Diffractive Metalens: From Fundamentals, Practical Applications to Current Trends

Traditional optical lenses and the corresponding imaging systems, which are based on the optical paths when light propagates inside the bulky media, usually suffer from the bulky size, Abbe-Rayleigh diffraction restricted resolution, and limited responses to different kinds of incident light. Recently, the burgeoning development of metasurfaces comprised of artificial microor nano-structures at the subwavelength scale have drawn more and more attentions of the scientific community due to the intriguing abilities such as efficient light-matter interactions and multi-dimensional manipulation of optical waves, which provide profound potentials to realize functional metalens with an ultrahigh numerical aperture (NA) and with super-resolution focal


Introduction
Optical lens is one of the cores in optical systems, such as telescopes, microscopes, spectrometers, and is widely investigated throughout the history of optics and photonics.
Traditional optical lens is developed by engineering transparent media or reflective metals to control the optical path of electromagnetic waves (EMWs), according to the laws of ray optics and wave optics developed by Snell, Fermat, Fresnel, Kirchhoff, and many other pioneers [1]. Although great achievements have been made by using such optical-path-based method, the challenges and drawbacks also arise as the rapid increment of the density of optical information. For example, traditional optical equipment is inevitably bulky compared with electronic circuits, which can even integrate much more components [2,3]. Such bulky size strikingly increases the cost and mass of the optical systems. Another challenge is the lack of multi-dimensional manipulation of optical fields, which confines the development of multifunctional optical devices and the investigation of new optical effects [2,4,5]. Traditional optical devices are also restricted by the Abbe-Rayleigh diffraction limit of about half of the operating wavelength [6]. In the past decades, researchers have developed different methods to increase the optical spatial resolutions, such as near-field scanning optical microscopy [7], far-field fluorescence-based microscopy [8][9][10][11], and label-free far-field microscopy [12][13][14]. However, such methods still suffer from specific limitations, and are suitable for certain scenarios.
Metasurfaces, which consist of numerous planar artificial building blocks, provide a wide platform for controlling light in ways that would not be possible with natural materials [15][16][17][18]. Such artificial building blocks at the subwavelength scale can interact strongly with the incident light, leading to efficient and versatile resonances in the near-field region, such as electric dipole [19], magnetic dipole [20], toroidal dipole [21], and anapole resonances [22]. By elaborately tailoring the geometry of each building block, one can locally modulate the abrupt phase change [23,24], polarization [25,26], reflection/transmission/absorption [27][28][29][30], and the combinations of these optical dimensions [4,[31][32][33][34][35] pixel by pixel, which results in many intriguing phenomena and devices such as anomalous refraction [36,37], photonic spin Hall effect [38], Cherenkov surface plasmon wakes [39], special beams generation [40,41], polarization converters [42], and waveguide modes converters [43]. In the past decade, researchers have exploited various kinds of materials to serve as metasurface building blocks. For example, metallic nanostructures are much smaller than the working wavelength, and the induced surface current is a facile tool to control the local resonances [44][45][46][47][48][49]. Compared with metallic nanostructures, the dielectric scatterer is larger and the height is even comparable with the operating wavelength due to the Mie scattering effect [50][51][52]. However, the working efficiency of dielectric nanostructures is high compared with plasmonic nanostructures since there is no intrinsic thermal loss, and the dielectric nanostructures could easily combine electric and magnetic dipole resonances within a single structure [53][54][55][56][57]. The two-dimensional (2D) materials such as graphene, WS2, MoS2 are also widely investigated due to the intrinsic surface effects and the van der Waals interactions [58][59][60][61][62]. In the past several years, researchers have exploited the realization of metasurface in a broad electromagnetic region, such as the optical [63], infrared [64], terahertz [65], and gigahertz wavebands [66]. The abundant resonances and building blocks provide revolutionary tools to modulate the wavefront of optical fields, and could totally change the optical lens designs on the metasurface platform, namely metalens.
Here, a review of the metalens design and the potential applications is given from the perspective of EMWs interference and coupling. We summarize the current research hotspots and the main challenges of metalens in engineering photonics. In Section 2, we discuss the fundamentals of the metalens design, including the physical principles and the design criteria. In Section 3, we summarize the schemes to realize basic metalens component, such as achromatic metalens and sub-resolution metalens.
Complex metalens combinations and systems are discussed in Section 4 to exemplify the distinguished significances and potentials in future photonic applications. An outlook presenting our opinions on the future trends and challenges in metalens is provided in the last section to guide the future development of metalens.

