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Abstract
In this article, we explored the design and simulation techniques of large-aperture metalenses, and the optimization design methods of metalenses. For verification and experimental demonstration, a centimeter-scale aperture single-layer metalens and a field of view optimized metalens doublet,composed of subwavelength-spaced Si nanopillars with an operating wavelength of 3.77 µm were designed and manufactured. Finally, the focusing performance of the two under narrow-band laser irradiation was characterized, and an imaging demonstration of the metalens doublet was performed under an optical bandwidth of 250 nm (3500-3750 nm). We envision that the calculation, design, sample manufacturing and demonstration research on large-aperture metalens presented here will provide an important reference for the design and verification of large-aperture metasurface lenses or special metasurface devices in the future, such as large-aperture compact multifunctional metalens optical equipment for low-load special application systems like airborne, spaceborne, missile, satellite and deep sea.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Traditional optical components rely on the thickness, surface curvature, and inherent properties of materials such as transmittance and refractive index to achieve the desired functions, which inevitably results in bulky and difficult to achieve high integration. On the contrary, metasurfaces have the ability to control electromagnetic wave properties (such as phase, amplitude, and polarization) in a subwavelength resolution by arranging the artificially designed sub-wavelength structured nanopillars array in a proper way [1–4]. Research on metasurfaces has made significant progress recently, and various planar optical devices have been realized, such as beam-bending generators [5,6], holograms [7–12], color filters [13,14], polarization converter [15–17], vortex beam generators [18–21] and metalenses [22–26], etc. Owing to their high integration and processing technology, and their compatibility for the manufacture of complementary metal-oxide-semiconductor (CMOS), metasurface devices have unprecedented advantages over traditional optical devices with the same functions [27–30]. Therefore, the metasurface is expected to revolutionize in various fields of optics and photonics. In principle, by replacing traditional optical elements with ultra-thin planar elements, any optical system can be made flatter and more compact, which offers greater advantages in terms of size, cost and ease of fabrication [30–34].
Metalenses are one of the most important metasurface types in practical applications, which highlights its potential of meeting the ever-increasing demand for miniaturization of imaging lenses. Moreover, the mid-infrared (MIR) region covers one of the atmospheric transmission windows, the characteristic absorption spectrum of most molecules, and is widely used in biomedical tissue imaging, material detection, night vision, infrared remote sensing, free-space communications, molecular fingerprint detection, and environmental monitoring [35]. Therefore, the field of MIR metalenses are promising, with recent results has realized Huygens metalenses [36], Pancharatnam–Berry phase-based metalenses [37–39], propagation phase-based metalenses [22,40], achromatic metalenses [39–42], polarization-controlled metalenses [43], and micro-lens arrays composed of metalenses [44,45]. However, metalenses for the MIR are still less reported than devices operating at shorter wavelengths due to the limited selectivity of MIR transparent high-refractive index materials and the high cost of mid-infrared detection devices [22]. At the same time, although various MIR metalenses have been studied, most researchers prefer small-diameter metalenses due to huge processing cost constraints, while little attention is paid to centimeter-scale devices. An important example is the research and exploration of large-field, which is one of the important properties of metalens that needs to be optimized. The existing reports of large field of view (FOV) metalens only have an aperture of hundreds of microns [46,47], however, as the aperture increases, the optimized design of the FOV becomes more and more difficult, so it is difficult to obtain an ultra-large distortion-free field with large sizes. Although ultra-large field metalens based on quadratic phase have been reported, the imaging of such lenses will produce great distortion, and further image processing algorithms such as image stretching are required to restore the distorted image [48,49]. And limited by the pixel resolution limit of the camera, there will still be problems such as poor resolution and blur in the larger FOV. More importantly, the reported aperture of the metalenses is still only 1 mm [48,49]. The use of such small-aperture metalenses will be restricted by larger application scenarios and is not suitable for most use scenarios. Therefore, more research on large-aperture metalenses, especially research involving actual large-aperture sample preparation and actual use (not just simulation), is of great significance.
In this study, we demonstrated the design, simulation, fabrication and practical application of large-aperture metalenses for MIR imaging. Contrary to previous demonstrations that only relied on small area metalenses approximation (hundred-micron size) simulation or cylindrical metalenses substitution simulation, we performed fast full-aperture light field calculations (based on the Huygens-Fresnel principle [50]) of large-aperture metalens as a verification during the design process. Then, we experimentally verified the feasibility of the design of the large-aperture metalenses, and explored the optimized design of distortion-free large-FOV metalens at centimeter-level apertures, optimized the FOV of the metasurface micro-optics from a practical perspective for large-aperture applications. Examples of proof-of-concept experiment demonstrations shown here include a single-layer hyperbolic phase metalens composed of sub-wavelength-spaced Si nanopillars, and a metalens doublet optimized for large FOV with both effective diameters greater than 10 mm. Both can be compatible with universal optical component mounting devices and realize the flexible integration of metalenses and CCDs. Due to the positive correlation between lens aperture and resolution, and the requirements for low loads in special applications such as airborne, spaceborne, missiles, satellites, and deep sea, etc., we believe that the large-aperture metasurface design and diffraction calculation method research demonstrated here is meaningful [34,51–54].
