Abstract

Metalenses consist of nanostructures that locally control the optical phase. They offer many degrees of freedom for manipulating a wavefront, which gives a number of advantages over bulk lenses, such as the straightforward elimination of spherical aberrations and an ultrathin dimension. Here, we compare the phase profiles of metalenses made of different dielectric materials and note the advantage of high refractive index materials. Higher refractive index materials such as silicon afford more degrees of freedom in terms of design and fabrication and are the basis for high-performance metalenses, even in the visible. Nevertheless, the imaging performance of single-element metalenses is still limited by coma and chromatic aberrations. This limitation is exacerbated by high numerical apertures and large areas. We review the challenges and trade-offs between numerical aperture, field of view, coma, chromatic aberration, and size. We also evaluate different phase engineering approaches to address these problems. We believe this review will help guide future developments in high-performance metalenses toward wide-field and high-resolution imaging, enabling scientific high-end miniature imaging systems.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Metasurfaces are two-dimensional (2D) metamaterials that can locally control the phase, polarization, amplitude, and dispersion of light via subwavelength optical meta-atoms. By spatially adjusting the geometrical parameters of these meta-atoms, the reflected or transmitted wavefront can be controlled at will [14]. Subwavelength meta-atoms have two main roles: (1) they enable the manipulation of light with high spatial resolution and (2) they avoid diffraction orders that would occur if the meta-atoms were spaced at distances larger than the wavelength. One of the most common realizations of a metasurface is the lens function (i.e., a metalens, where the goal is to replace bulky objective lenses with a nanostructured, lightweight, and compact thin film without loss of performance) [5,6]. In addition, the scientific value of the metalens concept is to introduce novel functionalities that traditional optical systems cannot realize. Here, we evaluate the progress in the development of high-performance metalenses and highlight routes for further improvement.

A. Metalens

As with any lens, the numerical aperture (NA) [7] is a key figure of merit for metalenses, both for achieving high imaging resolution and for maximizing light collection. The challenge is then to produce a phase profile that achieves high NA while minimizing other aberrations. By comparison, a conventional single high NA glass lens cannot overcome both monochromatic and chromatic aberrations, which makes it necessary to combine several lenses in a system such as an achromat to achieve a large field of view (FoV) over a wide wavelength range. Such a system, however, is usually bulky, complicated, and costly.

Finding a metalens or a combination of metalenses that addresses this challenge is a very active field of research. Applications in mobile phone cameras [810], endoscopes [11], emerging virtual/augmented reality viewers [12], and miniature optical planar cameras and detectors [13,14] have already been discussed. In these systems, high NA is not necessarily required, so coma and achromatic aberrations are more easily addressed. In high NA metalenses, however, these key parameters are much more sensitively connected. These optical concerns have not been resolved simultaneously with current low NA designs, and it would certainly hinder the applications of high NA metalenses in high-end optical microscope objectives [1518] and optical tweezers. To fully realize the promise of these applications, chromatic aberrations and limited FoV due to coma are the main bottlenecks that must be overcome.

B. Mechanisms to Introduce Phase

To introduce an arbitrary phase profile, the phase modulation imparted by the meta-atoms should cover the full 02πrange [1921]. This modulation is achieved either by resonant or nonresonant effects, or a combination of both. The resonant effects typically include extended Bragg scattering in a photonic crystal [2227] or a high-contrast grating configuration [2834], or, alternatively, localized Mie resonances [3540]. The nonresonant effects include effective index modulation achieved with subwavelength structures, with the special case of meta-atoms that impart phase modulation onto circularly incident light by rotation. The latter method has been particularly successful and is referred to as Pancharatnam–Berry (PB) phase modulation [4153], but it does require a circularly polarized input beam. While the resonant methods tend to have a smaller bandwidth, their multipass nature also means that they can be made thinner, which offers advantages in terms of fabrication and reproducibility. For example, 100 nm thin silicon gratings can achieve full phase control [30,54] while PB structures typically require a high aspect ratio (i.e., they consist of 500–700 nm tall nanostructures with sub-100 nm lateral dimensions). This advantage must be weighed against the fact that resonant structures are generally more sensitive to fabrication tolerances. The height h of the structure is a direct consequence of the effective index approach, whereby the maximum phase change Δφ accumulated in a single pass is given by the optical path difference provided by the structure,

Δφ=k0(nmetanback)h,
with nmeta the effective index of the meta-atom and nback the refractive index of the background. Equation (1) is the general expression, whereas the index contrast (nmetanback) for PB structures should be replaced by the effective index difference between the two orthogonal polarizations. In either case, high index contrast is advantageous for reducing the height h, which makes the structure easier to fabricate. A summary of the different principles used in resonant and nonresonant nanostructures is shown in Fig. 1.

 

Fig. 1. High-level schematic of different types of nanostructures to achieve phase control in metasurfaces, grouped into resonant and nonresonant effects. (a) Localized resonances, such as Mie resonances. Plasmonic resonances that were used in earlier work also fall into this category; (b) Extended resonances such as photonic crystals and high-contrast gratings; (c) Effective index, whereby the fill factor of the nanostructure controls the phase; and (d) Pancharatnam–Berry (PB) phase whereby the rotation of a meta-atom controls the phase of a circularly polarized beam.