Fundamentals of Diffractive Metalens
In principle, all the metalens design could be classified into two categories, i.e. the building blocks design and diffractive paths design. As mentioned in the introduction part, the subwavelength building blocks provide efficient light-matter interactions which guarantees EMWs behave far different from that in natural materials. In the focusing area, the EMWs follow the diffraction theory because the metalens usually works in isotropic media.

Design principles of metalens
In 2011, F. Capasso's group proposed to locally control the phase abrupt of EMWs using the V-shaped nanostructures and realized generalized laws of reflection and refraction, which makes metasurface a significant platform to manipulate the wavefront of EMWs [15]. This group also realized a metalens in the near infrared region, which opened up the possibilities of high-performance lenses in a flat surface [67]. The phase abrupt is decided by the local modes or local resonances of the nanostructures such as the electromagnetic dipole resonances [37] and Fabry-Perot cavity resonances [68].
Generally, the radiated power of the resonant nanostructures could be calculated by the sum of the multipole moments [21,69,70]: where P, M, T, Q  , M  are defined as the electric dipole, magnetic dipole, toroidal dipole, electric quadrupole, magnetic quadrupole, respectively. Thus, each location of the metasurface could be viewed as an independent wavelet similar to that described by the HuygensFresnel principle, no matter whether there are near-field coupling between nanostructures or not. The diffraction field could be written with the Rayleigh-Sommerfeld theory [71]: is the propagation kernel, and n is the refractive index of the background isotropic medium. Specifically, for metalens, which could convert the incident planar wavefront to the spherical one, the phase abrupt at each location of the metalens needs to be [67]: where f is the working focal length of the metalens. The hyperbolic phase distribution described in Equation (2.3) means a large phase gradient when the metelens is large.
Thus, the size of the unit cell U should be small enough to avoid high orders of diffraction, and should meet the Nyquist sampling criterion [72,73]: where NA = max{NAobj, NAimage}, and NAobj, NAimage are the numerical apertures in the object and image planes, respectively. Especially, NA is the numerical aperture of the metalens for normal incidence.

