GUO Yongcai （1963-）， female， professor， Ph.D. degree， mainly focuses on environmental monitoring， light scattering theory and so on. Email： ycguo@cqu.edu.cn

The traditional optical systems are usually single-aperture systems which are consisted of bulky optical elements with elaborate designs to eliminate aberrations and improve imaging qualities， such as doublet lenses and aspheric lenses. Benefitting from those excellent properties， they are widely used in many scenarios. However， some applications of rapid development （like drones and endoscopy imaging） in recent years have raised higher demands for the imaging system， such as light weight， small size， and large Field Of View （FOV）. The bulky volumes and heavy weights of traditional optical systems make them difficult to be miniaturized and integrated. A new methodology which can simultaneously realize the miniaturization and large FOV of the image systems is highly expected in the optical field.

To achieve such goals， Artificial Compound Eyes （ACEs） were developed based on the structures of the biotic compound eyes for their features including compact structure and large FOV^［1-3］. The ACEs were typically composed of a Micro Lens Array （MLA） with space-variant field angles to transfer different portions of the overall FOV independently. By combining the obtained subimages， a large FOV could be achieved. Compared with traditional single-aperture systems， the imaging lenses of the ACE had a much smaller size both radially and axially， making it convenient for the miniaturization of the optical system. In general， current ACE structures can be classified into the Three-Dimensional（3D） ACEs^［4-6］ and the planar ACEs^［7-9］. A 3D ACE fully realizes the characteristics of biotic compound eyes with a curved lens plane， which allows the micro lenses to be rotated and aimed for different directions. However， the original structure produces a curved image plane， making the subimages difficult to be collected with a planar CCD or CMOS detector. To handle this problem， a micro-lens array with radially decreasing focal length is proposed to ensure that the subimages are generated precisely on the detector plane^［10］. Another solution is adding an intermediate system， such as optical fibers or lenses， to transfer the optical path and produce a planar image plane. The planar ACEs， of which both the lens plane and the image plane are planar， are easier to be designed and realized than the 3D ACEs， while they have a lower FOV compared with the 3D ACEs. To increase the FOV of the planar ACEs， different methods are adopted， such as the utilization of optical prisms to deflect light beams^［11］， or introducing of multiple layers of MLA^［12］. Although the aforementioned methods could handle the drawbacks of ACE， the introduced components decrease the system's integration level and increase the system complexity. A new ACE structure that simultaneously guarantees a large FOV， small size and simple structure is highly desired in the ACE domain.

In this work， a planar ACE structure is proposed based on the utilization of metalenses. Metasurface lens （metalens）^［13-15］， which is a planar device with sub-wavelength phase-modulation structures， is an important branch of application of the metasurfaces^［16］. The Metalens Array （MA） of the proposed ACE is composed of metalenses with different off-axis angles to transfer different portions of the object space. Benefitting from the multi-function properties， metalenses can deflect the incident light’s axis without self-rotation nor additional devices， while maintaining the focusing function. Here， a planar ACE is designed with the size of 165 μm×165 μm and overall height of 18.6 μm. The simulation result reveals that the overall FOV of the designed planar ACE can reach 140°×140°， with nearly constant resolution （FWHM（Full-Width-Half-Maximum） =0.74±0.01 μm） in all directions. Compared with some previous results^［17-18］， the proposed planar ACE has a smaller overall size and a simplified structure. Our work provides a new approach for designing the planar ACE， promoting its application in fast positioning， monitoring， medical and industrial fields.