2. Theoretical model
2.1 Architecture of the metasurface
Currently, there are three methods for the design of metalenses: resonance phase, Pancharatnam-Berry phase, and propagation phase [55]. Our design is based on the propagation phase, which is achieved through the propagation of light in the nanostructure and achieved a tolerant wavelength and polarization applicability. Different effective refractive indices can be realized by adjusting the size of the high-aspect-ratio unit. Subsequently, the propagation of light in nanostructures with different size will achieve different modulated light fields. To realize a large-aperture metalens, the feasibility of actual processing must be considered in the design considerations. Therefore, cylindrical nanopillars are used as the unit of the metalenses for easier processing, while silicon is selected as the metalenses material owing to its high transmittance and high refractive index in the MIR band, and the mature large-area silicon-based etching process [56–63]. For single-step etching processing, all nanopillars are uniform in height, and different modulations are achieved by changing their diameters.
To characterize the Si nanopillars with different diameters and heights, we performed full-wave simulations using the commercial software CST Microwave Studio for the propagation of light (3.77 µm) through the Si nanopillars by applying unit cell boundary conditions in x- and y-directions under plane wave incidence, thereby obtaining the corresponding normalized transmission phase and amplitude response. We use a hexagonal lattice instead of a square because it has the densest planar packing arrangement, which leads to a smoother sampling of the phase near the boundary of each zone and results in better performance compared to a square lattice [22,24]. The Si nanopillars were placed at the centers of each hexagonal unit cell, as shown in Fig. 1 (The different colors in Fig. 1(a) are just to better visually distinguish between nanopillars and substrates). To avoid high-order diffraction, we set the lattice period P to 1.732 µm (the period selection principle is: P≤λ/2, that is, the centers of any adjacent unit cell are separated by 1.732 µm, ensuring that the periodicity of the entire unit cell array is consistent). The simulation results are shown in Fig. 1(b), wherein the white dashed lines are the final parameters. We increased the diameter of the Si nanopillars (with a fixed height of 2 µm) from 500 nm to 1 200 nm in 25 nm increments, enabling full 2π coverage as shown in Fig. 1(c). Owing to the symmetry of the nanopillar structure, the performance of the designed metalens is insensitive to the polarization of the incident beam. A detailed description of our Si nanopillars setup and simulation results in the CST is reported in Section S1 of Supplement 1.
Fig. 1. Simulation results of Si nanopillars. (a) Schematic of a metalens unit cell, consisting of a high-aspect-ratio Si nanopillar with height H, a diameter D, arranged on a Si substrate to form a hexagonal lattice with a subwavelength lattice spacing P. (b) Calculated transmission and phase as a function of the height and the post diameter at λ=3.77 µm. (c) The profile of the white dashed lines in panels (b), showing the full 2π phase coverage and the high transmission.
2.2 Light field calculation
The obstacle to large-aperture metalens light field calculations is: In the traditional light field calculation method, the calculation of the direct integration method is very slow, especially when it is applied to the calculation of a metasurface lens composed of tens of millions of elements, it takes hundreds of hours; while the Fast Fourier transform (FFT)-based algorithms can generate only the light field distribution within a fixed region and sampling numbers, which determined by the intrinsic characteristic of the Fourier transform, lacking flexibility in computing [50]. After analyzing the direct integration method and the characteristics of the optical field modulation of large-aperture metalenses, we implemented fast full-aperture arbitrary planar light field calculations through matrix calculation and GPU acceleration based on the Huygens-Fresnel principle.
For centimeter-level metasurface devices, tens of millions of meta-atoms are arranged on them. To obtain the modulation of the incident light field through the large-aperture metalens at a low computational cost, an analytical model based on the Huygens-Fresnel principle is utilized to simulate the output light field. As shown in Fig. 2(a), a coordinate system is established on which there is a metalens plane and an observation plane, both of which are perpendicular to the z-axis. The light propagates along the z-axis and is normally incident on the metalens. We approximate it as a discrete light source array, where the light field of the i-th sub-light source at position (xi, yi, zi) propagating to the observation target point (x0, y0, z0) is:
Fig. 2. Schematic diagram of the transmitted light field simulation. (a) Focal plane light field simulation. (b) Axial light field simulation.