Typical designs of metalens
One of the intriguing phase types is Pancharatnam−Berry (P-B) phase, which is based on the spatial symmetry of the local fields of the nanostructures [74]. As shown in Figure 1(a), the phase abrupt in each unit cell is  = , where = ±1 represents the left/right-handed circularly polarized (LCP/RCP) light, respectively, and  is the orientation angle of the nanostructure. Note here the phase  denotes the crosspolarization state of the incident light, namely the anomalous light. Since the phase of the anomalous light becomes its opposite number when changing the helicity of the incident light, the metalens serves as a convex lens and a convex lens for LCP and RCP incident light, respectively [75]. For the polarizer-based plasmonic antennas, no more than 25% of the incident LCP/RCP light could be cross-polarized due to the absorption and mirror effect of the polarizer [49]. Although half-wave-plate-based plasmonic antennas could realize cross-polarization conversion with high efficiency, multi-layered designs or fabrication-challenging building blocks are often required, especially for the transmission mode [76,77]. On the other hand, by employing dielectric high-ratio nanofins, which induces intrinsic waveguide modes and makes the dielectric antenna a half-wave-plate-like component, the cross-polarization conversion efficiency reaches about 100% [78][79][80][81][82]. By utilizing such nanofins, a high-efficiency metalens is realized in the visible (Figure 1(b)). The scanning electron microscope (SEM) image in Figure   1(b iii) shows that the nanofins could be fabricated with high precision following the atomic layer deposition method [83]. One of the main advantages of such high-ratio nanofins is that it only requires high refractive index and low thermal loss in the operating wavelengths, such as silicon in the infrared and titanium oxide in the visible.
Thus, the building blocks are easily designed for different wavebands. The engineering materials, especially silicon, are compatible with the commercial semiconductor industry and the complementary metal-oxide-semiconductor (CMOS) techniques [54,[84][85][86][87].
Since the P-B-phase-based metalens is dependent on the incident polarization state, chiral metalens can be realized by elaborate arrangement of the nanofin building blocks [88]. As shown in Figure 1(c), two nanofins arrays were arranged in a single metalens, resulting in different locations of the focal spots for LCP and RCP incident light. This kind of chiral metalens could map the circular dichroism of the object, such as a Chrysina gloriosa whose exoskeleton shows different reflectivity for LCP and RCP incident light. Recently, the intrinsic chiro-optical activity has been widely investigated and the working efficiency reaches a really high level [89,90]. The high-ratio dielectric nanopillars can be designed working in all the polarization states, just as a traditional lens, since the waveguide mode in the dielectric nanofins covers the phase range from 0 to 2 by adjusting the effective refractive index of the waveguide [55,72,83,[91][92][93].
A finite difference time domain analysis of the dielectric nanopillars was performed to demonstrate the waveguide modes, leading to polarization-insensitive metalens working in the visible (Figure 1(d)). An ultrahigh NA (reaching 1.48) metalens with efficiency of 48% can also be realized with a c-Si-based nanobrick array, which operates in immersion liquid with refractive index of 1.512 [94]. As shown in Figure   1(e), a diffraction limited ultrahigh resolution was realized (about 0.40) at the operating wavelength of 532 nm, and the measured full with at half maximum (FWHM) reaches 211 nm in the immersion liquid.

Basic Diffractive Metalens Components
Although many novel metalenses have been realized as introduced in Section 2, the basic components of metalenses still need to be expanded such as the achromatic metalens and sub-resolution metalens for realistic applications. In this section we will discuss the realization of aberrations-correcting metalens, sub-resolution metalens, nonlinear metalens, and artificial intelligence (AI) aided metalens.

Correcting monochromatic aberrations
In traditional optics, the devices suffer from five types of monochromatic aberrations, i.e. the spherical aberration, comas, astigmatism, field curvature and image distortion.
Generally, if one could accurately control the local phase function of each unit cell as deduced in Ref [95], the focusing metalens will be perfect:  [96]. Another method to correct the monochromatic aberrations was to learn from the traditional method: using a corrector and forming a doublet metalens. As shown in Figure 2(b), A. Faraon's group in detail studied the focusing of on-axis and off-axis light for a singlet metalens, and proposed to correct the off-axis aberrations by introducing another metalens on the other side of the substrate [102].
The phase profiles took the form of Taylor expansion: where  is the radial coordinate and R is the radius of the metalens. The coefficients an were optimized for minimizing the size of the focal spot at incident angles from 30° to 30°. The phase profiles were obtained through the ray tracing technique provided by the commercial optical design software, Zemax, and the working efficiency reached more than 40% for both TE and TM incidence in the field-of-view of 60°×60°. In this work the hydrogenated a-Si was utilized to decrease the thermal loss of a-Si at 850 nm incidence, and a layer of SU-8 polymer is applied to protect the fabricated samples. By applying a similar design scheme, i.e. using both the aperture metalens and the focusing metalens, a doublet metalens working in the visible was realized with the titanium dioxide nanofins [103] ( Figure 2(c)).
The abovementioned methods are based on ray tracing techniques. Another intriguing and practical method is to utilize the negative refraction effects, which was realized in 2000 by J. Pendry [104]. The negative refraction effect results from the simultaneous electric and magnetic resonances, which is a basic condition to realize negative permittivity and permeability [105,106]. As shown in Figure 2(d), A. Alù's group realized a Parity-Time symmetry based metasurface that operates in all-angle to remove the monochromatic aberrations [107]. A single plane mirror is aberration-free because the diffraction limited virtual image is the same as the point source. Similarly, a coherent absorber and a coherent emitter were proposed to mimic the imaging of a single plane mirror. By realizing the scattering matrix: which is independent of the incident angles, the device could absorb the complete angular spectra of the incident waves when illuminated from both sides with a specific phase relation. By employing both of the coherent absorber and the coherent emitter, a Parity-Time-symmetry-based metalens that can work in all angles was realized.

