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Circular-target-style bifocal zoom metalens

Yongmin Zhao, Fengfeng Liu, Zhanpeng Sui, Chi Kong, Shige Dai, Yu Lin, Zhongming Zeng, and Chunping Jiang

Open Access Open Access

Abstract

Optical zoom plays an important role in realizing high-quality image magnification, especially in photography, telescopes, microscopes, etc. Compared to traditional bulky zoom lenses, the high versatility and flexibility of metalens design provide opportunities for modern electronic and photonic systems with demands for miniature and lightweight optical zoom. Here, we propose an ultra-thin, lightweight and compact bifocal zoom metalens, which consists of a conventional circular sub-aperture and a sparse annular sub-aperture with different focal lengths. The imaging resolutions of such single zoom metalens with 164 lp/mm and 117 lp/mm at magnifications of 1× and 2× have been numerically and experimentally demonstrated, respectively. Furthermore, clear zoom images of a dragonfly wing pattern have been also achieved using this zoom metalens, showing its distinctive aspect in biological imaging. Our results provide an approach for potential applications in integrated optical systems, miniaturized imaging devices, and wearable devices.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Optical zoom imaging systems that allow the dynamic adjustment of the magnification and field of view are widely used in consumer electronics, microscopy, telescope, remote sensing [1,2], etc. In such systems, the optical zoom lens is a key determinant to the shot composition. However, conventional optical zoom lens suffers from bulky size, a more complex construction and difficulty in integration. As a result, they are incompatible with emerging miniaturized applications, such as micro-optics integrated systems [3], near-eye imaging devices [4], and wearable optics [5]. Ultra-thin, lightweight and easy-to-integrate zoom lenses are therefore greatly desired. Undoubtedly, recent advances in metalenses [6–10] demonstrate their great potential for use in the field of future advanced optical zoom lenses due to their powerful and versatile performance in modifying electromagnetic properties.

Over the last decade, metalenses have been proposed for various applications ranging from broadband achromatic focusing [11], spectral tomographic imaging [12], and super-resolution imaging [13]. Although prime metalens can also realize better quality images, but it has a fixed focal length that does not allow you to zoom in or out. Recently, multifocal metalenses have been extensively studied in imaging systems [14–16] and optical communications [17]. They allow the integration of two or more focal lengths into a single lens through a clever wavefront design. However, unlike prime metalens, the ability to manipulate those multifocal metalenses zoom imaging seems a little more complicated. For instance, bifocal metalenses that use polarization multiplexing technique [18–25] can focus the light with orthogonal polarization states to different focal lengths. As a result, a light source with tunable polarization states or an additional polarizing splitter must be added to assist imaging. This will increase the size and complexity of the zoom systems. Another metalens that uses wavelength multiplexing technique [26,27] also faces the problem of the use of broadband light sources and additional diffraction grating. Similarly, multifocal metalenses using cascade technique [28–30] rely on mechanical translation or rotation of the lens, leading to the introduction of mechanical control components into the imaging system. They are typically much heavier. Although this problem can be avoided by integrating the lens with various tunable materials [31–42], such as mechanical, thermal, or electrical control materials systems. Again, the stability and lifetime of the system will be inevitably affected by these materials. Therefore, the realization of a high quality zoom metalens with a compact, fixed and simple construction still remains a significant challenge.

In this study, a circular-target-style bifocal metalens (CBM) is proposed for zoom imaging. Using the sparse aperture technology, a circular sub-aperture and an annular sub-aperture with different focal lengths are integrated. The numerical calculations and experimental measurements are compared in terms of the modulation transfer functions (MTFs), point spread functions (PSFs), and imaging resolutions. In the CBM, each sub-aperture works independently, and bifocal zoom imaging can be realized. The experimental results well agreed with the numerical calculations. Finally, the pattern of a dragonfly wing is imaged with the CBM, and a clear zoom image with 2× magnification is obtained.

2. Results and discussion

2.1. Design and simulation

Figure 1 schematically displays the CBM design and working principle. As shown in Fig. 1(a), the CBM comprises a circular sub-aperture (blue part) and an annular sub-aperture (red part) with different focal lengths. The circular sub-aperture is a regular metalens with a diameter of D1 = 460 µm and a focal length of f1 = 4 mm. The annular sub-aperture is a sparse metalens with an inner diameter of D1 = 460 µm, an outer diameter of D2 = 650 µm, and a focal length of f2 = 8 mm. The two sub-apertures focus the light from the same object at different image distances (4 and 8 mm) behind the CBM, creating two coaxial images with different magnifications (1× and 2×, respectively). Herein, the metalens is designed using GaN nanoblocks on a sapphire substrate (see S1 in the Supplement 1 for details). The working frequency is in the visible region with a wavelength of λ = 632.8 nm, and its transmission phase follows the ideal phase equation:

