Abstract

Wavelength dispersion is a universal phenomenon in refractive optics that degrades optical performances. Current mitigation methods are being greatly challenged by the demanding requirements of miniaturization, low aberrations, high throughput, and accurate manufacture. Here, we propose an unconventional monolithic honeycomb-like lens concept with topological degrees of design freedom, capable of near diffraction-limited achromatic performance. To automate the design process, a methodological framework is presented that directly evolves the honeycomb lens from a flat window, instead of a knowledge-based starting geometry. The honeycomb lens performance at the full field of view is remarkably better than either traditional aspheric lenses or commercial cascaded lenses. It also overcomes limitations of flat metalenses, which have extremely small aperture sizes and suffer from multi-order aberrations. This topological honeycomb lens concept may pave the way to inexpensive and compact achromatic optics for focusing and imaging applications in consumer cameras, wearable optics, virtual reality, etc.

© 2022 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Optics plays an important role in enabling advances to human exploration of unknown worlds [1]. In particular, compared with reflective optical systems, refractive optical components potentially allow high integration and easy assembly in a small space. However, one of their significant limitations is the dispersion phenomenon whereby the index of refraction depends on the wavelength and results in chromatic aberration [2,3]. This can severely degrade the optical performance, especially in focusing and imaging optical systems.

The classical solution to eliminate chromatic aberration consists of cascading two lenses. This can satisfactorily achieve axially achromatic focusing of two ray colors. With more lenses, the same focusing length can be obtained for more wavelengths [4]. Although historically important, this commonly adopted method adds high volume, complexity, and cost to the optical system assembly. Also, more lenses implies a number of downsides such as larger accumulated manufacturing and assembling errors, while the over-use of aspheric surfaces leads to additional types of aberrations [5]. These shortcomings hinder progress in the miniaturization of high-performance optical devices. Therefore, a color compensating singlet is highly desirable for industrial and consumer applications. To this end, hybrid refractive–diffractive lenses using an aspherical meniscus element backed with a blazed zone plate have been shown to achieve comparable performance with achromatic doublets while using approximately half the volume of material [6]. As another solution, inhomogeneous gradient-index (GRIN) materials can be exploited for color correction, but involve delicate and costly material synthesis while requiring a substantial size to deliver adequate performance [7]. In recent years, metasurfaces have been investigated for their interesting compact and functional properties [811]. However, metasurface devices still exhibit high chromatic aberration due to intrinsic dispersion in the used materials and phase accumulation when light propagates at different wavelengths [12]. Lately, an achromatic converging metalens was designed and experimentally validated in the broad non-visible infrared bandwidth [13], though the demonstration was based on convergent focusing at 0° field angle. More recently, by simultaneously controlling the phase, group delay, and group delay dispersion, an achromatic metalens was designed and achieved imaging in the visible wavelength range [14]. But while showing great potential in phase manipulation, metalenses also have extremely limited aperture sizes [15,16]. This leads to a compromise between efficiency and achromaticity in a broad bandwidth [17]. Various other kinds of aberrations are observed in metalenses, such as off-axis, coma, and astigmatism [15]. Furthermore, metalenses generally have long focusing lengths as compared to their sizes [18], which affects the imaging resolution. To alleviate this or achieve a larger numerical aperture, high-aspect-ratio nanostructure (larger height or small lateral dimension) elements should be used [19], but this exponentially increases the difficulty of manufacturing by existing nanofabrication methods such as electron-beam lithography, atomic layer deposition [20], etc. Finally, high throughput production is costly and restricted to planar substrates, which poses severe limitations to optical designers considering practical application.

 figure: Fig. 1.

Fig. 1. Schematics of monolithic lens. (a) Principle of achromatic focusing and imaging and (b) ray simulation of proposed lens.

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The challenging aspects of achromatic focusing and imaging listed above have motivated us to propose a new class of achromatic lenses in this study, by reverse engineering topological segments on a single lens substrate. The monolithic design paradigm allows sufficient degrees of design freedom and allows highly integrated optics free from assembly or alignment errors, so as to fill the technological gap between traditional assembled optics and metalenses. To automate and simplify the design process, a methodological framework is proposed that addresses the skills and extensive human effort required in the selection of a starting geometry in generic optical layout software. This design framework simply starts from a flat surface and evolves to the final honeycomb-shaped achromatic lens, while considering reasonable local coordinates of segments for practical and accurate fabrication. As a proof of concept, we designed and fabricated a monolithic honeycomb singlet with customized prescriptions for three input colors (red, green, and blue), and demonstrated its capability to correct color dispersion in imaging at a full 4° field of view (FOV). As well as its high performance in focusing and aberration correction, the compact size and ease of manufacturing by conventional machining methods open the way for broad practical application.

2. MATERIALS AND METHODS

A. Monolithic Achromatic Lens Concept and Design

Figure 1 shows a schematic of the conceived honeycomb-like lens concept. As compared to the general plano–convex lens, the basic idea is to optimally design freeform segments at different zones with reference to the planar surface. In the design, a hexagonally segmented structure is adopted, allowing for a high filling factor without gaps. For each hexagonal zone, the segment shape is a rotationally asymmetric freeform with a unique prescription for transmitting specific rays corresponding to a central color wavelength. The freeform segments can be allocated any color chosen from an arbitrary wavelength palette, and are exploited to achieve satisfactory off-axis performance by focusing variously colored rays from a given field angle to the same spot of a charge-coupled device (CCD). Therefore, achromatic focusing and imaging can be practically achieved in one singlet. Moreover, it can be extended outwards with freedom customization of more prescriptions for multiple wavelengths in a topological way as illustrated in Fig. 1(a). Here, it is noted that each hexagonal segment shape is designed corresponding to a specific central color wavelength; thus, it allows transmission of rays only for a given bandwidth around that central color wavelength. In practice, this procedure of selection can be achieved by coating the lenslets or simply adding a filter in front of them.