Achromatic Metalens
The chromatic aberration results from the phase accumulation when light at different wavelengths travels, and is widely observed in traditional optical devices such as gratings, lenses, prisms, and wave plates. In the metalens scheme the chromatic aberration could be corrected in principle by elaborate control of the resonances at different working wavelengths. As shown in Figure 3(a), three wavelengths of 1300 nm, 1550 nm, and 1800 nm were optimized to remove the chromatic aberration by the nanowaveguide couplers [108], which means the phase function should satisfy: where l(r) contains the optical wavefront information of the device, such as a beam deflector or a lens, and C() contains the phase compensation for different wavelengths.
Another type of achromatic metalens is to combine different layers of metalenses into one, in which each layer of metalens serves as a single metalens operating at an independent wavelength. As shown in Figure 3(b), each of the layers (composed of three different metals: gold, silver, and aluminum) servers as a narrow band Fresnel binary zone plate, and the three zone plates were designed with the same focal length [109]. Such few-layer metasurfaces have been widely investigated recently due to the abundant interlayer interactions and the feasible fabrication processes [52,[110][111][112][113][114][115].
Since the required phase compensation lies in a wide range, the achromatic metalens working in a wide bandwidth is not easy to realize [116][117][118][119]. To achieve the broadband achromatic metalens, a continuous phase compensation is needed in the working waveband: where the former part in Equation (3.5) describes the basic focusing phase profiles and is independent on the operating wavelength , and the latter part in Equation (3.5) requires elaborate design of the resonators. By employing plasmonic nanostructures the chromatic aberration over a broadband region from 1200 to 1680 nm for circularly polarized light was corrected with the efficiency of about 12% [120].
Another method to realize the chromatic phase compensation is to investigate the directly describes the phase dispersion over different operating wavelengths [121]. As shown in Figure 3(c), a metacorrector was utilized in the wavepacket tracing, and the chromatic aberration could be corrected by meeting the wavelength-dependent phase profile: where d is the design frequency. With the designed titanium dioxide metacorrector, the achromatic lens works well from 460 nm to 700 nm incidence. Researchers also demonstrated the dispersion-tailored achromatic metalens with working wavelengths from 460 nm to 670 nm with a working NA of 0.2 for focusing and a working NA of 0.02 for imaging [122], and the working efficiency was about 20%. Another successful material in the visible to realize achromatic metalens was the gallium nitride. As shown in Figure 3(d), taking advantages of the strong resonances of the solid and the inverse gallium nitride nanopillars, a large phase dispersion was realized in the visible, from 400 nm to 640 nm [123]. The working NA was 0.106, and the operating efficiency was about 50%. The NA of the designed achromatic metalenses was low because for large NA the required phase compensation will also become a function of the incident angles, which makes the design procedure a time-consuming work.