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C. Material Choice

Early work on metalenses predominantly used plasmonic materials, but their poor forward-scattering performance and high optical losses have now led to a shift in attention toward all-dielectric materials, as already indicated in Fig. 1. The key requirements of low absorption, high refractive index, and ease of manufacture inform the choice of dielectric. For example, titanium dioxide (TiO2) [8,9,12], gallium nitride (GaN) [5557], and silicon nitride (Si3N4) [11,5860] are often used for visible wavelengths, poly-silicon (p-Si) [16,30,59], and amorphous silicon (a-Si) [15,49,6163] in the near-infrared and mid-infrared regimes, while aluminum nitride (AlN) [64,65] and hafnium dioxide (HfO2) [66] are suitable for the ultraviolet range. Interestingly, it has now also been recognized that, with careful design, crystalline silicon (c-Si) [54,6773] can also be used in the visible regime, with its high refractive index being particularly advantageous. Here, we focus on metasurfaces operating in the visible regime where TiO2, GaN, and c-Si are now emerging as the main candidates (Fig. 2).

 

Fig. 2. Examples of (a) TiO2, (b) GaN, and (c) c-Si metalenses, and their corresponding focusing performance. All data were taken at 532nm: (a) With permission from [8]; (b) With permission from [55]; and (c) With permission from [71].

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TiO2 and GaN are the obvious choices because they are lossless at visible wavelengths. Their refractive index is in the range of 2.0 to 2.4, which provides high contrast against air. However, in some applications, such as microscopy, it is often advantageous to use immersion oils for increasing the NA and improving resolution. As a reminder, the NA describes the ability of a lens to focus and collect light and to resolve small features. It is defined as

NA=nbacksinθ,
with θ representing the maximum acceptance angle of the lens. To achieve a high NA, the refractive index contrast (nmetanback) becomes more critical (e.g., for an immersion oil of nback=1.5, the contrast drops to below unity), and has two important consequences: first, the meta-atom aspect ratio becomes rather high [Eq. (1)], and structures become very difficult to fabricate; second, the low contrast reduces the confinement of the optical waves to the meta-atoms, thus increasing the coupling between adjacent elements, which decreases the total focusing efficiency.

Crystalline silicon provides an interesting alternative because it offers a high refractive index (Re[nmeta]4) and a relatively low absorption even in the visible range (Im[nmeta][0.01,0.1]); efficiencies of up to 67% have been reported at 532 nm [71], which is only marginally lower than those achieved with TiO2 [12]. Despite the apparently prohibitive absorption coefficient value of 104cm1 at this wavelength, the small size of the meta-atoms enabled by the high index partially compensates for this high absorption coefficient. It is this trade-off between size and absorption that makes c-Si such a promising material for metalenses. Furthermore, computational optimization techniques have recently been used to enable the realization of NA=1.48 immersion lenses, thereby combining high efficiency with ultrahigh NA [see Fig. 2(c)]. Due to its compatibility with large-scale manufacturing technologies, we therefore believe that silicon offers the best compromise between transmission, refractive index, and manufacturability. The only obvious downside of using silicon is that its extinction coefficient rises rapidly toward shorter wavelengths, so operating in the blue and UV wavelengths remains a challenge.

2. OPTICAL PERFORMANCES OF METALENSES

A. Ultrahigh Numerical Aperture

As already discussed, silicon metalenses have so far achieved the highest reported NA performance and it is important to put this result into context. For example, one alternative approach has been to increase the NA via back immersion, as illustrated in Fig. 3(a), where a NA=1.1 was achieved with an immersion oil of nback=1.5. This strategy is especially advantageous for lower refractive index materials, since the focusing efficiency is not degraded by the immersion. Nevertheless, back immersion limits the working distance by the substrate thickness, as is apparent from Fig. 3(a), as well as the maximum NA that can be achieved. Another relevant feature for metalenses with high NA is discretization, which is given by the spacing between adjacent meta-atoms (i.e., the unit cell size a). The unit cell size must satisfy the sampling (Nyquist) criterion to ensure diffraction-limited resolution [5,6,12], so

a<λ2NA.

 

Fig. 3. Schematic of (a) back immersion and (b) front immersion metalenses.

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Satisfying this criterion becomes more challenging as the NA increases. Notice that this equation only reflects the Nyquist criterion. In addition, the unit cell must be subwavelength (i.e., a<λ/n, to prevent unwanted diffraction). For the nonresonant case, a reduction in unit cell size implies a reduction in feature size, which, since the height h is fixed, implies a higher aspect ratio, thus making fabrication more difficult. Another design challenge is that, as adjacent meta-atoms move closer together with decreasing a and decreasing feature size, light confinement to each meta-atom decreases, causing a greater near-field coupling between adjacent elements. All of these constraints are relaxed with a higher refractive index, which again recommends silicon as a more suitable material. For the localized resonance structures, such as Mie resonators, their feature size is determined by the operating wavelength and therefore fixed. Reducing the sampling unit cell then gives rise to stronger near-field coupling between adjacent elements, similar to the nonresonant case. Extended resonances such as HCGs rely on multiple grating periods; once the sampling unit cell shrinks to below three periods [70], the diffraction efficiency drops and high NAs can no longer be achieved.