In traditional design of achromatic optical systems including doublets or triplets, it is usual to proceed from a starting geometry. The procedure to find the optimum geometrical coefficients of each optical element is generally realized by optical layout software (e.g., Zemax, Code V, etc.) based on three commonly used wavelengths for red, green, and blue colors [21,22]. This is effective for sequential structures, provided a good starting geometry is used as input. This input requires much know-how and effort to reach a satisfactory optimization result [23]. Therefore, it would be extremely challenging to rely on such software for the proposed design since it features topological zones with different prescriptions. Herein, it would be very helpful to develop a fully automated method to design and optimize the proposed honeycomb lens. For proof-of-concept purpose, and without loss of generality, the method will be demonstrated by designing a very compact monolithic lens (Φ16 mm) operating at F/2.5 over a full ${{4}}^\circ \times {{4}}^\circ$ FOV, with the goal of distortion-free and near diffraction-limited achromatic performance for red, green, and blue colors.

 figure: Fig. 2.

Fig. 2. Focusing performance at characteristic field angles for (a) traditional diffraction-limited aspheric lens with the closest size and $f$-number of 2.5, (b) non-segmented on-axis freeform lens based on the construction-iteration design method, (c) doublet lenses, and (d) honeycomb singlet based on the proposed design method (scale bar: ${{30}}\;{\rm{\unicode{x00B5}{\rm m}}} \times {{30}}\;{\rm{\unicode{x00B5}{\rm m}}}$ for each square element).

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In our design framework, the honeycomb structure can be automatically evolved from a single plate with any desirable thickness. Basically, an arbitrary $m$th hexagonal segment is attained on the basis of point cloud {$P_i^m$} and corresponding normal vectors {$n_i^m$}, which are determined on the basis of a construction–iteration approach [24]. The successive generation of all freeform segments is detailed in Supplement 1 Section 1 with reference to Supplement 1 Fig. S1. With all determined points {$P_i^m$} and {$n_i^m$}, the freeform segment generation procedure is performed as detailed in Supplement 1 Section 2. Further optimization can be adopted to refine the freeform parameters and make the actual focusing point $T_k^*$ as close as possible to the ideal target ${T_k}$. To achieve this, calculate the intersection points between feature rays and the constructed freeform segment, and obtain the actual focus points $T_k^*$. Then modify the target as $T_k^* + \delta ({T_k} - T_k^*$), based on which all the determined points {$P_i^m$} and normal vectors {$n_i^m$} are updated. This optimization loop is iterated until the difference between the actual focusing point and ideal target is within tolerance [24]. Consequently, an analytical freeform representation with the finally updated parameters ${{w}}$ for the $m$th segment can be obtained. On this basis, freeform segments can be flexibly designed at arbitrary locations that focus rays from different field angles onto common spots, as shown in Supplement 1 Fig. S3.

Following the overall framework (see Supplement 1 Fig. S2), a monolithic lens can be automatically designed. Note that the targets ${T_k}$ on the imaging plane are dependent only on the FOV rather than the specific segment or color wavelength of incident rays, so as to achieve achromatic focusing and imaging. The solid honeycomb model with three prescriptions [#1/#4 red, #2/#5/#7 green, and #3/#6 blue wavelengths with reference to Fig. 1(a)] can be accordingly built. Focusing performance under one specific color ray was tested with some allowance for wavelength deviation. Results on off-axis freeform segment #1 indicate that red rays with wavelengths between 617 and 667 nm can still converge well onto a common spot over the full FOV, as shown in Supplement 1 Fig. S4. The performance of the designed honeycomb lens was also cross checked by importing it as a 3D solid model into Zemax to perform ray simulations, as shown in Fig. 1(b). A quantitative characterization of the optical performance will be presented in the next sections.

 figure: Fig. 3.

Fig. 3. (a) Focusing performance of RGB colors at different field angles and (b) distortion grid at full FOV.

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B. Focusing and Distortion Analysis

The proposed honeycomb lens has a designated focus length of 40.5 mm and 4° FOV. The specific freeform parameters are detailed in Supplement 1 Table S1. To demonstrate the achromatic focusing performance of the designed lens, a comparison is conducted against conventional lenses. The typical candidates for comparison are chosen as follows: (a) commercial diffraction-limited aspheric (DLA) lens with closest size and $f$-number of 2.5 from Thorlabs Inc (Type AL2550G-A), (b) on-axis freeform lens ($\emptyset$16 mm, F2.5, focus length 40.5 mm) designed by the construction–iteration method, and (c) doublet lenses with the best available performance from Thorlabs Inc (Type AC254-200).

Spot diagram simulations were carried out with the optical layout software (Zemax), where we use six characteristic field angles and three-color wavelengths of 637 nm (red), 520 nm (green), and 480 nm (blue). For the DLA lens, the focusing spots of green rays are good at (0°, 0°); however, coma aberration becomes significant at nonzero field angles as shown in Fig. 2(a). The focusing spots of red and blue color rays are largely spread across a 300 µm wide area, as chromatic aberration is impossible to correct with a traditional singlet. The freeform lens based on the construction–iteration method suffers from less severe focusing degradation for all colors overall, as shown in Fig. 2(b). Nevertheless, it still clearly shows extensive spread of the spot. The focusing performance of the commercial doublet product is drawn in Fig. 2(c), from which it is clear that chromatic aberration is reduced. However, performance degrades with increasing field angle, especially at (0°, 2°) where the focusing spot size is obviously larger and accompanied by large coma aberration. Performance can be improved by cascading more lenses, at the expense of reduced compactness and additional tolerance errors from manufacturing and assembling. In comparison, Fig. 4(d) shows focusing results of the designed honeycomb singlet, indicating that the seven freeform segments with different prescriptions can still focus to a tight common spot, with a small spread equally achievable at all field angles. A quantitative comparison of root mean square (RMS) and geometry of spot size are listed in Supplement 1 Table S2, showing a considerably improved focusing performance for the new design over traditional lenses. This performance is comparable with triplets, but with a dramatic 15-fold reduction in volume and no manufacturing/assembly induced aberrations.

Figure 3(a) shows focusing positions in the image plane at different field angles, namely, (0°, 0°), (0°, ${{\pm 2}}^\circ$), (${{\pm 2}}^\circ$, 0°), (${{\pm 1}}^\circ$, ${{\pm 1}}^\circ$), and (${{\pm 1.414}}^\circ$, ${{\pm 1.414}}^\circ$). All the feature rays from 13 field angles are converging to the corresponding designated locations, e.g., (1.52 mm, 0 mm) at (0°, 2°). It is noted that all three colors through the honeycomb structure coincide to focus on the same point. Figure 3(b) shows the distortion grid of freeform segment #2 at full FOV, with a maximum distortion value of only 0.27%. Similarly, low values are obtained across all prescribed segments, which indicates excellent potential for wide-field achromatic imaging.

 figure: Fig. 4.

