the incident wavelength changed, presenting a good agreement with the numerical simulation. The anomalous reflected LCP beam can only be observed with cross-polarized component, which is also verified by changing the polarization state from detection. Fig. 5 Broadband achromaticterm·key gradient metasurfacesterm·key. a Schematic of beam deflection with BAGMS. All anomalously deflected angles are the same when the incident wavelength is changed. b Phase distribution for a BAGMS at different incident wavelengths. The Δ φ ( x , λ ) represents the phase difference between λ min and λ max at certain surface position. c Simulated intensity of RCP-to-LCP scattering light vs. angle of reflection at various incident wavelengths. The angle of reflection keeps at around 22.26˚ when the incident wavelength is changed from 1200 to 1650 nm. d SEM image of fabricated BAGMS. e ( Left ) Experimentally captured CCD images of RCP-to-LCP scattering light from the BAGMS. The intensities are normalized by the maximum value in each image. ( Right ) Cross section of normalized scattering light intensity along the central line of each corresponding CCD image for RCP-to-LCP ( navy curves ) and RCP-to-RCP ( olive curves ) components Discussion Compared with the flat optical devices using the strong resonance based unit elements, our design employs the integrated-resonantterm·key unit elements that enable the achromaticterm·key ability in a continuously broad wavelength band. Theoretically, the BAMLterm·dom with very high NA can also be realized with our design principle. For example, a BAMLterm·dom with NA as high as 0.86 is achieved with a smaller dimension (see Supplementary Fig. 9 ). Although the feature size of achromaticterm·key metalensesterm·dom with a fixed NA is limited by the largest phase compensationterm·key, namely the largest additional phase shift χ , it can be further increased through structural optimization by introducing more resonances/resonators into the integrated-resonantterm·key unit elements (Supplementary Note 8 ). We also would like to emphasize that the proposed design principle is not only valid to the reflective metasurfaceterm·key devices but can also be employed for metasurfaceterm·key devices in a transmission scheme if one can successfully introduce transparent integrated-resonantterm·key unit elements into the devices. One of the promising candidates is high-index dielectric metasurfacesterm·key, where multiple Fabry-Pérot resonances are realized because they can be regarded as truncated cross-sectional waveguides 44 . The versatility in the selective change of phase distribution and control of chromatic dispersion is beneficial for the development of specific functionalities like opposite phase dispersion and phase mismatch in nonlinear optical cavity that are difficult to be accomplished from bulky chromatic systems.

In summary, achromaticterm·key metasurfaceterm·key devices which can suppress the chromatic aberrationterm·dom in a wide wavelength range with continuous bandwidth are demonstrated. Through exploiting geometric phaseterm·dom combining with phase compensationterm·key from specially designed integrated-resonantterm·key unit elements, the metasurfacesterm·key can provide the exact phase profile as the ideal requirement for broadband achromaticterm·key flat optical devices like converging metalensterm·key and metasurfaceterm·key deflector. Although demonstrations in the near-IRterm·key regime, the working wavelength of proposed achromaticterm·key metasurfaceterm·key devices can be further pushed into the visible light by using aluminum or all-dielectric based unit elements as the building blocks. Our design paves an innovate class to control the phase dispersion at will and it will greatly advance the development of innovative metadevices in full color control to reach real practical applications.

Methods Sample Fabrication A 150-nm-thick Au mirror and a 3-nm-thick Cr were first deposited on a Si substrate by e-gun evaporator. A 60-nm-thick SiO 2 dielectric spacer is then deposited by using plasma-enhanced chemical vapor deposition (PECVD). A 100-nm-thick ZEP520A layer is consequently spin coated at 5000 rpm on the prepared substrate and then bake on a hot plate for 2 min at 180 °C. Subsequently, an Espacer layer is spin coated at 1500 rpm on the ZEP520A layer. Espacer is an organic polymer with high conductivity to reduce the positional error during the e-beam exposure process. An e-beam writing system at the acceleration voltage of 100 keV with 100 pico-ampere of current is used. The structural profile of metasurfacesterm·key is defined by the e-beam exposure and development process. The final sample will be obtained after the 3-nm-thick Cr and 30-nm-thick Au deposition and lift-off process.

Numerical simulation All numerical simulations were performed by using the commercial software Computer Simulation Technology (CST) Microwave Studio. For the design of unit elements, a unit cell boundary condition is employed for the simulation of reflection spectra and phase profile in an array configuration. For simplicity, perfect matched layer (PML) and periodic boundary conditions are respectively used for x and y direction for the simulation of metalensesterm·dom; that is, cylindrical lenses are simulated to simply evaluate the focal lengthterm·key of each metalensterm·key. In the case of gradient metasurfacesterm·key, PML is employed as the boundary condition for all boundaries to mimic a free space for far-field scattering simulation. The refractive index of SiO 2 is obtained from ref. 45 . The permittivity of gold in the near-IRterm·key regime is described by the Lorentz–Drude model with three times damping constant larger than the bulky material.

Data availability The data that support the findings of this study are available from the authors on reasonable request, see author contributions for specific data sets.

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