More complicated structures have been introduced to address the difficulty of efficient high-angle deflection; here, the repeating unit is a supercell consisting of multiple different features, or of free-form geometries designed to achieve particularly high efficiency for large deflection angles [7478]. Given the larger size of theses supercells, which typically extend over multiple unit cells, they still obey Eq. (3).

B. Coma/Field of View

Having discussed the material and design constraints of individual meta-atoms, let us now consider the phase profile of the overall metalens. The hyperbolic function was successfully introduced by the metalens community because it does not suffer from spherical aberrations [79]. For a high NA, however, this advantage is offset by the introduction of coma and other off-axis aberrations, which severely limit the FoV. These effects are illustrated in Fig. 4 for a metalens of 20 μm diameter with an NA of 0.8, with Figs. 4(a)4(c) referring to the hyperbolical phase profile described by Eq. (4). Figures 4(d)4(f) refer to a numerically optimized profile of Eq. (5) and Figs. 4(g)4(i) to the profile of an equivalent spherical lens [Eq. (6)], so

φhyp(r)=k0nback(f2+r2f),
φoptim(r)=k0nback(f2+r2f)+n=15an(rR)2n,
φsph(r)=k0nbackρf(ρρ2r2),
where k0 and f are the free-space wave number and focal length, respectively, nback is the refractive index of the background medium, an is an optimization coefficient, and R is the radius. Finally, ρ is the radius of curvature of an equivalent spherical lens. It can be shown from geometrical optics and the Fermat principle that rays emerging from a point source on the optical axis in the object plane of a hyperbolic lens [Eq. (4)] converge at the same point on the optical axis in the image plane, so the hyperbolic lens is free of spherical aberrations [80]. The hyperbolic profile, however, suffers from off-axis aberrations, which can be reduced by imposing a phase-correcting polynomial function, as shown in Eq. (5) [13,81]. Finally, Eq. (6) shows the phase profile imposed by a spherical lens [82].

 

Fig. 4. Diffraction reconstructions of three metalenses (f=15μm) with the following phase profiles: (a)–(c) hyperbolic, (d)–(f) hyperbolic superimposed with optimized polynomial, and (g-i) spherical. The first and second columns show the longitudinal field distributions at normal and oblique (30°) incidences, respectively. The third column shows the resulting point spread function (PSF) at 0° (black), 7.5° (red), 15° (green), 22.5° (blue), and 30° (orange). The operating wavelength is 532 nm. The dashed boxes in (d) and (e) highlight that the corresponding phase profiles impose an effective aperture onto the lens.

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For normal incidence, the optical field is tightly focused at a focal distance of 15 μm for all cases [Figs. 4(a), 4(d), and 4(g)]. The field plots beautifully demonstrate the strength of the hyperbolic profile in producing the tightest aberration-free focal spot. When the angle of incidence is increased to 30 deg, however, the focal spot of the hyperbolic lens is strongly distorted due to off-axis aberrations, as seen in Fig. 4(b). This aberration is also clearly apparent from the point spread functions (PSFs) shown in Fig. 4(c) for a number of angles of incidence. Notice how the lateral lobes of the PSF increase asymmetrically as the angle of incidence is increased, with the peak decreasing accordingly. This reduction is already apparent for very small angles, which severely limits the FoV. One of the main challenges in designing high NA metalenses, therefore, is to reduce off-axis (mainly coma) aberrations and to increase the FoV.

Addressing the coma issue is clearly important and has already attracted a lot of interest [7981,83,84]. Most attempts to reduce coma have relied on numerical optimization [13,81,84]. Typically, a polynomial function is superimposed onto the hyperbolic phase profile and its coefficients are optimized, as exemplified by the second term of Eq. (5). An example of a field profile obtained with such a procedure is shown for perpendicular and angular incidence in Figs. 4(d)4(f). It is clear that coma is much reduced, although careful observation of the PSF reveals that the focal spots are slightly broadened compared to Fig. 4(c). The reason for this broadening is apparent from Fig. 4(d); even though the incident plane wave covers the entire metalens, the rays contributing to the focus emerge only from a limited area, corresponding to approximately half the radius of the lens. This means that the optimized phase profile induces an effective aperture onto the metalens and reduces the NA. Interestingly, this effective aperture (highlighted by the dashed squares) is laterally displaced when the angle of incidence is increased, as indicated in Fig. 4(e).

In fact, the appearance of an effective aperture and its displacement as a function of incidence angle is the signature of a spherical phase profile [Eq. (6)]. Accordingly, we added a spherical profile to our comparison; Figs. 4(g) and 4(h) show the corresponding field profiles and effective aperture. The “moving” aperture appears again and the focal spot is unchanged irrespective of the angle of incidence, so the lens is free of coma. This observation is even more apparent from the PSFs shown in Fig. 4(i), which are nearly identical for all angles of incidence between 0 and 30 deg (see Supplement 1 for the simulation of a large-area metalens, which exhibits the same effects as shown for the smaller lens in Fig. 4).