To simplify the calculation, we assumed the incident light to be an ideal plane wave, that is, A = 1 and φ0 = 0. Based on the direct integration method, we can spread the light fields of all sub-light sources to the observation target point and superimpose them to obtain the light field on the observation target point (x, y, z):
Through the above matrixization, the integral summation in Eq. (3) is converted into a single matrix calculation:
In this way, we calculated the complex amplitude distribution of each point on the observation plane, and the light intensity distribution is the square of the resulting complex amplitude. By setting the observation plane perpendicular to the z-axis and centered on the focal point, the intensity distribution of the focal plane can be obtained, and by changing the setting of the observation plane, the light distribution along the z-axis can also be calculated.
2.3 Diffraction-limited large-aperture metalens
For simplicity, we first demonstrate the feasibility of designing large-aperture metalenses. To illustrate, we have designed a metalens with an aperture of 10 mm, with an operating wavelength of 3.77 µm and a focal length of 15.5 mm. Metalenses achieve focus by changing the phase of the incident plane wave, with a converging phase profile that is described by [22] (for normally incident light):
The mechanism of the metalenses is to arrange a series of selected meta-atoms in a specific pattern to achieve the function of focusing. Therefore, it is indispensable to simulate the light field propagation after the light passes through the arranged metasurface meta-atoms. The size of the metalens in most studies is on the order of hundreds of microns, and in the study of a few metalenses with a larger aperture, researchers usually use smaller-sized alternative simplified templates or one-dimensional simplified approximation [51], or even just crop the full-aperture light field to a few tens of pixels in the center for light field simulation verification, capturing key details of the metalens focusing trend. This is certainly a wise choice, but we would prefer to get a light field simulation result of an unreduced full-aperture metalens, as long as conditions permit. Therefore, we simulated the light field after the metalens as a verification of the design through the light field calculation method described in Section S2.2. The calculation time cost of the full-aperture light field of the metalens with the 10 mm aperture is only 5 minutes (All calculations are performed on a desktop computer, which is configured with an AMD 3700X (3.59 GHz) CPU, 40 GB memory, and an RTX 2060 GPU. The code is written and run in the MATLAB). The simulated intensity distribution of the focal plane and along the z-axis were shown in Fig. 4(a) and Fig. 4(b), respectively. The simulation results show that the transmittance (the ratio of the power passing through the metalens to the incident power) was 89.7%, and the relative and absolute efficiencies of the metalens were 95.3% and 85.5%, respectively. We defined the relative focusing efficiency of the metalens as the ratio of the focusing power (within the diameter of 3*FWHM) to the power after passing through the metalens. The absolute focusing efficiency is the ratio of the focusing power to the incident power, that is, the relative focusing efficiency multiplied by the transmittance.
Fig. 4. Simulation of the transmitted light field. (a) Focal plane light field. (b) Axial light field. For better observation, the focal position coordinates have been set to z = 0.
2.4 Metalens doublet with large aperture and optimized field
Due to the limitation of the design freedom of the single-layer metasurface, it cannot provide sufficient modulation, which makes the single-layer metasurface lens have a large aberration when imaging the off-axis FOV. The double-layer metasurface can provide greater design freedom, and the wide-angle metalenses design based on double layer has been realized, which proves that it is a feasible optimization design method [46,47,64]. As we all know, a small size lens can always be easily optimized for a large FOV, and in order to provide a sufficiently large modulation, there will always be a surface whose size is much larger than the effective size of the device. However, in the case of designing a large-aperture metalens, such an excessively large size will lead to a sharp increase in processing costs and reduce the significance of using metasurface devices for ultra-compact integration. In addition, there is generally distortion at the edges of large FOV images. Distortion refers to the unequal scaling between objects and images caused by different local magnifications of the lens, resulting in the differences between the actual image height and the ideal image height. The design of wide-angle metalens is generally affected by severe barrel distortion, resulting in a large image center and small edges, and the actual image height is smaller than the ideal image height. By relaxing the requirements for the FOV, we have realized a micro-optical system with field-of-view-optimized in the form of a double-layer metasurface devices, with nearly identical metasurface dimensions on both sides. More importantly, the actual image height of the metalens we designed basically meets the ideal image height-incident angle relationship, and barrel distortion is basically eliminated. As a verification, an all-silicon metalens doublet that supports ±11° FOV, effective diameter greater than 10 mm, and numerical aperture greater than 0.24 is described. The metalens doublet is realized by electron-beam lithography on both sides of a 1-inch round silicon substrate directly, and the effective size difference between the first surface and the second surface of the metalens doublet is small, which greatly reduces the processing cost.