Fig. 4. Modulation transfer functions (MTFs) of (a) traditional diffraction-limited aspheric lens under incidence of design green wavelength, (b) central lenslet of proposed honeycomb lens under similar green wavelength, (c) DLA with all RGB colors incident, and (d) edge lenslet of proposed honeycomb lens under its allocated RGB color.

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The RMS wavefront errors (see Supplement 1 Fig. S6a) of segment #2 (likewise for others in principle) is evaluated to an average value of 0.15 wave at 520 nm wavelength. Additionally, a Zernike-based full-field display (FFD) is adopted to calculate and plot the magnitude and orientation of a given aberration over the full FOV. Here, attention is particularly paid to the rotationally variant defocus ($Z4$), astigmatism ($Z5/Z6$), and coma ($Z7/Z8$), since these three aberration types are typically orders of magnitude larger than others [5]. The results are plotted in Supplement 1 Figs. S6(b)–(d). Due to the deterministic design method, the average value of absolute defocus aberration is about 0.2 wave, while average astigmatism aberration is 0.27 wave with standard deviation of 0.12 wave at 520 nm wavelength. Particularly, an extremely small coma aberration can be achieved as shown in Supplement 1 Fig. S6(d), with average coma aberration of 0.05 wave and standard deviation of 0.018 wave, whereas coma is conspicuous at a large field angle for the traditional doublet [refer to Fig. 4(c)]. The above analysis indicates that, in addition to eliminating chromatic problems with a very compact singlet, the proposed design also offers high focusing performance with low distortion from multi-order aberrations.

C. MTF Performance

In this section, to verify the ability to transfer contrast at a particular resolution (spatial frequency in unit of cycles/mm) from object to image through the lens, modulation transfer functions (MTFs) by Code V simulations are plotted to characterize the imaging quality. First, the MTF of the above-mentioned commercial DLA lens (Type AL2550G-A) is plotted in Fig. 4(a), from which it can be found that diffraction-limited performance can be achieved at (0°, 0°), but degrades quickly for nonzero field angles. In comparison, the MTF of lenslet #7, located in the center region of the honeycomb lens [Fig. 3(b)], is drawn under its targeted green prescription. The plot shows that a higher frequency (260 cycles/line) can be resolved, with considerably improved performance at all field angles approaching the diffraction limit.

When RGB rays are all incident to the DLA lens, MTF performance is significantly degraded as plotted in Fig. 4(c). In comparison, when RGB light is allowed to selectively go through the corresponding prescribed lenslets of the honeycomb lens, the MTF exhibits excellent performance. Figure 4(d) plots the MTF of edge lenslet #4, which is comparable to an on-axis diffraction-limited asphere lens. Similar performance can be verified across all segmented lenslets. In addition, the Strehl ratio is evaluated under different field angles based on the integrated area ratio between the diffraction-limited MTF curve and actual MTF curve. The comparison results between DLA and honeycomb lenses are listed in Supplement 1 Table S3. Similar ratios are obtained for both lenses when pure green light is incident. However, the Strehl ratio is significantly lowered to 22%–33% when the DLA lens is illuminated with full RGB colors. On the contrary, a high ratio up to 65%–94% is kept for all honeycomb lenslets as they are matched to their specific color wavelengths (by filtering). Since 80% is generally regarded as diffraction-limited performance, we consider the honeycomb lens to be near diffraction limited over both its entire aperture and full FOV regime (diffraction limited at half FOV regime).

D. Imaging Performance and Comparison

To demonstrate achromatic imaging characteristics, a RGB picture simulation is implemented in Zemax. The DLA lens (type AL2550G-A), doublet lenses (type AC254-200), and honeycomb singlet models are imported for comparison. In the simulation, the object is placed at infinity with a height of 1.414º in semi-diagonal direction, while three RGB color bands allocated to the nominal wavelengths of 637 nm, 520 nm, and 480 nm go through corresponding segments. Figure 5(a) shows the obtained image through the DLA lens, showing good focusing but obvious chromatic aberration especially at a large field angle. Color aberration is most prominent at the edge of obtained images, especially relative to the green color (chimney at upper right, tote bag at lower right). When an off-axis sub-aperture is selected on the DLA lens, the image is severely degraded due to strong axial and lateral chromatic aberration, as shown in Fig. 5(b). For the doublet under the same object angle, the obtained image is highly blurred even though chromatic aberration is not dominant, as shown in Fig. 5(c). This is because, under the same condition, imaging resolution is not high enough to resolve high-frequency spatial content. In contrast, the honeycomb singlet can produce a well-focused image without chromatic aberration, as shown in Fig. 5(d). This difference can be further visualized by imaging discs of the three basic colors. For the DLA, the red and blue circles are highly blurred and shifted by axial chromatic aberration, as shown in Fig. 5(e). In contrast, sharp images of all three colored discs can be achieved with the honeycomb singlet design, as shown in Fig. 5(f).

 figure: Fig. 5.

Fig. 5. Imaging simulations. (a) Traditional diffraction-limited aspheric lens, (b) off-axis aspheric lens, (c) doublet lens, and (d) proposed honeycomb singlet. Three color circles imaged by (e) diffraction-limited aspheric lens and (f) proposed honeycomb singlet.

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 figure: Fig. 6.

Fig. 6. (a) Experimental setup for fundamental demonstration, (b) confocal point of green laser through segments #2 and #5, (c) strong defocusing of “wrongly allocated” red laser through segments #2 and #5, (d) confocal point of red laser through segments #1 and #4, and (e) confocal performances of correctly allocated red, green, and blue lasers at different field angles.