This comparison points to the conclusion that the numerical optimization procedure essentially converts the hyperbolic into a spherical phase profile. It also highlights the difficulty of correcting both spherical and off-axis aberrations simultaneously in a single metasurface. For example, the hyperbolic phase profile corrects for spherical aberrations yet introduces coma, while the spherical profile does the opposite. Multilayered metasurfaces, in contrast, can correct for both aberrations at the same time [13,81,84] at the cost of fabrication complexity. Which trade-off is most favorable depends on the specific application.

A second conclusion is that the coma reduction is related to the imposition of an effective aperture, which limits the effective NA of the lens. Indeed, separate studies (not shown) of metalens performance as a function of NA revealed that the focal spot does not change once when the NA of the lens increases beyond NA0.7, indicating that this value is some fundamental limit of a coma-corrected metalens. The obvious question is then whether this effective aperture is an accident or whether it is fundamentally related to coma reduction.

Studying the Fourier transform (FT) of the field distribution helps us understand the problem. Figures 5(a) and 5(e) show the 2D FT of the metalens’ field distribution with spherical and hyperbolic phase profiles, respectively, as a function of k-vector. The light line is shown as a dashed white circle. Any k-vector component outside the circle is evanescent and therefore does not contribute to focusing. Figures 5(c) and 5(g) (red lines) show a corresponding line plot through the origin with the light line now indicated as a dashed black line. The hyperbolic phase profile has its Fourier components tightly confined inside the light line, and so gives the best performance for perpendicular incidence. The fact that the amplitude of its k-vector components increases toward the light line explains its high performance at a normal incidence, because a large amplitude of high k-vector components ensures a tight focal spot. The spherical phase profile, on the other hand, has components outside the light line (i.e. the lens imposes k-components above kx2+ky2/k0>1 onto the incoming beam). These components are evanescent and do not contribute to the focal spot. Furthermore, in real space, they are generated at the edge of the metalens, and are the cause of the effective aperture; so, at first sight, they appear wasted. When the input angle changes, however, it is precisely the presence of these high k-components that avoids coma, because the high-k components become available at higher input angles and then contribute to image formation. This effect is apparent when comparing k-space for perpendicular incidence [red lines in Figs. 5(c) and 5(g)] with angular incidence [blue lines in Figs. 5(c) and 5(g)]. The effect of angular incidence is to increase the k-vector in that particular direction, thereby moving the spectrum sideways [see also Figs. 5(b) and 5(f)]. The hyperbolic lens now loses k-vectors, thereby losing focusing power; in particular, the k-vector distribution becomes very asymmetric, which is a clear signature of coma and other off-axis aberrations. For the spherical lens, however, the k-vector components that were previously evanescent now come into play and move into the light line. Overall, its k-vector distribution remains largely similar to the unshifted distribution at a perpendicular incidence, so the focusing performance will also be similar. Therefore, the imposition of the effective aperture by high k-vector components and the reduction of coma are directly related and are not an accident.

 

Fig. 5. Fourier transform amplitude of the field at the exit of the spherical metalens at normal (a) and oblique (b) incidences as a function of a normalized k-vector. (c) Corresponding line plot through the origin showing normal incidence (red) and oblique incidence (blue). (e)–(g) Same line plot for the hyperbolic metalens. The light line is shown by the white dashed circle in (a), (b), (e), and (f) and as dashed black lines in (c) and (g). Ray tracing of a bulk spherical lens is shown in (d) for perpendicular incidence and (h) for oblique incidence, superimposed onto the field distributions of an equivalent metalens with spherical phase profile.

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The origin of the effective NA can also be appreciated from a ray optics point of view, as we illustrate with a conventional (“bulk”) lens with a spherical profile. Figure 5(d) shows the ray tracing picture of such a lens for normal incidence and we superimpose the field profile of an equivalent metasurface with spherical phase profile [as in Eq. (6)]. Notice that the effective aperture of the metalens coincides with the area of the rays forming the focal spot of the bulk lens. Figure 5(h) shows the same for incidence at 30 deg and we note that the analogy largely holds. So, a conventional spherical lens also imposes an effective aperture. This effective aperture does not act as a physical aperture, however, since light entering the high gradient region may pass through undiffracted, producing haze and reducing image contrast. Therefore, it may be advantageous to use a physical aperture, as, for example, provided by a multilayer lens [13].

It is worth emphasizing at this point that it is not possible to obtain a single phase profile that corrects perfectly for coma and for spherical aberration at the same time [79,80]. Any phase profile will be a trade-off between NA, spherical aberration, and coma, so the challenge is to find the best compromise.

One approach that has been pursued in this regard is the introduction of a second metasurface (i.e. to form a metasurface doublet [81,83]). Let us consider such a system as introduced by Groever et al. [81] as an example. The doublet consists of a metalens with a spherical profile at the front and a Schmidt plate at the back, with the Schmidt plate aiming to correct the spherical aberration.