Sub-Resolution Metalens
Metalens also suffers from Abbe-Rayleigh diffraction limit, just as the traditional optical lens does. The advantages or superiorities of metalens lie in multi-dimensional manipulations of the optical fields, which makes metalens an intuitive method to realize super-oscillatory sub-resolution focusing without fluorescence labeling [124]. Since M.
Berry and S. Popescu demonstrated that the diffraction from a grating could create ultrasmall localization of EMWs in far-field region [125], researchers have exploited different methods to realize super-oscillation such as using radially polarized light [126][127][128][129] and binary apertures [130][131][132]. In 2009, N. Zheludev's group realized subresolution focusing by judicious design of the optical mask which created constructive interference of EMWs in a far-field distance, without the need for evanescent fields [133]. The fields of the EMWs were given by a limited series of the orthogonal prolate spheroidal wave functions n(c,x): Theoretically, the FWHM of the sub-resolution focus could be arbitrarily small by sacrificing the working efficiency and the field-of-view.
As shown in Figure 4(a), a P-B-phase-based binary phase plate was realized with the Cr nanorods [134]. Since the P-B phase is symmetry-induced and is wavelength independent, the designed super-oscillatory phase plate is broadband. A strong white focus with size of 0.625 times of the Airy spot was observed, surrounded by a bright lobe ring pattern. By employing both amplitude and phase manipulation, a metalens with NA as high as 1.52 and the focal size as small as 0.33 was demonstrated [135].
The schematic illustration was shown in Figure 4 broadband quarter-wave-plate-based sub-resolution metalens was also realized in the reflection mode (Figure 4(d)). The cross-shaped plasmonic nano-antennas generates azimuthally or longitudinally polarized focusing light, and forms sub-resolution hot spot and hollow spot [138]. Based on the outstanding abilities of multi-dimensional manipulation of the optical fields, metalens may realize high-performance label-free sub-resolution focusing, and further achieve practical imaging techniques someday.

Nonlinear Metalens
Nonlinear metalens is based on the intrinsic nonlinearity of the materials. When tailoring the geometry of the building blocks, the nonlinear optical responses are different from those of the linear media. For example, the P-B phase depends not only on the incident polarization states and the symmetry of the nanostructures, but also on the order of the nonlinearity [139][140][141][142][143][144][145]. As demonstrated in Ref [141], the geometric phases are (n1) and (n1) for the nth harmonic generation with the same or opposite circular polarization to that of the fundamental EMWs. Such continuous control of the nonlinear P-B phase could be utilized to manipulate the wavefront the nonlinear light [146,147]. A C3 symmetric nanoantenna array was applied to realize the second harmonic generation (SHG) and the P-B phase manipulation ( Figure 5(a)). The simulated localized surface plasmon polariton was at 1064 nm, and the measured resonances was slightly shifted to 1085 nm. By controlling the polarization states of the SHG signals, the focused SHG light was observed, and further the SHG imaging of an L-shaped aperture was captured by the CCD camera [148]. Taking advantages of the strong local resonances and symmetries of the nanostructures, many novel nonlinear phenomena and devices could be realized such as the rotational nonlinear Doppler effect [149], simultaneous control of the spin and orbital momentum of SHG light [150], high harmonic generation [151], and a broadband optical frequency mixer [152].
Another intriguing platform to investigate the nonlinear photonics is the 2D materials.
For example, a WS2 layer was combined with the gold nano-hole arrays to form a WS2-Au hybrid metasurface ( Figure 5(b)). A large SHG susceptibility of ~10 -1 nm/V was realized at the working wavelength of 810 nm, and the SHG susceptibility was 2 or 3 orders of magnitude larger than the typical plasmonic metasurface [153]. By controlling the P-B phase of the hybrid metasurface, the SHG focusing was also achieved. The WS2-Au hybrid metasurface also provides a feasible platform for coherent steering of nonlinear chiral valley photons, which may benefit the realization of nonlinear quantum and valleytronic nanodevices [154]. Nowadays, the development of nonlinear metasurfaces and nonlinear wavefront-shaping devices are growing faster and faster, which may enable the practical applications such as super-resolution imaging, quantum optical information processing, and biosensing.