As illustrated in Fig. 5(a), we show the schematics of the mid-infrared all-silicon metalens doublet. The metasurfaces on both sides of the substrate are composed of Si nanopillars with the same height but different diameter, and arranged with a hexagonal lattice, and there is an aperture diaphragm in front of the lens. The design concept is based on the fact that the aperture diaphragm before the lens can effectively improve the imaging quality of the lens [48], and the double-sided phase modulation can compensate for the phase error under the inclined FOV [46,47,64].
Fig. 5. Schematic of the metalens doublet with field-of-view-optimized. (a) Schematic illustration of the metalens doublet. (b) The modulation transfer function (MTF) for the designed metalens doublet. (c) Focal plane normalized light field simulation for 0°, 7.8°, and 11° incidence.
First, we set the first surface to realize the focusing phase function according to Eq. (9), while the second surface acts as a correction plate to compensate for the phase error in oblique incidence, which is defined as an even order polynomial of the radial coordinate [65], as expressed in Eq. (1)0:
where M is the diffraction order, N is the number of polynomial coefficients in the series, Ai is the coefficient, r is the radial height of the surface, and R is the normalized radial aperture coordinate. We placing an aperture in front of the metalens and optimized the phase profile coefficient Ai of the second surface by using the damped least-squares method, to ensure that the focus of each FOV has high convergence performance and meets the ideal image height-incident angle relationship: where h is the image height, EFL is the effective focal length, and θ is the incident angle.We set the focal length of all-silicon metalens doublet of f = 20 mm and work at λ=3.77 µm, with an aperture of 10 mm diameter, which located 5 mm in front of the first surface. The thickness of the silicon substrate, that is, the distance between the two metasurfaces is 1 mm. The optimized first surface has a diameter of 11.95 mm, and the optimized second surface has a diameter of 11.89 mm. We still carry out light field simulation, Fig. 5(b) shows the modulation transfer function (MTF) for the designed metalens doublet at different incident angles and Fig. 5(c) shows the focal plane simulation at various incident angles (see Supplement 1, Section S2 for more details of the design and optimization simulation). We also simulated the actual image height under different incident angles, showing the relationship between image height and incident angle, as shown in Fig. S5 (see Supplement 1, Section S2).
3. Results and discussion
3.1 Characterization of single-layer metalens
The all-silicon metalens was fabricated on a Si substrate using electron beam lithography (EBL) followed by inductively coupled plasma (ICP) dry etching (see Section S3 of Supplement 1 for details). To evaluate the imaging performance of the metalens, we characterize the focal plane intensity distribution and the three-dimensional (3D) intensity distribution of the light exiting the fabricated metalenses (see Supplement 1, Section S4 for details of the customized measuring system). The incident light focused into a point through the metalens and an IR CCD (WinCamD-IR-BB, 640 × 480, 10.88 mm × 8.16 mm active area, 17 µm pixels) is required to collect the focus image. Because the CCD pixel size is much larger than the focal spot size, the focus image cannot be collected directly. Therefore, we created a magnification system (∼32×) through a lens tube and two MIR lenses. Figure 6(c), d shows the measured results of the metalens at λ=3.77 µm. The FWHM of the lens focal point is approximately 8 µm, which is close to the theoretical limit λ/2 NA(6.14µm), and the normalized cross-sectional view of the focal point and ideal airy function are similar, as shown in Fig. 6(e). The transmittance of the metalenses was measured to be 76.27% (see Supplement 1, Section S4 for details of the measurement), which is 13.42% less than that estimated from the simulation (89.7%). We attribute the loss to manufacturing defects, defect absorption, and phase undersampling caused by a relatively large unit period compared to the rapidly changing phase near the edge of the metalens. According to the aforementioned definition, the relative and absolute efficiencies of the fabricated metalenses were 75.9% and 57.9%, respectively.
Fig. 6. Characterization and focusing performance of the metalens. (a) Optical image of metalens installed in lens tube (Scale bar: 1 cm). (b) Scanning electron microscopy (SEM) image of the metalens (magnification 10 000 times, Scale bar: 1 µm). (c) Normalized intensity distribution along the axial direction. For easy observation, the focal position coordinates are set to z = 0. (d) Normalized intensity distributions in the focal plane. (e) Normalized cross-sectional view of the focal point and ideal airy function. (f) MTF obtained from the focal spot.
An imaging experiment was also performed at a laser wavelength λ=3.77 µm, the experimental setup is shown in Fig. 7. The incident light is collimated and passes through a combined resolution and distortion Test Targets (Thorlabs, R1L1S1N), and is finally imaged on the CCD by the metalens. No extra lens is added between the metalens and the CCD, the image resolution is limited owing to the large pixel size of 17 µm, as shown in Fig. 7(b).
Fig. 7. The imaging results of the metalens at the laser wavelength λ=3.77 µm. (a) Optical setup for characterizing the imaging performance of metalens. (b) The imaging results of the 1951 USAF Resolution Test Targets. (c) Ideal image of the imaging target. (d) Schematic diagram of installing a metalens through a C-Mount extension tube (Thorlabs, CM1L03).