The goal of the arrangement is to turn the spherical profile into a hyperbolic profile, yet make the operation angle-independent. We start by directly superimposing the Schmidt-plate onto the spherical lens [Fig. 6(a)]. For perpendicular incidence, the procedure does indeed correct spherical aberration, as shown by the solid orange line representing the desired hyperbolic profile. The blue and green solid lines represent the spherical profile and the Schmidt-plate phase profile, respectively. For angular incidence, however, coma is still present. While the spherical profile “moves up” with the angle, [blue dashed line in Fig. 6(a)], the correcting phase profile (green dashed line) does not move up, resulting in an asymmetric phase profile (orange dashed line). To be coma free, the correcting phase profile should also move up with the spherical profile. In fact, this can be achieved by separating the two plates by a distance d. In this case, the propagation along d projects the phase profile of the Schmidt plate onto the correct position on the spherical metasurface, as shown in Fig. 6(b); the doublet now produces a hyperbolic profile for both perpendicular (orange solid line) and for oblique incidence (orange dashed line). The system therefore corrects for both coma and spherical aberrations at the same time. Unfortunately, the system imposes a trade-off between NA and FoV. Note that the entrance aperture of the first lens limits the system’s NA and the size of the output lens limits the FoV, as is apparent from the geometry. Following this logic, one could simply increase the size of both lenses as long as the second lens is larger and d is kept small. The resulting large operating angles, however, lead to a deformation of the phase profile of the Schmidt plate with respect to that of the focusing spherical lens, which introduces aberrations. In practice, the doublet approach is therefore limited to moderate angles. For example, the doublets demonstrated in [81,83] have NAs equal to 0.48 and 0.41, respectively, with a FoV of 50 deg each.

 

Fig. 6. Illustration to explain how a metalens doublet removes both coma and spherical aberrations by adding a Schmidt plate for correcting spherical aberrations. When the Schmidt plate is placed directly onto the focusing lens (a), a hyperbolic profile is created, but only for normal incidence; the profile for angular incidence is still distorted. By placing the two lenses a distance d apart (b), the Schmidt plate correctly projects its correction onto the focusing lens, resulting in a corrected profile for both normal and angled incidence.

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An alternative compromise between NA, spherical aberration, and coma is to immerse a spherical profile metalens into a high refractive index medium. The image quality of this arrangement would be limited by spherical aberrations, yet high NA would be achievable without coma. For example, we found that immersion in an oil of refractive index n=1.56 raises the maximum effective NA to 1.56×0.707=1.1, without image quality deterioration compared to the non-immersed case. The possibility of oil immersion as offered by high-refractive-index materials, therefore, is important to achieve coma-free and high NA metalenses.

C. Chromatic Aberration and Working Bandwidth

Finally, we consider wavelength dependence. The chromatic aberration of metalenses intrinsically stems from the wavelength dependence of diffraction and from the wrapping of the Fresnel zones [62], even if the meta-atoms were dispersionless. One approach to reducing the chromatic aberration is to introduce dispersion engineering techniques on the meta-atoms [62,85] that counter these intrinsic effects. The concept of dispersion engineering can be illustrated by considering a spatial- and frequency-dependent phase profile φ(r,ω). This phase profile can be expanded in a Taylor series around a target frequency ωd [86] as

φ(r,ω)=φ(r,ωd)+φ(r,ω)ω|ω=ωd(ωωd)+2φ(r,ω)2ω2|ω=ωd(ωωd)2+.
To achieve achromatic focusing with a given bandwidth Δω around ωd, an optical element placed at a radial coordinate r must satisfy not only the required relative phase φ(r,ωd), but also the higher-order derivative terms. The nearest two higher-order terms, φ(r,ω)/ω and 2φ(r,ω)/ω2 are the group delay and group delay dispersion, respectively. The group delay compensates for the difference in the wave packets’ arrival times at the focus, while the group delay dispersion ensures that the outgoing wave packets are identical. The net effect is the minimization of the spread in the arrival times of wave packets at the focus. The smaller the time spread, the larger the achievable bandwidth. Figure 7(a) shows the focusing performance of an achromatic metalens modified by dispersion engineering, which tunes not only the phase profile at the design wavelength, but also the higher-order derivative terms to achieve achromatic focusing.

 

Fig. 7. Metalenses with color corrections. (a) Single-layer achromatic metalens made of TiO2 nanofins to achieve achromatic imaging with a bandwidth of 200 nm. (b) Multilayer metalens to correct chromatic aberration at three specific wavelengths: 1180, 1440, and 1680 nm: (a) with permission from [86], and (b) with permission from [87].

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Let us examine the inevitable trade-off. Shrestha et al. [88] showed that the dispersion required at the center of the lens φ(r,ω)/ω|max monotonically increases with the metalens radius. They described the phase dispersion as

ΔΦ=(φ(r,ω)ω|maxφ(r,ω)ω|min)Δω,
which can be used to show that the maximum radius Rmax and the corresponding NA of an achromatic metalens are limited, with the bandwidth Δω given by [88]
ΔωΔΦcRmax(1NA1NA21).
This equation shows that the metalenses’ radii are limited by the NA and the operational bandwidth, and that a large radius requires a large phase dispersion. For example, W. T. Chen et al. [86,89] demonstrated an achromatic metalens with a diameter of 220 μm and wavelength range from 470 to 670 nm (i.e., a bandwidth of 200 nm), yet a very small NA of 0.02; Wang et al. [90,91] fabricated a lens with a diameter of 50 μm and a wavelength range from 400 to 660 nm, corresponding to a bandwidth of 260 nm, but an NA of only 0.106; Shrestha et al. [88] achieved a diameter of 100 μm and a relatively smaller wavelength range from 1200 to 1400 nm (a bandwidth of 200 nm), but with a much higher NA of 0.85. The best results used a large library of meta-atoms with a wide range of dispersive responses [92], which in turn increases fabrication complexity. Nevertheless, considering the higher-order dispersion terms is clearly an important aspect of achromatic metasurface design.