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3. EXPERIMENTS

A. Lens Fabrication

The proposed honeycomb lens ($\emptyset$ 16 mm, thickness 4.52 mm, focusing length 40.5 mm, with design geometry in Supplement 1 Fig. S5 and prescription parameters listed in Supplement 1 Table S1). In detail, a ${{16}}\;{\rm{mm}} \times {{16}}\;{\rm{mm}} \times {{5}}\;{\rm{mm}}$ PMMA block with rough shape (3 mm thick substrate with 2 mm high spherical cap) was first prepared by a traditional milling machine. Then, a spiral path was generated that follows contours of the designed 3D model. An algorithm considers the tool radius of the employed cutting insert (material: natural polycrystalline diamond with nose radius 0.1 mm) as well as the smoothness of the step when the path crosses adjacent prescription segments along the spiral path [25]. The fine machining process was conducted on a single-point diamond turning machine (ULG100, Toshiba), where the spindle speed was set to five revolutions per minute and radial feed rate of 5 µm per revolution. During the machining process, lubricant spray was provided for cooling purposes. Processing of the entire surface takes about 2 h. The diamond turning process can also machine nickel plated dies, to generate replication molds for mass production purposes. To produce the same design on hard materials such as glass or tungsten carbide molding inserts, micro-grinding using a miniature diamond wheel can be realized on the same machine. In cases where mechanical-tool-based techniques have trouble with the interferential edge effect between the segments, ion beam figuring technology that uses accelerated ions to remove materials can be utilized to generate correct shapes all the way to the edges [26]. This means the new design can be flexibly produced on various materials by existing fabrication methods, widely available in industry.

B. Experiments on Achromatic Focusing and Imaging

The machined honeycomb lens is shown in Fig. 6(a), which also shows the optical test setup used for focusing and imaging experiments (see details in Supplement 1 Section 3 and Supplement 1 Fig. S7). Three highly collimated lasers (divergence: 0.76 mrad) of different wavelengths were adopted to experimentally test its focusing performance. First, at 0° field angle, the green laser is passed through hexagonal apertures overlaying segments #2 and #5 of the honeycomb lens, producing a confocal point on the CCD as shown in Fig. 6(b). Switching to “a wrongly allocated” red laser, and for the same segments of a honeycomb lens, the focusing point [Fig. 6(c)] is far away from the original point. However, after rotating the mask apertures to overlay segments #1 and #4, the focus point [Fig. 6(d)] now coincides with that obtained for the green laser. The experimental focusing results are in high agreement with the numerical simulation results shown in the insets of Figs. 6(b)–6(d). By adjusting the relative angle of the light source with the lens and CCD (see Supplement 1 Fig. S7), focusing performance at various field angles can be assessed. The confocal points are plotted in Fig. 6(e), showing that the red, green, and blue lasers coincide on the CCD at all locations within the designed FOV of ${{\pm 2}}^\circ$. Note that hexagonal filters can be inserted or the lenslets coated, in practical applications, to ensure that only the right wavelength band is transmitted through each corresponding lenslet.

By choosing the field angles of (0º, 0º), (0º, 1º), (1.414º, 1.414º), we compared the focal spot profile of the honeycomb lens and conventional aspheric lens. Spots were measured at the focal plane according to the intensity detected on CCD. For the DLA lens, the green laser can at best focus on several pixels as shown in Fig. 7(a). From the intensity profiles underneath the spot images, the full-width at half-maximum (FWHM) of the spot is about 10 µm. However, the DLA lens shows significant defocusing with a spot radius of about 70 µm when the red laser is incident. The spot size is also very large for the blue laser. Considerable chromatic aberration can be found at other field angles. In contrast, the proposed honeycomb singlet is able to realize focal spots at these same locations with FWHM of approximately 8 µm, for all red, green, and blue lasers, as shown in Fig. 7(b).

 figure: Fig. 7.

Fig. 7. Focusing and imaging test results: confocal spots taken with (a) traditional diffraction-limited asphere (DLA) and (b) proposed honeycomb lens. Off-axis imaging of RGB circles with (c) traditional DLA lens and (d) proposed honeycomb lens. Building pictures taken by (e) DLA lens and (f) proposed honeycomb lens. Insect pictures taken by (g) DLA lens and (h) proposed honeycomb lens.

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Finally, to verify applicability of the new lens in imaging, proof-of-concept experiments were carried out (see schematics in Supplement 1 Fig. S7b). First, a picture with typical RGB circles was selected as the object and placed at a large distance from the lens (see method in Supplement 1 Section 3). In accordance with simulations, due to the high chromatic aberration of the DLA lens as the aperture increases (up to the same position as edge lenslets of the honeycomb), the obtained image shows obvious defocusing of red and blue circles, as shown in Fig. 7(c). This is further verified with a strongly aberrated image of the building picture by the DLA, as shown in Fig. 7(e), which shows a strongly green background as the red and blue colors are defocused on the CCD. In contrast, the honeycomb lens shows a clear improvement on both RGB circles and the building picture, as shown in Figs. 7(d) and 7(f). After applying an averaging filter every two pixels, some background noise is still visible in the images (mostly due to parasite illumination in the laboratory). However, this could be improved with better tight control of the testing setup and environment. Finally, images of an insect were also taken with the DLA lens and honeycomb lens, as compared in Figs. 7(g) and 7(h), respectively. The honeycomb lens produced a noticeably sharper image overall.

4. DISCUSSION AND CONCLUSION

In this work, we proposed a new honeycomb lens concept, to realize chromatic aberration-free focusing and imaging. The monolithic singlet structure is constructed by an array of extendable hexagonal freeform zones that can be tailored with different color prescriptions for multi-wavelength focusing. Theory and experiments demonstrate the feasibility of this approach, which can remarkably reduce the color dispersion unavoidable in conventional aspheric lenses, and show significant focusing enhancement with about four times smaller spot size than classical doublet lenses (see Supplement 1 Table S2).

While the achromatic triplet additionally suffers from spherochromatism of intermediate wavelengths and is associated with problematic manufacturing and assembly errors due to the use of group lenses, the honeycomb singlet evades all these issues. And as for the state-of-the-art metasurface coating on a GRIN lens with performance similar to the triplet [27], achromatic performance and efficiency are heavily dependent on the choice of nanostructure. Also, the numerical aperture is relatively small, especially for broadband achromatic imaging [14]. Further research and development are therefore required, whether by means of dispersion engineering approaches [28] or using difficult-to-machine high-aspect-ratio nanostructure elements as aforementioned [29]. Meanwhile, the existing off-axis aberration may be corrected if the nanostructures could be etched or deposited on curved surfaces [17], but this is well beyond the capabilities of current nanofabrication methods in industry [15]. In contrast, the monolithic honeycomb lens can be mass produced by one-step replication from mold dies, which can be readily manufactured by single-point diamond machining. It is noteworthy that, with fabrication methods such as femtosecond laser machining or ion beam milling, segment size as small as 50 µm is feasible, which could be potentially useful in miniature electronic devices [30].