Artificial Intelligence Aided Metalens
In the past decade, the geometric effects and the intrinsic light-matter interaction modes of the subwavelength nanostructures were widely investigated, which greatly boosted the rapid development of nano-photonics. However, with the striking increment of the multi-dimensional parameter spaces in the metasurfaces designs, the realization of some high-performance metasurfaces becomes time-consuming, such as the high-NA, high-efficiency metalens, and the ultra-wideband multifunctional meta-devices.
Recently, the development of AI techniques has become a research hot spot, and enables novel microwave and photonic devices, which may relieve the researchers from tedious trials and errors-testing works [155][156][157][158][159][160][161][162][163]. For example, a topology-optimized method was applied to optimize the phase design of the metalens [164]. As shown in Figure   5(c), conventional metalens is realized by designing the nanostructures in the unit cell (smaller than 0.5), while the proposed topology-design aims at optimizing the nanostructures in a section of ~3. Thus, the designing restriction on the size is relieved by about an order of magnitude, leading to the improvement of the working efficiency (exceeding 90%) of the high-NA and large-area metalens. Another intriguing high-NA achromatic metalens was achieved recently by an inverse design [165]. As mentioned in Section 3.2, the high-NA achromatic metalens is hard to realize because the unit-cellbased design leads to rapid variations of the phases for different operating wavelengths when the working NA is large. Researchers employed the inverse design that did not have unit cell limit. The total scattering and diffractive properties of the device was incorporated ( Figure 5(d)). Considering the electric fields at the exit plane: and the time-reversed field at the desired focal point: a "mimimax" optimization was applied over the geometrical degrees of freedom and the frequency domain: Two design methods based on the inverse design, namely constant-z geometry and freeform geometry, were compared by the focusing efficiency ( Figure 5(d ii)).
Specifically, the freeform inverse design was employed to realize the near-unity-NA (0.99) achromatic metalens, which works well across the visible waveband from 450 nm to 700 nm ( Figure 5(e iii)).

Applications of Metalens Systems
As introduced in the previous sections, metalens has been systematically investigated in the past several years and many novel types of metalenses arise. Nowadays, almost every kind of traditional lens has a counterpart in the metalens research area.
Researchers also developed metalens systems, some of which are really fascinating and promising. In this section, we will discuss the applications of metalens systems, including the multifunctional metalens, tunable metalens, and the metalens cameras/microscopy.
Generally, the multifunctional metalens is also based on the phase manipulation of the EMWs. For example, by taking the n phase locations of the hyperbolic phase distribution, a convex-concave double lens could be realized (Figure 6(a)) [73]. The simulated results illustrate the diverging and focusing wavefronts simultaneously, with the real and virtual focal points at the focal planes. Taking advantages of the different values of the P-B phases for different orders of harmonic generation [141], researchers have realized focused optical vortices in both linear and nonlinear regions with a single metasurface [176]. As shown in Figure 6(b), the P-B phases for the fundamental EMWs () and for the SHG signals (, and ) are 2, , and 3, respectively, leading to the corresponding focusing with different focal lengths. The differences in the P-B phases also resulted in different topological charges in each channel. Such kind of multifunctional metalens expands the multi-vortices generation to the nonlinear region, and the capacity of information channels were tripled. By combining different metalenses with the segmented [177], or interleaved [178,179] arrangements, multifoci metalenses that can focus the incident light at different locations were also realized.
Such multifunctional metalenses will enable the possibilities for future integrated metalens systems.

Tunable and Reconfigurable Metalens
The functions are invariable for most of the metasurfaces and metalenses once they are fabricated. However, it is very useful and cost saving to realize the tunable and reconfigurable metalenses for realistic applications, such as the scanning microscopy and cameras. Today, there are two major methods to realize the tunable metalens.