3.2 Characterization of metalens doublets
Electron beam lithography (EBL) and inductively coupled plasma (ICP) dry etching are used to process the front and rear surfaces of the Si substrate to manufacture the all-silicon metalens doublet (see Section S3 of Supplement 1 for details). Then the focal plane intensity distribution and the three-dimensional (3D) intensity distribution of the light exiting the fabricated metalens doublet are characterized as shown in Fig. 8. The transmittance of the metalens doublet was measured to be 54.91% (see Supplement 1, Section S4 for details of the measurement). According to the definition in Section 2.3, the relative efficiency and absolute efficiency of the metalens doublet are 77.6% and 42.6%, respectively. The results show that the focus quality of the metalens doublet in the normal incident FOV is slightly reduced, but there is still a focal point close to the diffraction limit. One possible main reason for the reduction in efficiency is that AR coating can no longer be carried out due to double-sided processing.
Fig. 8. Characterization and focusing performance of metalens doublet. (a), (b) The first surface (a) and the second surface (b) of the metalens doublet (scale bar: 12 mm). (c) Normalized intensity distribution along the axial direction. The focal position coordinates are set to z = 0. (d) Normalized intensity distributions in the focal plane. (e) Normalized cross-sectional view of the focal point and ideal airy function. (f) MTF obtained from the focal spot.
To verify the optimized FOV of the designed lens, a self-made measurement system based on a rotating stage was built (see Supplement 1, Section S4 for details of the customized measuring system and results). For comparison, we also performed the same measurement on the single-sided metalens mentioned in this article, which is unoptimized for FOV (with the same unit structure, an aperture of 10 mm, and a focal length of 15.5 mm). The focal points of the optimized metalens doublet and the unoptimized single-sided metalens at different incident angles are shown in Fig. 9(a) and Fig. 9(b), respectively. Figure 10(a)-(c) shows the focus profile, FWHM, and MTF of the optimized metalens doublet at different incident angles, and Fig. 10(d)-(e) shows the corresponding results of the unoptimized single-sided metalens at different incident angles. The results show that the change in MTF is not linear. For our optimized metalens doublet, the focusing performance of the focal point and MTF decreases after the incident angle increases to 1°, and there is a similar performance in the range of 1°-11°, which only decreases slowly as the incident angle increases. It still maintains high focus quality and high MTF value when the half FOV reaches 11°. For the unoptimized single-sided metalens, when the incident angle increases to 1°, its MTF is still close to the value at 0°. However, as the incident angle increases to 2° and 3° respectively, the focusing performance and MTF drops suddenly and significantly, and becomes extremely low after 3° (see Supplement 1, Section S4 for details of the Focus image and MTF curve at different incident angles).
Fig. 9. The focus for different angles of incidence at the laser wavelength λ=3.77 µm. (a) The focal points of the optimized metalens doublet at different incidence. (b) The focal points of the unoptimized single-sided metalens at different incidence.
Fig. 10. The performance for different angles of incidence at the laser wavelength λ=3.77 µm. (a)-(c) The focused profile, FWHM, and MTF of the optimized metalens doublet at different incident angles. (d)-(e) The focused profile, FWHM, and MTF of the unoptimized single-sided metalens at different incident angles.
Finally, we characterize the imaging quality of the optimized metalens doublet within the target FOV. A blackbody furnace is used as the mid-infrared light source to obtain a large illumination range, and the bandwidth (250 nm) is limited by inserting bandpass filters. A hollow school badge obtained by 3D printing is used as an imaging target, which is illuminated by a black body radiation source and is imaged on the CCD through the proposed metalens doublet. The metalens doublet and color filter are directly integrated on the CCD through the lens tubes, that is, no extra lens is added between the metalens and the CCD (see Supplement 1, Section S4 for details). The result of imaging is shown in Fig. 11, which has good imaging quality within the designed ±11° FOV. Since the bandwidth of the color filter is too wide, the image quality is degraded. Future work will focus on further eliminating aberrations, that is, developing the achromatic methods of metalenses suitable for large-aperture design conditions to improve image quality. At the same time, the camera used in the experiment is a beam quality analyzer, which is greatly affected by environmental radiation noise, which means that the study of denoising algorithms may be an effective way to improve clarity.
Fig. 11. Characterization results of the metalens imaging quality under the broad spectrum. (a) Optical image of the hollow school badge. (b) Broadband mid-infrared imaging with an optical bandwidth of 250 nm (3500-3750 nm). The FOV zones marked by the solid circles are 11°.