We would further emphasize that the honeycomb lens can be flexibly extended with tailored prescriptions not limited to three RGB colors, but can be $N$-color over a broad electromagnetic range from UV to infrared wavelengths, owing to the flexible degrees of design freedom described in this work. The interval between wavelengths can be tailored to the requirements of specific applications. We envision that lenses based on this new concept could open a new chapter in the design of compact achromatic optics with wide use in the research community and industry.

Funding

Incubation Program of Kyoto University (9th round).

Acknowledgment

The authors acknowledge the help of Mr. Kominami from Kimura Inc. Japan, for manufacturing the honeycomb lens described in the paper.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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24. T. Yang, G.-F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6, e17081 (2017). [CrossRef]  

25. W.-L. Zhu, F. Duan, X. Zhang, Z. Zhu, and B.-F. Ju, “A new diamond machining approach for extendable fabrication of micro-freeform lens array,” Int. J. Mach. Tools Manuf. 124, 134–148 (2018). [CrossRef]  

26. M. Ghigo, O. Citterio, P. Conconi, and F. Mazzoleni, “Ion beam figuring of nickel mandrels for x-ray replication optics,” Proc. SPIE 4145, 28–36 (2001). [CrossRef]  

27. J. Nagar, S. Campbell, and D. H. Werner, “Apochromatic singlets enabled by metasurface-augmented GRIN lenses,” Optica 5, 99–102 (2018). [CrossRef]  

28. M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015). [CrossRef]  

29. S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010). [CrossRef]  

30. G.-X. Jin, X.-Y. Hu, Z.-C. Ma, C.-H. Li, Y.-L. Zhang, and H.-B. Sun, “Femtosecond laser fabrication of 3D templates for mass production of artificial compound eyes,” Nanotechnol. Precis. Eng. 2, 110–117 (2019). [CrossRef]  

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  24. T. Yang, G.-F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6, e17081 (2017).
    [Crossref]
  25. W.-L. Zhu, F. Duan, X. Zhang, Z. Zhu, and B.-F. Ju, “A new diamond machining approach for extendable fabrication of micro-freeform lens array,” Int. J. Mach. Tools Manuf. 124, 134–148 (2018).
    [Crossref]
  26. M. Ghigo, O. Citterio, P. Conconi, and F. Mazzoleni, “Ion beam figuring of nickel mandrels for x-ray replication optics,” Proc. SPIE 4145, 28–36 (2001).
    [Crossref]
  27. J. Nagar, S. Campbell, and D. H. Werner, “Apochromatic singlets enabled by metasurface-augmented GRIN lenses,” Optica 5, 99–102 (2018).
    [Crossref]
  28. M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
    [Crossref]
  29. S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010).
    [Crossref]
  30. G.-X. Jin, X.-Y. Hu, Z.-C. Ma, C.-H. Li, Y.-L. Zhang, and H.-B. Sun, “Femtosecond laser fabrication of 3D templates for mass production of artificial compound eyes,” Nanotechnol. Precis. Eng. 2, 110–117 (2019).
    [Crossref]

2020 (1)

D. Lee, J. Gwak, T. Badloe, S. Palomba, and J. Rho, “Metasurfaces-based imaging and applications: from miniaturized optical components to functional imaging platforms,” Nanoscale Adv. 2, 605–625 (2020).
[Crossref]

2019 (4)

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, “Controlling three-dimensional optical fields via inverse Mie scattering,” Sci. Adv. 5, eaax4769 (2019).
[Crossref]

G. Beadie and J. N. Mait, “Material selection for GRIN-based achromatic doublets,” Opt. Express 27, 17771–17794 (2019).
[Crossref]

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
[Crossref]

G.-X. Jin, X.-Y. Hu, Z.-C. Ma, C.-H. Li, Y.-L. Zhang, and H.-B. Sun, “Femtosecond laser fabrication of 3D templates for mass production of artificial compound eyes,” Nanotechnol. Precis. Eng. 2, 110–117 (2019).
[Crossref]

2018 (6)

J. Nagar, S. Campbell, and D. H. Werner, “Apochromatic singlets enabled by metasurface-augmented GRIN lenses,” Optica 5, 99–102 (2018).
[Crossref]

S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light Sci. Appl. 7, 85 (2018).
[Crossref]

W.-L. Zhu, F. Duan, X. Zhang, Z. Zhu, and B.-F. Ju, “A new diamond machining approach for extendable fabrication of micro-freeform lens array,” Int. J. Mach. Tools Manuf. 124, 134–148 (2018).
[Crossref]

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 (2018).
[Crossref]

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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9, 1756 (2018).
[Crossref]

2017 (5)

M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
[Crossref]

O. Avayu, E. Almeida, Y. Prior, and T. Ellenbogen, “Composite functional metasurfaces for multispectral achromatic optics,” Nat. Commun. 8, 14992 (2017).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W.-T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

T. Yang, G.-F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6, e17081 (2017).
[Crossref]

2016 (4)

P. Wang, N. Mohammad, and R. Menon, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6, 21545 (2016).
[Crossref]

Y. L. Gagnon, D. C. Osorio, T. J. Wardill, N. J. Marshall, W.-S. Chung, and S. E. Temple, “Can chromatic aberration enable color vision in natural environments?” Proc. Natl. Acad. Sci. USA 113, E6908–E6909 (2016).
[Crossref]

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).
[Crossref]

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).
[Crossref]

2015 (1)

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

2013 (1)

2010 (2)

L. Billings, “Space science: the telescope that ate astronomy,” Nat. News 467, 1028–1030 (2010).
[Crossref]

S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010).
[Crossref]

2001 (1)

M. Ghigo, O. Citterio, P. Conconi, and F. Mazzoleni, “Ion beam figuring of nickel mandrels for x-ray replication optics,” Proc. SPIE 4145, 28–36 (2001).
[Crossref]

1994 (1)

D. Shafer, “Global optimization in optical design,” Comput. Phys. 8, 188–195 (1994).
[Crossref]

1992 (1)

Aieta, F.

Almeida, E.

O. Avayu, E. Almeida, Y. Prior, and T. Ellenbogen, “Composite functional metasurfaces for multispectral achromatic optics,” Nat. Commun. 8, 14992 (2017).
[Crossref]

Arbabi, A.