Inducing the Material Changes
The geometric parameters of the nanostructures are not easy to be repetitively and reversibly varied, but the phase of the building materials could be changed at certain conditions. For example, germanium antimony telluride (Ge2Sb2Te5, GST) is a promising reconfigurable material with a crystallization temperature at about 160 ℃ and a melting temperature of about 600 ℃ [180]. GST has different refractive indices at different phases of crystalline and amorphous states, leading to the dynamic modulation of the transmitted / reflected amplitude / phase [180][181][182][183][184][185][186]. By controlling the crystallization fraction of GST, the refractive index can also be continuously modulated between that of the crystalline and the amorphous states [187]. Based on the phase changing GST layer underneath the nanostructures, a cylindrical bifocal metalens was realized with the focal lengths of 0.5 mm and 1 mm for the amorphous and crystalline states, respectively [188]. Another phase-changing material is vanadium dioxide, which could switch between the metallic and the dielectric phases in multiwavebands such as in the infrared and the terahertz [189,190]. Recently, the magnesium based nanorods were employed in a dynamic metalens design [191]. As shown in Figure   6(c), with the hydrogenation and the dehydrogenation processes, the phase distributions were altered from a longer focal length metalens to a shorter one. Graphene, as a typical 2D material whose Fermi level could be changed by controlling the gate voltage or doping, has been widely investigated due to the potentials as a tunable material [30,59,60,192,193]. The optical indices of such materials could be changed by different inducing methods, which further results in wavefront manipulation of the EMWs.

Varying the Working Configurations
Another commonly used method to realize tunable metalens is by varying the working configurations of the metalens [194]. With Au nanorod arrays fabricated on a stretchable substrate (a PDMS film), the focal lengths varies when stretching the substrate by four linear translation stages (Figure 6(d)) [195]. However, since the required phase distribution of focusing is not linear, the focusing suffers from some aberrations a little bit when stretching the substrate, leading to the increment of the DOF ( Figure 6(d iii)). A. Faraon's group realized a tunable doublet metalens based on the microelectromechanical systems (MEMS) [196]. By applying a voltage to the doublet MEMS metalens, the distance between the two layers of metalens varies, and the focal point also moves a distance away ( Figure 6(e)). The monochromatic aberrations could be further removed by a triplet design using the metacorrector as introduced in Ref [102]. Interestingly, the MEMS-based tunable metalens possesses a scanning frequency potentially reaching a few kHz, which is very fascinating in practical scanning and imaging systems.
Researchers also employed the coherent absorption in a plasmonic metalens to control the focal intensity from 'on' to 'off' states [197]. In this configuration, two coherent beams illuminated from the opposite sides of the metalens, and the coherent structured control beam could modify the signal beam by controlling the absorption, leading to a modified focal spot or an eliminated focal spot. To date, full and independent tunable phase manipulation in each unit cell is still challenging, especially for the near infrared and the visible region because the building blocks are only about hundreds of nanometers. Using electrically controlled diodes, the state of each unit cell of the coding metasurface has been switched between '0' and '1' in the GHz region [198]. By applying the gate voltage, a graphene-gold hybrid reconfigurable metasurface was also demonstrated which could modulate the phase in a range larger than 230 at a wavelength of 8.50 m [199].

Metalens Cameras and Microscopy
Recently, some intriguing metalens-based techniques have arose, which may benefit the realistic applications of metalens, and may enlighten future developments of novel metalenses. An off-axis metalens was realized as a compact high resolution spectroscopy working in the wavelength range of 1.1 m to 1.6 m [200]. Different from traditional grating-based spectroscopy, the spectral resolution of the metalens is given by: where  is off-axis angle of the metalens. The resolution of the metalens-based spectrometer (2.9 nm) could be designed as a constant when shrinking the size of the device, which is essential for the compact integration. By employing the dispersion engineering, an aberration-corrected off-axis metalens-based spectrometer was also realized [201]. Metalens could also be designed as an independent camera by combining a CMOS detector [102]. As shown in Figure 7(a), the total size of the miniature optical camera is 1.6 mm × 1.6 mm × 1.7 mm, with a correcting metalens on the top to revise the monochromatic aberrations as introduced in Section 3. The modulation transfer function (MTF) that represents the relative contrast of the image and the spatial details shows that the cascaded doublet metalens could improve the diffraction limited performance. Such miniature camera design indicates the potential of portable metalens-based imaging devices. With an array of 60 × 60 small achromatic metalenses, a full-color light-field camera was also realized [202]. The building block of the metalens is gallium nitride unit element, which has been demonstrated capable of correcting the chromatic aberration in the visible [123].
Similar to the traditional light-field camera, the raw light-field image contains numerous sub-images due to the existence of the metalens array (Figure 7(b)). By rendering the images with different focusing depths, the three objects (the three letters A, B, and C) at different depths were reconstructed. Furthermore, the object in the scene could be reconstructed slice by slice with the corresponding rendered images. Taking advantages of the abilities of metasurface to manipulate polarizations of EMWs, researchers have realized a compact full-Stokes polarization camera [203]. As shown in Figure 7