The detailed layout of the proposed planar ACE is shown in Fig.1. It comprises a single layer of planar MA， which is usually supported by a layer of transparent base （which is silicon dioxide （SiO₂） in this work） and a light receiver focal plane to collect the generated subimages. The MA is composed of metalenses to generate the subimages of different portions of the object field. The metalenses are designed with a side length d=10.2 μm and height h=0.6 μm. The FOV of a single metalens φ reaches 40º according to the simulation results， and it is here taken as φ=40º. In addition to focusing， each metalens is designed with an off-axis angle α， which represents its off-axis angle in the object space. When the incident direction is parallel to the metalens’ off-axis direction， the transmitted light beams are normally focused onto the focal plane. Thus， a portion of the object field （α-φ/2， α+φ/2） is transferred successfully. The inter-ommatidia angle Δα is defined as the difference of the off-axis angles between adjacent metalenses. With Δα set smaller than φ to eliminate blind areas， the overall FOV of the MA Φ can reach ±（α_max+φ/2）， where α_max is the maximum off-axis angle. To prevent crosstalk， optical isolators should be added between adjacent channels^［19］. In this design， with Δα=10º， α_max=50º， and φ=40º， an array of 11×11=121 metalenses can cover the overall field （-70º， 70º）. The adjacent metalenses are distributed with an interval D=15 μm to avoid conflicts between adjacent metalenses， resulting in the ACE's size of 165 μm×165 μm. The overall height of the proposed ACE， which is mainly determined by the height of the metalenses （h=0.6 μm） and the focal length （f=18 μm）， is 18.6 μm （the overall height does not include the thickness of the supporting SiO₂ base， which depends on the manufacture technology in practical）. Here， because the focal points of the metalenses are on a flat plane， the image plane of the proposed ACE is also planar， making it much easier for the detectors to collect the produced subimages without additional converting components or curving process.

The metalenses used to construct the MA is a newly developed planar lens that controls light based on the geometric phase. The geometric phase， also named as Pancharatnam-Berry （PB） phase， is always frequency-independent and can be conveniently implemented through the rotation of the nano-structures^［20-22］. In this design， the metalenses are constructed by nanopillars with space-variant orientation angles （Fig.2（a）） to modulate the transmitted phase and realize off-axis focusing. Titanium dioxide （TiO₂） is an ideal material to construct such a metalens because of its high refractive index with near-zero imaginary parts and negligible absorption across the visible range^［23］. In order to obtain good performance， the geometric dimensions of the rectangle nanopillars， including its height， length， width， and period， are specifically optimized based on the cross-polarization amplitude and phase responses， which are simulated using the Computer Simulation Technology （CST） Microwave Studio. As a result， the height， length， width， and period shown in Fig.2（a） are chosen as 0.6 μm， 0.2 μm， 0.09 μm and 0.3 μm， respectively.

Under the normal incidence of Left Circular Polarized （LCP） light at 467.5 nm wavelength， the amplitude and phase response of the transmitted cross-polarization light， which in this case is the Right Circular Polarized （RCP） light， is calculated and shown in Fig.2（b）. The amplitude is above 99% and the phase is almost in a linear relation with the rotation angle， which agrees with the geometric phase anticipation. Fig. 2（c） shows the phase shift of the transmitted cross-polarization light produced by nanopillars with different orientation angles throughout the visible wavelength. The phase of the nanopillar with 0° orientation is set zero as the baseline. It can be seen that the relative phase shift is almost in linear relation with the orientation angle in the wavelength from 450 nm to 700 nm. The broadband amplitude responses of the proposed nanopillars are shown in Fig.2（d）. Although the amplitude responses are different for the variation of the incident wavelengths， the cross-polarized amplitude nearly keeps constant with the change of the orientation angles. The broadband properties shown in Fig.2（c） and Fig.2（d） prove that the designed nanopillar can be operated in a broad wavelength range. The phase responses and average amplitude of the transmitted cross-polarization light for the off-axis illumination are shown in Fig.2（e） and （f）. It can be seen that the phase shift produced by the nanopillars with an incident angle is similar to the normal incidence situation and basically follows a linear relation with the orientation angle of the unit structure （some deviations at large off-axis angles will not affect focus seriously because of the tolerance of the metalenses^［24］）. Therefore， metalenses with an off-axis angle can be designed based on the phase modulation relation of the TiO₂ nanopillars with normal incidence.