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).
[Crossref]

Arbabi, E.

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).
[Crossref]

Avayu, O.

O. Avayu, E. Almeida, Y. Prior, and T. Ellenbogen, “Composite functional metasurfaces for multispectral achromatic optics,” Nat. Commun. 8, 14992 (2017).
[Crossref]

Badloe, T.

D. Lee, J. Gwak, T. Badloe, S. Palomba, and J. Rho, “Metasurfaces-based imaging and applications: from miniaturized optical components to functional imaging platforms,” Nanoscale Adv. 2, 605–625 (2020).
[Crossref]

Bauer, A.

A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9, 1756 (2018).
[Crossref]

Beadie, G.

Billings, L.

L. Billings, “Space science: the telescope that ate astronomy,” Nat. News 467, 1028–1030 (2010).
[Crossref]

Brener, I.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Campbell, S.

Capasso, F.

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 (2018).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W.-T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
[Crossref]

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).
[Crossref]

F. Aieta, P. Genevet, M. Kats, and F. Capasso, “Aberrations of flat lenses and aplanatic metasurfaces,” Opt. Express 21, 31530–31539 (2013).
[Crossref]

Chen, B. H.

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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Chen, J.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Chen, J.-W.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Chen, M. K.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
[Crossref]

Chen, M.-K.

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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Chen, W. T.

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 (2018).
[Crossref]

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).
[Crossref]

Chen, W.-T.

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W.-T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

Chen, Y. H.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
[Crossref]

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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Chu, C. H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Chung, T. L.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
[Crossref]

Chung, W.-S.

Y. L. Gagnon, D. C. Osorio, T. J. Wardill, N. J. Marshall, W.-S. Chung, and S. E. Temple, “Can chromatic aberration enable color vision in natural environments?” Proc. Natl. Acad. Sci. USA 113, E6908–E6909 (2016).
[Crossref]

Citterio, O.

M. Ghigo, O. Citterio, P. Conconi, and F. Mazzoleni, “Ion beam figuring of nickel mandrels for x-ray replication optics,” Proc. SPIE 4145, 28–36 (2001).
[Crossref]

Conconi, P.

M. Ghigo, O. Citterio, P. Conconi, and F. Mazzoleni, “Ion beam figuring of nickel mandrels for x-ray replication optics,” Proc. SPIE 4145, 28–36 (2001).
[Crossref]

David, C.

S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010).
[Crossref]

Decker, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Devlin, R. C.

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).
[Crossref]

Dominguez, J.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Duan, F.

W.-L. Zhu, F. Duan, X. Zhang, Z. Zhu, and B.-F. Ju, “A new diamond machining approach for extendable fabrication of micro-freeform lens array,” Int. J. Mach. Tools Manuf. 124, 134–148 (2018).
[Crossref]

Ellenbogen, T.

O. Avayu, E. Almeida, Y. Prior, and T. Ellenbogen, “Composite functional metasurfaces for multispectral achromatic optics,” Nat. Commun. 8, 14992 (2017).
[Crossref]

Falkner, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Faraon, A.

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).
[Crossref]

Gagnon, Y. L.

Y. L. Gagnon, D. C. Osorio, T. J. Wardill, N. J. Marshall, W.-S. Chung, and S. E. Temple, “Can chromatic aberration enable color vision in natural environments?” Proc. Natl. Acad. Sci. USA 113, E6908–E6909 (2016).
[Crossref]

Genevet, P.

Ghigo, M.

M. Ghigo, O. Citterio, P. Conconi, and F. Mazzoleni, “Ion beam figuring of nickel mandrels for x-ray replication optics,” Proc. SPIE 4145, 28–36 (2001).
[Crossref]

Gibson, R.

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, “Controlling three-dimensional optical fields via inverse Mie scattering,” Sci. Adv. 5, eaax4769 (2019).
[Crossref]

Gorelick, S.

S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010).
[Crossref]

Guzenko, V. A.

S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010).
[Crossref]

Gwak, J.

D. Lee, J. Gwak, T. Badloe, S. Palomba, and J. Rho, “Metasurfaces-based imaging and applications: from miniaturized optical components to functional imaging platforms,” Nanoscale Adv. 2, 605–625 (2020).
[Crossref]

Han, S.

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).
[Crossref]

Hendrickson, J. R.

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, “Controlling three-dimensional optical fields via inverse Mie scattering,” Sci. Adv. 5, eaax4769 (2019).
[Crossref]

Horie, Y.

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).
[Crossref]

Hu, X.-Y.

G.-X. Jin, X.-Y. Hu, Z.-C. Ma, C.-H. Li, Y.-L. Zhang, and H.-B. Sun, “Femtosecond laser fabrication of 3D templates for mass production of artificial compound eyes,” Nanotechnol. Precis. Eng. 2, 110–117 (2019).
[Crossref]

Huang, T.-T.

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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Huang, Y.-T.

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
[Crossref]

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T. Yang, G.-F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6, e17081 (2017).
[Crossref]

Jin, G.-X.

G.-X. Jin, X.-Y. Hu, Z.-C. Ma, C.-H. Li, Y.-L. Zhang, and H.-B. Sun, “Femtosecond laser fabrication of 3D templates for mass production of artificial compound eyes,” Nanotechnol. Precis. Eng. 2, 110–117 (2019).
[Crossref]

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W.-L. Zhu, F. Duan, X. Zhang, Z. Zhu, and B.-F. Ju, “A new diamond machining approach for extendable fabrication of micro-freeform lens array,” Int. J. Mach. Tools Manuf. 124, 134–148 (2018).
[Crossref]

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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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Khorasaninejad, M.

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 (2018).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W.-T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
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M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
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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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M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
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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, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
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R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
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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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
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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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
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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, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
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D. Lee, J. Gwak, T. Badloe, S. Palomba, and J. Rho, “Metasurfaces-based imaging and applications: from miniaturized optical components to functional imaging platforms,” Nanoscale Adv. 2, 605–625 (2020).
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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 (2018).
[Crossref]

Li, C.-H.