4. Conclusion
In this study, we demonstrated the design, simulation, fabrication, and practical application of large-aperture metalenses. We explored the design and optimization of metalenses in the case of large apertures. Examples of proof-of-concept experiment demonstrations shown here include a single-layer hyperbolic phase metalens composed of sub-wavelength-spaced silicon (Si) nanopillars, and a micro-optical system consisting of a metalens doublet optimized for a large FOV, with both effective diameters greater than 10 mm. The metalens demonstrated in this study have limited functionality as the nanoparticles can scatter light of different wavelengths, making it possible to design achromatic metalens by further improvising on the design. It’s noteworthy that our designed metalens is compatible with universal optical component mounting devices and realize flexible integration with CCD, which broadens the scope of the design of large-aperture MIR metalenses and flexible system integration with various devices, which will provide an important reference for the design of large-aperture compact multi-functional metasurface optical equipment for special application systems such as airborne and spaceborne, missiles, satellites, and deep seas.
Funding
National Natural Science Foundation of China (62305191, 62175131, 62075232, 92163134); Key Technology Research and Development Program of Shandong Province (2023JMRH0105); Taishan Scholar Foundation of Shandong Province.
Acknowledgments
We would like to thank the National Natural Science Foundation of China (62305191, 62175131, 62075232, 92163134), Key Technology Research and Development Program of Shandong Province (2023JMRH0105), and Taishan Scholar Foundation of Shandong Province for their financial support. The authors acknowledge the contribution of Chuanning Niu of Shandong University from his useful discussion during the metalenses designing and are indebted to Yi Zhou of Shanghai Institute of Microsystem and Information Technology for her important assistance in the fabrication.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. B. H. Chen, P. C. Wu, V.-C. Su, et al., “GaN metalens for pixel-level full-color routing at visible light,” Nano Lett. 17(10), 6345–6352 (2017). [CrossRef]
2. A. Arbabi, Y. Horie, M. Bagheri, et al., “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). [CrossRef]
3. S. B. Glybovski, S. A. Tretyakov, P. A. Belov, et al., “Metasurfaces: From microwaves to visible,” Phys. Rep. 634, 1–72 (2016). [CrossRef]
4. S. Chen, W. Liu, Z. Li, et al., “Metasurface-empowered optical multiplexing and multifunction,” Adv. Mater. 32(3), 1805912 (2020). [CrossRef]
5. Z. Zhou, J. Li, R. Su, et al., “efficient silicon metasurfaces for visible light,” ACS Photonics 4(3), 544–551 (2017). [CrossRef]
6. Z. Liu, X. Li, J. Yin, et al., “Asymmetric all silicon micro-antenna array for high angle beam bending in terahertz band,” IEEE Photonics J. 11(2), 1–9 (2019). [CrossRef]
7. D. Wen, F. Yue, G. Li, et al., “Helicity multiplexed broadband metasurface holograms,” Nat. Commun. 6(1), 8241 (2015). [CrossRef]
8. B. Wang, F. Dong, Q.-T. Li, et al., “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016). [CrossRef]
9. F. Walter, G. Li, C. Meier, et al., “Ultrathin nonlinear metasurface for optical image encoding,” Nano Lett. 17(5), 3171–3175 (2017). [CrossRef]
10. C. Zhang, S. Divitt, Q. Fan, et al., “Low-loss metasurface optics down to the deep ultraviolet region,” Light: Sci. Appl. 9(1), 55 (2020). [CrossRef]
11. G. Zheng, N. Zhou, L. Deng, et al., “Full-space metasurface holograms in the visible range,” Opt. Express 29(2), 2920–2930 (2021). [CrossRef]
12. I. Javed, J. Kim, M. A. Naveed, et al., “Broad-band polarization-insensitive metasurface holography with a single-phase map,” ACS Appl. Mater. Interfaces 14(31), 36019–36026 (2022). [CrossRef]
13. J. S. Clausen, E. Højlund-Nielsen, A. B. Christiansen, et al., “Plasmonic metasurfaces for coloration of plastic consumer products,” Nano Lett. 14(8), 4499–4504 (2014). [CrossRef]
14. M. Miyata, H. Hatada, and J. Takahara, “Full-color subwavelength printing with gap-plasmonic optical antennas,” Nano Lett. 16(5), 3166–3172 (2016). [CrossRef]
15. Y. Yang, W. Wang, P. Moitra, et al., “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett 14(3), 1394–1399 (2014). [CrossRef]
16. P. C. Wu, W.-Y. Tsai, W. T. Chen, et al., “Versatile polarization generation with an aluminum plasmonic metasurface,” Nano Lett. 17(1), 445–452 (2017). [CrossRef]
17. P. C. Wu, W. Zhu, Z. X. Shen, et al., “Broadband wide-angle multifunctional polarization converter via liquid-metal-based metasurface,” Adv. Opt. Mater. 5(7), 1600938 (2017). [CrossRef]
18. K. Zhang, Y. Yuan, D. Zhang, et al., “Phase-engineered metalenses to generate converging and non-diffractive vortex beam carrying orbital angular momentum in microwave region,” Opt. Express 26(2), 1351–1360 (2018). [CrossRef]
19. Y. Yuan, K. Zhang, X. Ding, et al., “Ultra-thin metalens generating coverging vortex beam in microwave region,” in 2018 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (2018), pp. 443–444.