The required group delays have made the demonstration of achromatic metalenses with large sizes and significant NAs a challenge. Specifically, the group delay is proportional to the quality factor (Q-factor) of the meta-atoms’ resonances [93], and metalenses with moderate sizes and NAs already require meta-atoms with a high Q. The simultaneous requirement of a high Q and subwavelength dimensions for the meta-atoms poses a very difficult challenge in the design of achromatic metalenses [93].

An alternative path to correcting the wavelength aberration is to cascade or spatially multiplex multiple metasurfaces, each designed for a specific working wavelength [94,95]. This approach removes the phase-dispersion requirement of Eq. (7), thus enabling a metalens design with both high NA and a large size, although we note that this approach does not achieve achromaticity. The trade-off is efficiency and color uniformity; Zhou et al. [87], for example, demonstrated a doublet metalens with an NA of 0.42, and they obtained very respectable efficiencies of 38% at 1180 nm and 52% at 1680 nm. More recently, Menon et al.introduced an alternative method to obtain multiwavelength operation by requiring that only the intensity in the focal plane be maintained at different wavelengths, while letting the phase be a free parameter [96]. Realizing this principle via a multilevel diffractive lens, the authors demonstrated achromatic behavior in the range 450–850 nm with an impressive average efficiency of 60%, although only by limiting the NA to a very low value of 0.075 [96]. In reality, an achromat with high NA that can achieve 60%–80% efficiency over the entire visible range has not yet been demonstrated and remains an open challenge.

3. CONCLUSIONS AND OUTLOOK

Metalenses based on all-dielectric materials have proven their ability to complement and possibly replace their traditional bulk optics counterparts. Some of their important features are the straightforward CMOS–compatible fabrication method, corresponding reduction in thickness, and easier optical alignment and packaging in camera modules. Despite the recent and substantial progress in the performance of metalenses, many areas remain to be explored and improved. High-quality metalenses with ultrahigh NA and high efficiency have been demonstrated, but their imaging performance is still below that of traditional microscope objectives. The imaging performance must be further improved before applications in biological research, material science, or even lithography and confocal laser scanning microscopy, can be seriously considered.

Coma correction is a necessary condition to improve the imaging performance and to enlarge the FoV. Our careful analysis has highlighted key issues, especially by considering the Fourier space. It hopefully will guide further improvements. In conjunction with chromatic aberration correction, metalenses have the potential for extensive use in wearable displays for AR and VR or in cellphone camera modules and light-field imaging.

Material choice is another important consideration and the high-volume manufacturing of metalenses at a low cost is an essential part of the promise they offer [97101]. We note that silicon has a major role to play in this respect, not only because of the maturity of silicon technology, but also because silicon has the highest refractive index of all materials being considered. Its absorption can be minimized by designing suitable meta-atoms to the extent that efficiencies approaching those of TiO2 have already been achieved. Its high index offers more design flexibility, especially for high NA operation, and may offer a better trade-off between the many conflicting requirements outlined above. We are confident that these challenges will be addressed given the significant interest in applications in advanced scientific imaging and trust that the critical review provided here will make a contribution to these developments.

Funding

The National Key R&D Program of China (2016YFA0301300); National Natural Science Foundation of China (11534017, 11761131001, 11674402, 11704421, 91750207); The Key R&D Program of Guangdong Province (2018B030329001, 2019B010152001); Guangzhou Science and Technology Project (201805010004); Natural Science Foundation of Guangdong Province (2016A030312012, 2016A030313333); the Fundamental Research Funds for the Central Universities; FAPESP (2015/21455-1, 2016/05809-0, 2018/25372-1); EPSRC (EP/P030017/1); Royal Society Wolfson Research Merit Award scheme.

 

See Supplement 1 for supporting content.

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2019 (5)

W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10, 335 (2019).
[Crossref]

M. Decker, W. T. Chen, T. Nobis, A. Y. Zhu, M. Khorasaninejad, Z. Bharwani, F. Capasso, and J. Petschulat, “Imaging performance of polarization-insensitive metalenses,” ACS Photon. 6, 1493–1499 (2019).
[Crossref]

L. Guo, Z. Hu, R. Wan, L. Long, T. Li, J. Yan, Y. Lin, L. Zhang, W. Zhu, and L. Wang, “Design of aluminum nitride metalens for broadband ultraviolet incidence routing,” Nanophotonics 8, 171–180 (2019).
[Crossref]

Y. Qiu, F. Zhao, X. Zhu, J. Li, H. Liang, J. Wang, and Z. Cai, “Deflecting transmissive light beams with metasurfaces based on crystalline silicon high-contrast grating,” J. Phys. D 52, 084001 (2019).
[Crossref]

R. Sawant, P. Bhumkar, A. Y. Zhu, P. Ni, F. Capasso, and P. Genevet, “Mitigating chromatic dispersion with hybrid optical metasurfaces,” Adv. Mater. 31, 1805555 (2019).
[Crossref]

2018 (27)