$$\varphi ({\xi ,\eta } )= \frac{{2\mathrm{\pi }}}{\lambda }\left( {{f_1} - \sqrt {{\xi^2} + {\eta^2} + {f_1}} } \right),while\sqrt {{\xi ^2} + {\eta ^2}} < \frac{{{D_1}}}{2}$$
$$\varphi ({\xi ,\eta } )= \frac{{2\mathrm{\pi }}}{\lambda }\left( {{f_2} - \sqrt {{\xi^2} + {\eta^2} + {f_2}} } \right),while\frac{{{D_1}}}{2} < \sqrt {{\xi ^2} + {\eta ^2}} < \frac{{{D_2}}}{2}.$$

 figure: Fig. 1.

Fig. 1. Schematic of the design and working principle of a circular-target-style bifocal metalens (CBM). (a) CBM structure. The CBM comprises a circular sub-aperture with a diameter of D1 and a focal length of f1 as well as an annular sub-aperture with an inner diameter of D1, an outer diameter of D2, and a focal length of f2. (b) Coaxial zoom imaging of the CBM. The image displays magnifications of 1× and 2×. The CBM has no requirements for the polarization state of the light source. (c) Schematic of the image restoration. Clear images can be restored from the direct imaging in (b) using the Wiener filtering algorithm.

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Figure 1(b) schematically displays the CBM imaging process. When the light from the object is incident on the CBM, two images with different magnifications coaxially form behind the metalens due to the sub-apertures. The direct image formed by the CBM may be blurred because of the diffraction and aberrations caused by the two sub-apertures. According to Fourier optics [43], the image irradiance distribution can be described as a convolution of the ideal image and the PSF as follows:

$${g_1}({{x_i},{y_i}} )= {f_1}({{x_i},{y_i}} )\otimes \textrm{PS}{\textrm{F}_1}({{x_i},{y_i}} )+ {n_1}({{x_i},{y_i}} )$$
$${g_2}({{x_i},{y_i}} )= {f_2}({{x_i},{y_i}} )\otimes \textrm{PS}{\textrm{F}_2}({{x_i},{y_i}} )+ {n_2}({{x_i},{y_i}} )$$
where g1(xi, yi), g2(xi, yi); f1(xi, yi), f2(xi, yi); PSF1, PSF2; and n1 and n2 represent the direct imaging, ideal imaging, PSF, and external noise of the CBM at the two focal lengths, respectively. Additionally, ⊗ represents the convolution. To eliminate the diffraction and aberration of the direct imaging, a deconvolution operation is necessary. Figure 1(c) schematically displays the CBM process for achieving clear coaxial zoom imaging using the Wiener filtering deconvolution algorithm. As one of the proven deconvolution algorithms, the Wiener algorithm [44,45] can simply and quickly restore an image.

To evaluate the CBM imaging performance, the pupil functions and MTFs of the CBM with the two sub-apertures are numerically simulated and compared. Unlike conventional monofocal metalenses, when the CBM is imaged at its focal lengths, the infocus and defocus effects simultaneously occur. Therefore, the pupil functions of the CBM are always a combination of an infocus pupil function Pinfocus(ξ, η) and a defocus pupil function Pdefocus(ξ, η):

$${P_{infocus}}({\xi ,\eta } )= A({\xi ,\eta } )$$
$${P_{defocus}}({\xi ,\eta } )= A({\xi ,\eta } )\exp \left[ {\frac{{ik}}{2}\left( {\frac{1}{{{z_i}}} - \frac{1}{{{z_a}}}} \right)({{\xi^2} + {\eta^2}} )} \right]$$
where A (ξ, η) is the amplitude factor with A (ξ, η) ≡ 1 for any ξ, η within the pupil, and A (ξ, η) ≡ 0 for any ξ, η outside pupil. Moreover, zi is the distance from the pupil to the imaging plane, za is the distance from the pupil to the focus wavefront convergence point, and k is a free space wave vector. Figure 2(a) and (b) display the pupil functions of the CBM when imaging at f1 and f2, respectively. As shown in Fig. 2(a), when imaging at f1, the circular sub-aperture focuses with zi = f1 and the annular sub-aperture defocuses with za = f2. As shown in Fig. 2(b), when imaging at f2, the annular sub-aperture focuses with zi = f2 and the circular sub-aperture defocuses with za = f1.

 figure: Fig. 2.