20. R. Zhang, Y. Guo, X. Li, et al., “Angular superoscillatory metalens empowers single-shot measurement of OAM modes with finer intervals,” Adv. Opt. Mater., 2300009 (2023).
21. G. Cao, H. Lin, and B. Jia, “Broadband diffractive graphene orbital angular momentum metalens by laser nanoprinting,” Ultrafast Science 3, 0018 (2023). [CrossRef]
22. H. Zuo, D.-Y. Choi, X. Gai, et al., “High-efficiency all-dielectric metalenses for mid-infrared imaging,” Adv. Opt. Mater. 5(23), 1700585 (2017). [CrossRef]
23. R. Paniagua-Domínguez, Y. F. Yu, E. Khaidarov, et al., “A metalens with a near-unity numerical aperture,” Nano Lett. 18(3), 2124–2132 (2018). [CrossRef]
24. S. Shrestha, A. C. Overvig, M. Lu, et al., “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7(1), 85 (2018). [CrossRef]
25. Z.-B. Fan, Z.-K. Shao, M.-Y. Xie, et al., “Silicon nitride metalenses for close-to-one numerical aperture and wide-angle visible imaging,” Phys. Rev. Appl. 10(1), 014005 (2018). [CrossRef]
26. F. Presutti and F. Monticone, “Focusing on bandwidth: achromatic metalens limits,” Optica 7(6), 624–631 (2020). [CrossRef]
27. D. Lin, P. Fan, E. Hasman, et al., “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014). [CrossRef]
28. J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, et al., “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118(11), 113901 (2017). [CrossRef]
29. L. Wang, S. Kruk, H. Tang, et al., “Grayscale transparent metasurface holograms,” Optica 3(12), 1504–1505 (2016). [CrossRef]
30. H. Hou, Y. Zhang, Z. Luo, et al., “Design and fabrication of monolithically integrated metalens for higher effective fill factor in long-wave infrared detectors,” Optics and Lasers in Engineering 150, 106849 (2022). [CrossRef]
31. M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358(6367), eaam8100 (2017). [CrossRef]
32. M. L. Tseng, H.-H. Hsiao, C. H. Chu, et al., “Metalenses: advances and applications,” Adv. Opt. Mater. 6(18), 1800554 (2018). [CrossRef]
33. P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photonics Rev. 11(3), 1600295 (2017). [CrossRef]
34. L. Zhang, S. Chang, X. Chen, et al., “High-Efficiency, 80 mm Aperture Metalens Telescope,” Nano Lett. 23(1), 51–57 (2023). [CrossRef]
35. R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010). [CrossRef]
36. L. Zhang, J. Ding, H. Zheng, et al., “Ultra-thin high-efficiency mid-infrared transmissive Huygens meta-optics,” Nat. Commun. 9(1), 1481 (2018). [CrossRef]
37. A. Wang, Z. Chen, and Y. Dan, “Planar metalenses in the mid-infrared,” AIP Adv. 9(8), 085327 (2019). [CrossRef]
38. C. He, T. Sun, J. Guo, et al., “Chiral metalens of circular polarization dichroism with helical surface arrays in mid-infrared region,” Adv. Opt. Mater. 7(24), 1901129 (2019). [CrossRef]
39. H. Zhou, L. Chen, F. Shen, et al., “Broadband achromatic metalens in the midinfrared range,” Phys. Rev. Appl. 11(2), 024066 (2019). [CrossRef]
40. I. Tanriover and H. V. Demir, “Broad-band polarization-insensitive all-dielectric metalens enabled by intentional off-resonance waveguiding at mid-wave infrared,” Appl. Phys. Lett. 114(4), 043105 (2019). [CrossRef]
41. C. Sha, W. Xiong, B. Zhang, et al., “Broadband achromatic mid-infrared metalens with polarization-insensitivity,” AIP Advances 12, 025123 (2022). [CrossRef]
42. W. Xiong, C. Sha, and J. Ding, “Polarization-independent broadband achromatic metalens in the mid-infrared (3–5 µm) region,” Appl. Phys. Express 15(2), 022001 (2022). [CrossRef]
43. K. Ou, F. Yu, G. Li, et al., “Mid-infrared polarization-controlled broadband achromatic metadevice,” Sci. Adv. 6(37), eabc0711 (2020). [CrossRef]