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

A. Martins, J. Li, A. F. da Mota, V. M. Pepino, Y. Wang, L. G. Neto, F. L. Teixeira, E. R. Martins, and B.-H. V. Borges, “Broadband c-Si, metasurfaces with polarization control at visible wavelengths: applications to 3D stereoscopic holography,” Opt. Express 26, 30740–30752 (2018).
[Crossref]

S. Colbrun, A. Zhan, E. Bayati, J. Whitehead, A. Ryou, L. Huang, and A. Majumdar, “Broadband transparent and CMOS-compatible flat optics with silicon nitride metasurfaces [Invited],” Opt. Mater. Express 8, 2330–2344 (2018).
[Crossref]

G.-Y. Lee, J.-Y. Hong, S. H. Hwang, S. Moon, H. Kang, S. Jeon, H. Kim, J.-H. Jeong, and B. Lee, “Metasurface eyepiece for augmented reality,” Nat. Commun. 9, 4562 (2018).
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R. Paniagua-Domínguez, Y. F. Yu, E. Khaidarov, S. Choi, V. Leong, R. M. Bakker, X. Liang, Y. H. Fu, V. Valuckas, L. A. Krivitsky, and A. I. Kuznetsov, “A metalens with a near-unity numerical aperture,” Nano Lett. 18, 2124–2132 (2018).
[Crossref]

M. Jang, Y. Horie, A. Shibukawa, J. Brake, Y. Liu, S. M. Kamali, A. Arbabi, H. Ruan, A. Faraon, and C. Yang, “Wavefront shaping with disorder-engineered metasurfaces,” Nat. Photonics 12, 84–90 (2018).
[Crossref]

A. M. H. Wong and G. V. Eleftheriades, “Perfect anomalous reflection with a bipartite Huygens’ metasurface,” Phys. Rev. X 8, 011036 (2018).
[Crossref]

A. Martins, J. Li, A. F. da Mota, V. M. Pepino, Y. Wang, L. G. Neto, J. P. do Carmo, F. L. Teixeira, E. R. Martins, and B.-H. V. Borges, “Highly efficient holograms based on c-Si metasurfaces in the visible range,” Opt. Express 26, 9573–9583 (2018).
[Crossref]

B. Groever, C. Roques-Carmes, S. J. Byrnes, and F. Capasso, “Substrate aberration and correction for meta-lens imaging: an analytical approach,” Appl. Opt. 57, 2973–2980 (2018).
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E. Arbabi, J. Li, R. J. Hutchins, S. M. Kamali, A. Arbabi, Y. Horie, P. V. Dorpe, V. Gradinaru, D. A. Wagenaar, and A. Faraon, “Two-photon microscopy with a double-wavelength metasurface objective lens,” Nano Lett. 18, 4943–4948 (2018).
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Y. Zhou, I. I. Kravchenko, H. Wang, J. R. Nolen, G. Gu, and J. Valentine, “Multilayer noninteracting dielectric metasurfaces for multiwavelength metaoptics,” Nano Lett. 18, 7529–7537 (2018).
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Y. Bao, Y. Yu, H. Xu, Q. Lin, Y. Wang, J. Li, Z.-K. Zhou, and X.-H. Wang, “Coherent pixel design of metasurfaces for multidimensional optical control of multiple printing-image switching end encoding,” Adv. Funct. Mater. 28, 1805306 (2018).
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W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
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Z. Guo, H. Xu, K. Guo, F. Shen, H. Zhou, Q. Zhou, J. Gao, and Z. Yin, “High-efficiency visible transmitting polarizations devices based on the GaN metasurface,” Nanomaterials 8, 333 (2018).
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W. T. Chen, A. Y. Zhu, J. Sisler, Y.-W. Huang, K. M. A. Yousef, E. Lee, C.-W. Qiu, and F. Capasso, “Broadband achromatic metasurface-refractive optics,” Nano Lett. 18, 7801–7808 (2018).
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H. Pahlevaninezhad, M. Khorasaninejad, Y.-W. Huang, Z. Shi, L. P. Hariri, D. C. Adams, V. Ding, A. Zhu, C.-W. Qiu, F. Capasso, and M. J. Suter, “Nano-optics endoscope for high-resolution optical coherent tomography in vivo,” Nat. Photonics 12, 540–547 (2018).
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Z.-B. Fan, Z.-K. Shao, M.-Y. Xie, X.-N. Pang, W.-S. Ruan, F.-L. Zhao, Y.-J. Chen, S.-Y. Yu, and J.-W. Dong, “Silicon nitride metalenses for close-to-one numerical aperture and wide-angle visible imaging,” Phys. Rev. Appl. 10, 014005 (2018).
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A. She, S. Zhang, S. Shian, D. R. Clarke, and F. Capasso, “Adaptive metalenses with simultaneous electrical control of focal length, astigmatism, and shift,” Sci. Adv. 4, eaap9957 (2018).
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R. Zuo, W. Liu, H. Cheng, S. Chen, and J. Tian, “Breaking the diffraction limit with radially polarized light based on dielectric metalenses,” Adv. Opt. Mater. 6, 1800795 (2018).
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2017 (17)