The metalenses are constructed with numerous nanopillars to modulate the phase of the transmitted light. In order to realize a planar ACE， the constructed metalenses focus the incident light with different inclination angles with an acceptable transmittance. According to the equal optical path principle， to focus the normally incident plane wave， the abrupt phase shift generated by nanopillars on the metalens should be a part-spherical shell^{［25， 26］} （Fig. 3（a）） that satisfies this relation

ω(x,y)=2π/λ‧(x2+y2+f2-f)±2mπ（1）

where ω_（x，y） is the needed abrupt phase shift on different positions of the metalens， x and y are coordinates on the metalens， λ is the working wavelength （467.5 nm， which is also the wavelength of the Ar-Kr laser）， f is the focal length （18 μm）， m is an integer to make sure that the final value is within the range 0~2π.

To counteract the effect of the incident light's inclination on the focusing performance， the wavefront of the transmitted light needs to remain a part-spherical shell. As is shown in Fig.3（b）， similar to the traditional method of adding a glass wedge to steer light beams^［27］， an off-axis phase shift δ_（x，y）=2π/λ‧x‧sin α is introduced， where α is the off-axis angle. It is defined by the angle between the incident wave vector and the z-axis （here， the wave vector of the incident light is in the x-z plane）. Thus， the needed phase distribution of the designed off-axis lens is determined by ω_（x，y）=ω_（x，y）+δ_（x，y）， as illustrated in Fig.3（c）. The off-axis lens is coded by the nanopillars shown in Fig.2（a） with designed geometric phase relation， which can be described as

θ(x,y)=ω(x,y)'/2=π/λ⋅(x2+y2+f2-f)+π/λ⋅x⋅sinα±mπ（2）

where θ（x，y） is the nanopillars' orientation angle at different positions on the metalens. Fig. 3（d） shows an example of the metalens with the off-axis angle α=30º， focal length f=18 μm and size length d=10.2 μm. It is constructed with an array of 34×34 TiO₂ nanopillars. High-throughput lithography methods， such as deep-ultraviolet^［28］， can be utilized for the fabrication of the designed sample. A process can be used to manufacture the proposed metalens， it includes electron-beam lithography to create the lens pattern in the resist， atomic layer deposition to deposit the amorphous TiO₂ onto the developed resist， followed by controlled blanket reactive ion etching and stripping process^［29］. The practical processing of the metalens array can be achieved using similar methods^［30］.

The FOV of a single metalens is very important for the imaging ability of the proposed planar ACE. The bigger it is， the less metalenses are needed to cover a large FOV. For metalenses， their FOVs are difficult to be acquired using the traditional glass-based formulas. In order to determine the FOV of the 0° off-axis metalens， the Point Spread Functions （PSFs） under different incidence angles are analyzed. Here， the electric fields of the metalenses are simulated and observed using the CST Microwave Studio. It should be noted that， because of the limited computing resources， direct calculation of the light field distribution at the focal plane is extremely difficult. To handle the problem， the near-field light field distribution on the plane of 0.5 µm above the metalens is extracted. Subsequently， the field distribution of the final focal spot is calculated using the vectorial angular spectrum theory^［31-33］. The normalized intensity distribution of the transmitted electric field of the 0° off-axis metalens under 0º， 10º and 20º off-axis incidence is shown in Fig. 4. The produced FWHM under 0º， 10º and 20º off-axis angles are 0.74 μm， 0.77 μm and 0.89 μm， respectively. The FWHM under the 20º off-axis illumination increased 20.3% compared with the 0º situation. From the results， it can be concluded that the metalens is functional with the inclination angle of the incidence reaching as large as 20º. When the inclination angle is beyond such a value， the focal spot becomes less sharp and deformation becomes obvious， making it unable to focus properly. That is to say， the results indicate that the FOV of a single metalens reaches 40º.