G.-X. Jin, X.-Y. Hu, Z.-C. Ma, C.-H. Li, Y.-L. Zhang, and H.-B. Sun, “Femtosecond laser fabrication of 3D templates for mass production of artificial compound eyes,” Nanotechnol. Precis. Eng. 2, 110–117 (2019).
[Crossref]

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R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
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S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light Sci. Appl. 7, 85 (2018).
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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, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

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G.-X. Jin, X.-Y. Hu, Z.-C. Ma, C.-H. Li, Y.-L. Zhang, and H.-B. Sun, “Femtosecond laser fabrication of 3D templates for mass production of artificial compound eyes,” Nanotechnol. Precis. Eng. 2, 110–117 (2019).
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Majumdar, A.

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, “Controlling three-dimensional optical fields via inverse Mie scattering,” Sci. Adv. 5, eaax4769 (2019).
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Y. L. Gagnon, D. C. Osorio, T. J. Wardill, N. J. Marshall, W.-S. Chung, and S. E. Temple, “Can chromatic aberration enable color vision in natural environments?” Proc. Natl. Acad. Sci. USA 113, E6908–E6909 (2016).
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M. Ghigo, O. Citterio, P. Conconi, and F. Mazzoleni, “Ion beam figuring of nickel mandrels for x-ray replication optics,” Proc. SPIE 4145, 28–36 (2001).
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P. Wang, N. Mohammad, and R. Menon, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6, 21545 (2016).
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P. Wang, N. Mohammad, and R. Menon, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6, 21545 (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).
[Crossref]

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Y. L. Gagnon, D. C. Osorio, T. J. Wardill, N. J. Marshall, W.-S. Chung, and S. E. Temple, “Can chromatic aberration enable color vision in natural environments?” Proc. Natl. Acad. Sci. USA 113, E6908–E6909 (2016).
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S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light Sci. Appl. 7, 85 (2018).
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D. Lee, J. Gwak, T. Badloe, S. Palomba, and J. Rho, “Metasurfaces-based imaging and applications: from miniaturized optical components to functional imaging platforms,” Nanoscale Adv. 2, 605–625 (2020).
[Crossref]

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M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
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O. Avayu, E. Almeida, Y. Prior, and T. Ellenbogen, “Composite functional metasurfaces for multispectral achromatic optics,” Nat. Commun. 8, 14992 (2017).
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D. Lee, J. Gwak, T. Badloe, S. Palomba, and J. Rho, “Metasurfaces-based imaging and applications: from miniaturized optical components to functional imaging platforms,” Nanoscale Adv. 2, 605–625 (2020).
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A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9, 1756 (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 (2018).
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M. Khorasaninejad, Z. Shi, A. Y. Zhu, W.-T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
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A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9, 1756 (2018).
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D. Shafer, “Global optimization in optical design,” Comput. Phys. 8, 188–195 (1994).
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R. R. Shannon, The Art and Science of Optical Design (Cambridge University, 1997).

Shi, Z.

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 (2018).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W.-T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

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S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light Sci. Appl. 7, 85 (2018).
[Crossref]

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A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, “Controlling three-dimensional optical fields via inverse Mie scattering,” Sci. Adv. 5, eaax4769 (2019).
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M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

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S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light Sci. Appl. 7, 85 (2018).
[Crossref]

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R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
[Crossref]

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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Sun, H.-B.

G.-X. Jin, X.-Y. Hu, Z.-C. Ma, C.-H. Li, Y.-L. Zhang, and H.-B. Sun, “Femtosecond laser fabrication of 3D templates for mass production of artificial compound eyes,” Nanotechnol. Precis. Eng. 2, 110–117 (2019).
[Crossref]

Temple, S. E.

Y. L. Gagnon, D. C. Osorio, T. J. Wardill, N. J. Marshall, W.-S. Chung, and S. E. Temple, “Can chromatic aberration enable color vision in natural environments?” Proc. Natl. Acad. Sci. USA 113, E6908–E6909 (2016).
[Crossref]

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S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010).
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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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

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P. Wang, N. Mohammad, and R. Menon, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6, 21545 (2016).
[Crossref]

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R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
[Crossref]

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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

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Y. L. Gagnon, D. C. Osorio, T. J. Wardill, N. J. Marshall, W.-S. Chung, and S. E. Temple, “Can chromatic aberration enable color vision in natural environments?” Proc. Natl. Acad. Sci. USA 113, E6908–E6909 (2016).
[Crossref]

Werner, D. H.

Whitehead, J.

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, “Controlling three-dimensional optical fields via inverse Mie scattering,” Sci. Adv. 5, eaax4769 (2019).
[Crossref]

Wood, A.

Wu, P. C.

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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Xu, B.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

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T. Yang, G.-F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6, e17081 (2017).
[Crossref]

Yu, N.

S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light Sci. Appl. 7, 85 (2018).
[Crossref]

Zaidi, A.

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W.-T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

Zhan, A.

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, “Controlling three-dimensional optical fields via inverse Mie scattering,” Sci. Adv. 5, eaax4769 (2019).
[Crossref]

Zhang, X.

W.-L. Zhu, F. Duan, X. Zhang, Z. Zhu, and B.-F. Ju, “A new diamond machining approach for extendable fabrication of micro-freeform lens array,” Int. J. Mach. Tools Manuf. 124, 134–148 (2018).
[Crossref]

Zhang, Y.-L.

G.-X. Jin, X.-Y. Hu, Z.-C. Ma, C.-H. Li, Y.-L. Zhang, and H.-B. Sun, “Femtosecond laser fabrication of 3D templates for mass production of artificial compound eyes,” Nanotechnol. Precis. Eng. 2, 110–117 (2019).
[Crossref]

Zhu, A. Y.

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 (2018).
[Crossref]

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W.-T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

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).
[Crossref]

Zhu, J.

T. Yang, G.-F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6, e17081 (2017).
[Crossref]

Zhu, W.-L.

W.-L. Zhu, F. Duan, X. Zhang, Z. Zhu, and B.-F. Ju, “A new diamond machining approach for extendable fabrication of micro-freeform lens array,” Int. J. Mach. Tools Manuf. 124, 134–148 (2018).
[Crossref]

Zhu, Z.