44. S. Zhang, A. Soibel, S. A. Keo, et al., “Solid-immersion metalenses for infrared focal plane arrays,” Appl. Phys. Lett. 113(11), 111104 (2018). [CrossRef]
45. F. Li, J. Deng, J. Zhou, et al., “HgCdTe mid-Infrared photo response enhanced by monolithically integrated meta-lenses,” Sci. Rep. 10(1), 6372 (2020). [CrossRef]
46. B. Groever, W. T. Chen, and F. Capasso, “Meta-lens doublet in the visible region,” Nano Lett. 17(8), 4902–4907 (2017). [CrossRef]
47. A. Arbabi, E. Arbabi, S. M. Kamali, et al., “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7(1), 13682 (2016). [CrossRef]
48. J. Engelberg, C. Zhou, N. Mazurski, et al., “Near-IR wide-field-of-view Huygens metalens for outdoor imaging applications,” Nanophotonics 9(2), 361–370 (2020). [CrossRef]
49. A. Martins, K. Li, J. Li, et al., “On metalenses with arbitrarily wide field of view,” ACS Photonics 7(8), 2073–2079 (2020). [CrossRef]
50. Y. Hu, Z. Wang, X. Wang, et al., “Efficient full-path optical calculation of scalar and vector diffraction using the Bluestein method,” Light: Sci. Appl. 9(1), 119 (2020). [CrossRef]
51. J. Hao, T. Ma, Z. Ye, et al., “Simulation for multiwavelength large-aperture all-silicon metalenses in long-wave infrared,” Nanotechnology 33(22), 225203 (2022). [CrossRef]
52. T. D. Milster, Z. Wang, and Y. S. Kim, “Design aspects of large-aperture MODE lenses,” OSA Continuum 4(1), 171–181 (2021). [CrossRef]
53. I. M. Barton, J. A. Britten, S. N. Dixit, et al., “Fabrication of large-aperture lightweight diffractive lenses for use in space,” Appl. Opt. 40(4), 447–451 (2001). [CrossRef]
54. N. V. Tabiryan, D. E. Roberts, Z. Liao, et al., “Advances in transparent planar optics: enabling large aperture, ultrathin lenses,” Adv. Opt. Mater. 9, 2001692 (2021). [CrossRef]
55. S. Chen, Z. Li, Y. Zhang, et al., “Phase manipulation of electromagnetic waves with metasurfaces and its applications in nanophotonics,” Adv. Opt. Mater. 6(13), 1800104 (2018). [CrossRef]
56. M. Kenney, J. Grant, D. Hao, et al., Large Area Metasurface Lenses in the NIR Region (SPIE, 2019).
57. Z. Zhang, Z. Cui, Y. Liu, et al., “Design of a broadband achromatic dielectric metalens for linear polarization in the near-infrared spectrum,” OSA Continuum 1(3), 882–890 (2018). [CrossRef]
58. Q. Fan, M. Liu, C. Yang, et al., “A high numerical aperture, polarization-insensitive metalens for long-wavelength infrared imaging,” Appl. Phys. Lett. 113(20), 201104 (2018). [CrossRef]
59. Q. Fan, Y. Wang, M. Liu, et al., “High-efficiency, linear-polarization-multiplexing metalens for long-wavelength infrared light,” Opt. Lett. 43(24), 6005–6008 (2018). [CrossRef]
60. F. Zhao, X. Jiang, S. Li, et al., “Optimization-free approach for broadband achromatic metalens of high-numerical-aperture with high-index dielectric metasurface,” J. Phys. D: Appl. Phys. 52(50), 505110 (2019). [CrossRef]
61. T. Phan, D. Sell, E. W. Wang, et al., “High-efficiency, large-area, topology-optimized metasurfaces,” Light: Sci. Appl. 8(1), 48 (2019). [CrossRef]
62. M. Mansouree, H. Kwon, E. Arbabi, et al., “Multifunctional 2.5D metastructures enabled by adjoint optimization,” Optica 7(1), 77–84 (2020). [CrossRef]
63. Y. Zhou, T. Hu, Y. Li, et al., “A performance study of dielectric metalens with process-induced defects,” IEEE Photonics J. 12, 1–14 (2020). [CrossRef]
64. C. Kim, S.-J. Kim, and B. Lee, “Doublet metalens design for high numerical aperture and simultaneous correction of chromatic and monochromatic aberrations,” Opt. Express 28(12), 18059–18076 (2020). [CrossRef]
65. C.-Y. Fan, C.-P. Lin, and G.-D. J. Su, “Ultrawide-angle and high-efficiency metalens in hexagonal arrangement,” Sci. Rep. 10(1), 15677 (2020). [CrossRef]