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E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces,” Optica 4, 625–632 (2017).
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S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, M. Faraji-Dana, and A. Faraon, “Angle-multiplexed metasurfaces: encoding independent wavefront in a single metasurface under different illumination angles,” Phys. Rev. X 7, 041056 (2017).
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S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
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2016 (15)

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E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3, 628–633 (2016).
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S. J. Byrnes, A. Lenef, F. Aieta, and F. Capasso, “Designing large, high-efficiency, high-numerical-aperture, transmissive meta-lenses for visible light,” Opt. Express 24, 5110–5124 (2016).
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A. Arbabi, E. Arbabi, S. M. Kamali, Y. Horie, S. Han, and A. Faraon, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun 7, 13682 (2016).
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M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: diffraction-limited focusing and subwavelength resolution imaging,” Science 352, 1190–1194 (2016).
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R. C. Devlin, M. Khorasaninejad, W. T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. USA 113, 10473–10478 (2016).
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M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
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2015 (7)

B. Desiatov, N. Mazurski, Y. Fainman, and U. Levy, “Polarization selective beam shaping using nanoscale dielectric metasurfaces,” Opt. Express 23, 22611–22618 (2015).
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A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
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F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347, 1342–1345 (2015).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
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M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1, 119–122 (2007).
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
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A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon, “Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays,” Nat. Commun. 6, 7069 (2015).
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A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
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Y. Bao, Y. Yu, H. Xu, Q. Lin, Y. Wang, J. Li, Z.-K. Zhou, and X.-H. Wang, “Coherent pixel design of metasurfaces for multidimensional optical control of multiple printing-image switching end encoding,” Adv. Funct. Mater. 28, 1805306 (2018).
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Supplementary Material (1)

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Figures (7)

Fig. 1.
Fig. 1. High-level schematic of different types of nanostructures to achieve phase control in metasurfaces, grouped into resonant and nonresonant effects. (a) Localized resonances, such as Mie resonances. Plasmonic resonances that were used in earlier work also fall into this category; (b) Extended resonances such as photonic crystals and high-contrast gratings; (c) Effective index, whereby the fill factor of the nanostructure controls the phase; and (d) Pancharatnam–Berry (PB) phase whereby the rotation of a meta-atom controls the phase of a circularly polarized beam.
Fig. 2.
Fig. 2. Examples of (a) TiO2, (b) GaN, and (c) c-Si metalenses, and their corresponding focusing performance. All data were taken at 532nm: (a) With permission from [8]; (b) With permission from [55]; and (c) With permission from [71].
Fig. 3.
Fig. 3. Schematic of (a) back immersion and (b) front immersion metalenses.
Fig. 4.
Fig. 4. Diffraction reconstructions of three metalenses (f=15μm) with the following phase profiles: (a)–(c) hyperbolic, (d)–(f) hyperbolic superimposed with optimized polynomial, and (g-i) spherical. The first and second columns show the longitudinal field distributions at normal and oblique (30°) incidences, respectively. The third column shows the resulting point spread function (PSF) at 0° (black), 7.5° (red), 15° (green), 22.5° (blue), and 30° (orange). The operating wavelength is 532 nm. The dashed boxes in (d) and (e) highlight that the corresponding phase profiles impose an effective aperture onto the lens.
Fig. 5.
Fig. 5. Fourier transform amplitude of the field at the exit of the spherical metalens at normal (a) and oblique (b) incidences as a function of a normalized k-vector. (c) Corresponding line plot through the origin showing normal incidence (red) and oblique incidence (blue). (e)–(g) Same line plot for the hyperbolic metalens. The light line is shown by the white dashed circle in (a), (b), (e), and (f) and as dashed black lines in (c) and (g). Ray tracing of a bulk spherical lens is shown in (d) for perpendicular incidence and (h) for oblique incidence, superimposed onto the field distributions of an equivalent metalens with spherical phase profile.
Fig. 6.
Fig. 6. Illustration to explain how a metalens doublet removes both coma and spherical aberrations by adding a Schmidt plate for correcting spherical aberrations. When the Schmidt plate is placed directly onto the focusing lens (a), a hyperbolic profile is created, but only for normal incidence; the profile for angular incidence is still distorted. By placing the two lenses a distance d apart (b), the Schmidt plate correctly projects its correction onto the focusing lens, resulting in a corrected profile for both normal and angled incidence.
Fig. 7.
Fig. 7. Metalenses with color corrections. (a) Single-layer achromatic metalens made of TiO2 nanofins to achieve achromatic imaging with a bandwidth of 200 nm. (b) Multilayer metalens to correct chromatic aberration at three specific wavelengths: 1180, 1440, and 1680 nm: (a) with permission from [86], and (b) with permission from [87].

Equations (9)

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Δφ=k0(nmetanback)h,
NA=nbacksinθ,
a<λ2NA.
φhyp(r)=k0nback(f2+r2f),
φoptim(r)=k0nback(f2+r2f)+n=15an(rR)2n,
φsph(r)=k0nbackρf(ρρ2r2),
φ(r,ω)=φ(r,ωd)+φ(r,ω)ω|ω=ωd(ωωd)+2φ(r,ω)2ω2|ω=ωd(ωωd)2+.
ΔΦ=(φ(r,ω)ω|maxφ(r,ω)ω|min)Δω,
ΔωΔΦcRmax(1NA1NA21).

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