Conclusions and Outlook
In summary, with the innovation in fundamental design principles, the basic materials, and the manufacturing techniques, metalens has become a promising platform for future practical photonic devices. Herein, we have reviewed the design motivation, principles, and applications of diffractive metalens based on the wavefront manipulation of EMWs.
We reviewed the diffractive performance of metalenses composed of different building blocks such as metallic, dielectric, 2D, and nonlinear materials. The phase in each unit cell is decided by the materials type, geometric design, and the symmetry of the nanostructures, leading to wavefront manipulations of EMWs pixel by pixel. We reviewed the basic metalens components such as monochromatic aberrations corrected metalens, achromatic metalens, sub-resolution metalens, nonlinear metalens, and AIaided metalens. All of these metalens components are important in the understanding of metasurface designs and future applications. Currently, different kinds of highperformance metalenses have been developed step by step, and approach the practical applications day after day. We also reviewed several metalens systems such as the multifunctional metalens, tunable and reconfigurable metalens, and metalens cameras, which are challenging to realize with traditional optical designs. Recently, multi-level diffraction lens provides another way to realize ultrathin flat lens with high efficiency, and shows inspiring potentials to correct the imaging aberrations [205][206][207]. Quantum effects and modes such as Casimir effect and large nonlinearity are exploited [208,209]. We believe the rapid development of metalens will make a difference in future photonic and quantum techniques, at least partially replacing conventional optical devices.
There are some challenges to be overcome in the metalens design. For example, although the ultrahigh working NA metalens has been experimentally demonstrated, the aberration-free high NA metalens operating at large field-of-view with high efficiency is still challenging. In this review we also envision several directions in future metalens designs.
Theoretically the super-oscillatory sub-resolution focusing is a tradeoff among the focal size, working efficiency and the size of the field-of-view. As discussed in Section 3.3, a number of methods have been proposed to realize the label-free super-oscillatory metalens, which more or less suffered from some specific limitations. One of the possible solutions is by combining the multi-dimensional manipulation of the optical fields with judicious nanostructures design [31,210].
The figure of merit could also be improved by combining some postprocessing algorithms, instead of direct optimization of the multi-parameters in the metalens design, such as improving the field-of-view by multi-shots or composite combination of the sub-resolution images. Another promising method may be utilizing coherent or structured incident light [9,211]. Taking advantages of the versatile abilities of the metalens and its high design degree of freedom, metalens provides a promising platform for practical label-free sub-resolution imaging techniques.
Compared with the bulky size of traditional optical devices and microscopy, metalens enables focusing and imaging on a compact size with multi-functions.
Recently, the rapid development of functional metalens-based cameras provides potentials for integrated metalens systems, which combine numerous metalens components or functions all together. How to design and to optimize such metalens systems and how to postprocess the vast captured images remain questions.
Recently, AI techniques have drawn much attention in both commercial and the scientific community [155,155,161,[212][213][214], and may enable the realization of super-resolution imaging, photonic quantum computing, and a plenty of intriguing branches. AI techniques even provide possibilities for loop-locked design from materials choosing, geometric design, array arrangement, to fabrication processes, which may give birth to future high-performance metalenses and corresponding systems.