Fig. 2. The complex pupil functions of the CBM imaging at (a) f1 and (b) f2. The simulated modulation transfer functions (MTFs) of the CBM imaging at (c) f1 and (d) f2. (e) Comparison of the MTF of a circular monofocal metalens (CMM, red dashed line) with that of the CBM at f1 (blue solid line) denoted by a white dashed line in (c). (f) Comparison of the MTF of an annular monofocal metalens (AMM, red dashed line) with that of the CBM at f2 (blue solid line) denoted by a white dashed line in (d).

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To evaluate the CBM imaging performance, the MTFs of the CBM at f1 and f2 are calculated (see S2 in the Supplement 1 for details), as shown in Fig. 2(c) and (d), respectively. In comparison, the MTFs of two monofocal metalenses with the same apertures and focal lengths as those of the CBM are also calculated. One is a circular monofocal metalens (CMM) with a diameter of 460 µm and a focal length of f1, while the other is an annular monofocal metalens (AMM) with an inner diameter of 460 µm, an outer diameter of 650 µm, and a focal length of f2. Figure 2(e) presents the comparison between the MTF values of the CBM and CMM at f1. The MTF values of the CBM are lower than those of the CMM, but their maximum cut-off frequencies (MaxCFs) are roughly similar: 169 lp/mm for the CBM and 174 lp/mm for the CMM. Figure 2(f) compares the MTF values of the CBM and AMM at f2. The MTF values of the CBM are lower than those of the AMM, but their MaxCFs are roughly the same: 123 lp/mm for the CBM and 125 lp/mm for the AMM. Since the MaxCFs of the CBM are comparable to those of the monofocal metalenses, the imaging resolutions of the CBM at each focal length are also as high as those of the monofocal metalenses. Although the MTF values of the CBM in the entire spatial frequencies seem low in both cases, the image can still be well restored with the Wiener filtering algorithm when the minimum value of the MTF is ≥0.01.

2.2. Fabrication and characterization

To experimentally verify the CBM imaging performance, the CBM, CMM, and AMM samples are designed and fabricated (see S3 in the Supplement 1 for details). The metalenses are designed to be polarization-independent and all-dielectric using GaN nanobricks. Figure 3 (a) – (c) depict the SEM images of the CMM, AMM, and CBM, respectively. Figure 3 (d) – (f) present the enlarged views of the CBM. The GaN nanobricks have a height of 600 nm and are arranged in a square lattice with spacing of 360 nm. All the metalenses have a wavelength of 632.8 nm. The simulated focusing efficiency of the metalens is 63.5%. The experimentally measured focusing efficiencies of the fabricated CMM and AMM are 51.3% and 40.0%, respectively, and focusing efficiencies of the CBM are 49.3% at f1 and 37.2% at f2. Due to the difficulties in deep etching of GaN, the unit cells of high aspect ratios were not adopted here. In addition, the side-etching issues in the process also reduces the accuracy and steepness of the nanobricks. Therefore, the focusing efficiency in the experiment is lower than that in the simulation. To further enhance the focusing efficiency of the metalenses, advanced etching processes can be explored to achieve GaN nanobricks with higher aspect ratios and better quality in the future.

 figure: Fig. 3.

Fig. 3. SEM images of the fabricated GaN metalenses. (a) CMM with dimeter of 460 µm and focal length of 4 mm. (b) AMM with inner dimeter of 460 µm, outer dimeter of 650 µm, and focal length of 8 mm. (c) CBM with focal lengths of 4 and 8 mm. The (d) top and (e), (f) oblique views of the CBM.

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To realize high-quality image restoration, accurate PSFs need to be obtained. Hence, the PSFs for CMM, AMM, and CBM are calculated and measured. Figure 4(a) and (b) depict the simulated PSFs of the CMM and CBM at f1, respectively. Figure 4(c) and (d) display the simulated PSFs of the AMM and CBM at f2, respectively. Figure 4(e) – (h) show the experimental PSFs for the CMM and CBM at f1 and those for the AMM and CBM at f2, respectively. Figure 4(i) – (l) present the comparison between the calculated and experimental PSFs along the horizontal direction, where the solid blue and dashed red lines represent the calculated and experimental PSFs, respectively. The PSFs of the CBM and CMM exhibit a similar half-peak width at f1, and those of the CBM and AMM exhibit similar main peaks and side lobes at f2. Remarkably, the PSFs obtained via experimental measurements well agree with those numerically calculated.

 figure: Fig. 4.