To verify the feasibility of the proposed ACE structure， the optical performances of all the composed off-axis metalenses should be evaluated. However， although the metalenses are designed with different off-axis angles， their basic structures are similar. Here， three metalenses with the off-axis angles of 0º，30º and 50º are chosen to verify the feasibility of the MA. For each metalens， the incident angle is set equal to its off-axis angle， making the emergent light normally focus onto the focal plane. The focusing intensity distribution and PSFs of the three metalenses are demonstrated in Fig.5（a）~（f）. The FWHMs of the 0°， 30° and 50° off-axis metalenses are 0.74 μm， 0.74 μm and 0.75 μm， respectively. The FWHM of the 50º off-axis metalens is nearly the same as the 0º off-axis metalens， indicating that the imaging abilities of the metalenses are almost constant at large off-axis angles. The focusing efficiency is calculated by E_foci/E_inci， where E_foci is the energy within the first zero point， and E_inci is the overall incident energy. The focusing efficiencies of the 3 metalenses are 75.5%， 46.8% and 20.9%， respectively. The drop of the focusing efficiency at large off-axis angles indicate that fewer light beams are focused into the focal spot as the off-axis angle increases， and that the image quality and intensity may be reduced. However， the intensity differences for metalenses with large off-axis angles can be relieved through reverse-compensation in the post-treatment process.

To verify the imaging ability， imaging simulation of all three metalenses are conducted using convolution computation. Here， two 1 μm-diameter points with the interval of 2 μm are taken as the object to generate the respective images. Fig. 6（a） shows the intensity distribution of the original 2-point object and its cross section （shown in the inset）. Fig. 6（b）， （c） and （d） showed the produced images and their cross sections （shown in the insets） for the 0º， 30º and 50º metalenses， respectively. It can be seen that despite some overlapping， the produced images of the 2-point object are discriminable， proving the off-axis metalenses’ feasibility for imaging.

A more complicated picture （the badge of Chongqing University （Fig. 7 （a）） is chosen as the object to further verify the feasibility of the proposed scheme. The imaging performance of the 0º， 30º and 50º metalenses are shown in Fig. 7（b） ~（d）. It can be seen that， although the image quality of the 50º off-axis metalens is mildly poorer， it can still be regarded as visible because the badge details remain recognizable after transmission. The reason for the degradation of the image quality is that the noise of the background is increased and the focusing efficiency is dropped with the increase of the incident angle. Although the imaging abilities of metalenses are influenced by the off-axis angle to some extent， it is good enough to produce a clear image of a complicated object.

A comparison of different ACE structures is shown in Table 1. Some parameters are compared including the surface type （planar/ 3D）， layer number （number of the optical device layers）， FOV （the overall FOV of the ACE）， size （the size of the whole ACE）， and overall height （the distance between the first layer of optical device and the image plane）. It can be seen that the proposed metalens-based planar ACE obtains a large FOV with a single-layered planar structure. Due to the compact structure of metalenses， the geometric dimensions of the ACE are also extremely small.

In this work， a scheme to realize a planar ACE with a large FOV is proposed. It is composed of a transparent SiO₂ substrate to hold the whole structure， a receiver to collect the produced images， and a metalens array， which uses metalenses in this work to image different portions of the object field. Although a single metalens covers a limited FOV， the combined image of the metalenses cover a large FOV with proper arrangement of the off-axis angles of the metalenses， which reaches as large as 140º×140° in this work. Importantly， because the off-axis angle is embedded within the structure of the metalenses， they do not require additional components to aim for different fields. The metalenses and their produced subimages both lie on a planar plane， making it beneficial for designing and manufacturing as no complicated curving process or any intermediate devices are required. In practical use， the intensity difference between the subimages should be compensated in the post-treatment process to avoid abrupt change of local brightness. Combined with the fast development of metasurfaces， the metasurfaces-based ACEs allow for not only large FOV and compact size， but also color imaging ability^［36］ and polarization sensitivity^［37］. With advantages on small size and multiple-imaging， the proposed ACE has wide utilization in micro security camera， medical inspection， and distance estimation.