W.-L. Zhu, F. Duan, X. Zhang, Z. Zhu, and B.-F. Ju, “A new diamond machining approach for extendable fabrication of micro-freeform lens array,” Int. J. Mach. Tools Manuf. 124, 134–148 (2018).
[Crossref]

Adv. Opt. Mater. (1)

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Appl. Opt. (1)

Comput. Phys. (1)

D. Shafer, “Global optimization in optical design,” Comput. Phys. 8, 188–195 (1994).
[Crossref]

Int. J. Mach. Tools Manuf. (1)

W.-L. Zhu, F. Duan, X. Zhang, Z. Zhu, and B.-F. Ju, “A new diamond machining approach for extendable fabrication of micro-freeform lens array,” Int. J. Mach. Tools Manuf. 124, 134–148 (2018).
[Crossref]

Light Sci. Appl. (2)

T. Yang, G.-F. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6, e17081 (2017).
[Crossref]

S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light Sci. Appl. 7, 85 (2018).
[Crossref]

Nano Lett. (1)

M. Khorasaninejad, Z. Shi, A. Y. Zhu, W.-T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic metalens over 60 nm bandwidth in the visible and metalens with reverse chromatic dispersion,” Nano Lett. 17, 1819–1824 (2017).
[Crossref]

Nanoscale Adv. (1)

D. Lee, J. Gwak, T. Badloe, S. Palomba, and J. Rho, “Metasurfaces-based imaging and applications: from miniaturized optical components to functional imaging platforms,” Nanoscale Adv. 2, 605–625 (2020).
[Crossref]

Nanotechnol. Precis. Eng. (1)

G.-X. Jin, X.-Y. Hu, Z.-C. Ma, C.-H. Li, Y.-L. Zhang, and H.-B. Sun, “Femtosecond laser fabrication of 3D templates for mass production of artificial compound eyes,” Nanotechnol. Precis. Eng. 2, 110–117 (2019).
[Crossref]

Nanotechnology (1)

S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology 21, 295303 (2010).
[Crossref]

Nat. Commun. (4)

O. Avayu, E. Almeida, Y. Prior, and T. Ellenbogen, “Composite functional metasurfaces for multispectral achromatic optics,” Nat. Commun. 8, 14992 (2017).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, and C.-H. Kuan, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

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).
[Crossref]

A. Bauer, E. M. Schiesser, and J. P. Rolland, “Starting geometry creation and design method for freeform optics,” Nat. Commun. 9, 1756 (2018).
[Crossref]

Nat. Nanotechnol. (3)

R. J. Lin, V.-C. Su, S. Wang, M. K. Chen, T. L. Chung, Y. H. Chen, H. Y. Kuo, J.-W. Chen, J. Chen, and Y.-T. Huang, “Achromatic metalens array for full-colour light-field imaging,” Nat. Nanotechnol. 14, 227 (2019).
[Crossref]

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 (2018).
[Crossref]

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, and J.-H. Wang, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Nat. News (1)

L. Billings, “Space science: the telescope that ate astronomy,” Nat. News 467, 1028–1030 (2010).
[Crossref]

Opt. Express (2)

Optica (1)

Proc. Natl. Acad. Sci. USA (1)

Y. L. Gagnon, D. C. Osorio, T. J. Wardill, N. J. Marshall, W.-S. Chung, and S. E. Temple, “Can chromatic aberration enable color vision in natural environments?” Proc. Natl. Acad. Sci. USA 113, E6908–E6909 (2016).
[Crossref]

Proc. SPIE (1)

M. Ghigo, O. Citterio, P. Conconi, and F. Mazzoleni, “Ion beam figuring of nickel mandrels for x-ray replication optics,” Proc. SPIE 4145, 28–36 (2001).
[Crossref]

Sci. Adv. (1)

A. Zhan, R. Gibson, J. Whitehead, E. Smith, J. R. Hendrickson, and A. Majumdar, “Controlling three-dimensional optical fields via inverse Mie scattering,” Sci. Adv. 5, eaax4769 (2019).
[Crossref]

Sci. Rep. (1)

P. Wang, N. Mohammad, and R. Menon, “Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing,” Sci. Rep. 6, 21545 (2016).
[Crossref]

Science (2)

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).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
[Crossref]

Other (3)

K. Moore, ZEMAX Optical Design Program, User’s Guide (Zemax Development Corp., 2006).

R. R. Shannon, The Art and Science of Optical Design (Cambridge University, 1997).

M. Laikin, Lens Design (CRC Press, 2018).

Supplementary Material (1)

NameDescription
Supplement 1       Supplemental document

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (7)

Fig. 1.
Fig. 1. Schematics of monolithic lens. (a) Principle of achromatic focusing and imaging and (b) ray simulation of proposed lens.
Fig. 2.
Fig. 2. Focusing performance at characteristic field angles for (a) traditional diffraction-limited aspheric lens with the closest size and $f$-number of 2.5, (b) non-segmented on-axis freeform lens based on the construction-iteration design method, (c) doublet lenses, and (d) honeycomb singlet based on the proposed design method (scale bar: ${{30}}\;{\rm{\unicode{x00B5}{\rm m}}} \times {{30}}\;{\rm{\unicode{x00B5}{\rm m}}}$ for each square element).
Fig. 3.
Fig. 3. (a) Focusing performance of RGB colors at different field angles and (b) distortion grid at full FOV.
Fig. 4.
Fig. 4. Modulation transfer functions (MTFs) of (a) traditional diffraction-limited aspheric lens under incidence of design green wavelength, (b) central lenslet of proposed honeycomb lens under similar green wavelength, (c) DLA with all RGB colors incident, and (d) edge lenslet of proposed honeycomb lens under its allocated RGB color.
Fig. 5.
Fig. 5. Imaging simulations. (a) Traditional diffraction-limited aspheric lens, (b) off-axis aspheric lens, (c) doublet lens, and (d) proposed honeycomb singlet. Three color circles imaged by (e) diffraction-limited aspheric lens and (f) proposed honeycomb singlet.
Fig. 6.
Fig. 6. (a) Experimental setup for fundamental demonstration, (b) confocal point of green laser through segments #2 and #5, (c) strong defocusing of “wrongly allocated” red laser through segments #2 and #5, (d) confocal point of red laser through segments #1 and #4, and (e) confocal performances of correctly allocated red, green, and blue lasers at different field angles.
Fig. 7.
Fig. 7. Focusing and imaging test results: confocal spots taken with (a) traditional diffraction-limited asphere (DLA) and (b) proposed honeycomb lens. Off-axis imaging of RGB circles with (c) traditional DLA lens and (d) proposed honeycomb lens. Building pictures taken by (e) DLA lens and (f) proposed honeycomb lens. Insect pictures taken by (g) DLA lens and (h) proposed honeycomb lens.