Fig. 4. (a), (b) Simulated point spread functions (PSFs) of the CMM and CBM at f1. (c), (d) Simulated PSFs of the AMM and CBM at f2. (e), (f) Measured PSFs of the fabricated CMM and CBM at f1. (g), (h) Measured PSFs of the fabricated AMM and CBM at f2. (i), (j) Comparison of the calculated and measured PSFs of the CMM and CBM at f1. (k), (l) Comparison of the calculated and measured PSFs of the AMM and CBM at f2.

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To verify the zoom imaging performance of the CBM, imaging tests are performed on the 1951 United States Air Force resolution test chart. As shown in Fig. 5(a), the measurements are performed with a self-built optical system (see S4 in the Supplement 1 for details). Wiener filtering algorithm is used to restore the images formed by the metalenses. The principle of the algorithm can be found in S5 in the Supplement 1. Figure 5(n) and (r) display the directly obtained and restored imaged of the single circular aperture metalens, respectively. In comparison, Fig. 5(o) and (s) display the directly obtained and restored images of the CBM with the image distance f1, respectively. These images are restored using the measured PSFs in Fig. 4(e) and (f), respectively. After restoration, the contrast of both images improves. The imaging resolution of both cases is the fourth element of group 3, corresponding to 164 lp/mm. Figure 5(p) and (t) show the directly obtained and restored images of the AMM, respectively. Figure 5(q) and (u) display the directly obtained and restored images of the CBM, respectively, with the image distance f2. The measured PSFs in Fig. 4(g) and (h) are adopted to restore these images. For the directly obtained image, the CBM image has slightly lower contrast than the AMM image. After image restoration, the contrast of the image details improves. The imaging resolution of both cases is the first element of group 3, corresponding to 117 lp/mm.

 figure: Fig. 5.

Fig. 5. Simulated and measured images of the 1951 USAF resolution test chart. (a) Schematic of the optical imaging setup for the metalenses. (b), (c) Simulated images directly obtained by the CMM and CBM at f1. (d), (e) Simulated images directly obtained by the AMM and CBM at f2. (f) – (i) Images restored from (b) – (e), respectively, by the Wiener filtering algorithm using the simulated the PSFs. (j) – (m) Images enlarged from the red dash line in (f) – (i), respectively. (n), (o) Measured images directly obtained by the CMM and CBM at f1. (p), (q) Measured images directly obtained by the AMM and CBM at f2. (r) – (u) Images restored from (n) – (q), respectively, by the Wiener filtering algorithm using the measured PSFs.

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To gain deep insights into the zoom performance of the CBM, the dragonfly wing pattern is imaged using the CBM, as shown in Fig. 6. Due to the lower MTF values of the CBM, the direct zoom imaging at 4 and 8 mm yields images with a low contrast [Fig. 6 (b) and (d)]. However, after the restoration with the Wiener filtering algorithm, the sharpness of both images greatly improves [Fig. 6 (c) and (e)]. The images obtained with the long focal length of 8 mm have a 2× magnification relative to those obtained with the short focal length of 4 mm, allowing the identification of the vein pattern details. Notably, although the width of dragonfly wing veins is only about 20 µm, clear zoom images can be obtained using only a single CBM.

 figure: Fig. 6.

Fig. 6. Zoom imaging of a dragonfly wing vein pattern by the CBM. (a) Photograph of the dragonfly specimen. The inset displays an enlargement of the black dotted box, and the red dashed box denotes the imaging position for the CBM. (b), (c) Directly obtained and restored images of the dragonfly wing pattern with the CBM focal length of 4 mm. (d), (e) Directly obtained and restored images of the dragonfly wing pattern with the CBM focal length of 8 mm.

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Undoubtedly, more focal lengths can also be realized by integrating more annular sub-apertures around the CBM. For example, by integrating more annular sub-apertures with different focal lengths around the CBM, a multifocal metalens can be achieved. The coaxial interference may be the greatest challenge of the added sub-apertures. One possible solution is to optimize the shapes and focal lengths of the sub-apertures. Another choice is to use the off-axis design to avoid coaxial interference of the sub-apertures.

In terms of fabrication, the CBM employs electron beam exposure (EBL) and the reactive-ion etching processes, so the precise unit structures could be created and are easy to on-chip integrate. However, due to the high cost of EBL, it still faces some challenges in large-scale production. Recently, there are several ongoing efforts to develop low-cost mass production methods for metalenses such as Deep-Ultraviolet Lithography (DUV) [46], nanoimprinting [47] and self-assembly [48,49], which may produce more cost-effective metalenses in large scale in the future.

3. Conclusion

This study proposed and implemented the CBM. The CBM integrates circular and sparse annular sub-apertures with different focal lengths. The feasibility and effectiveness of the CBM were demonstrated via numerical simulation and experimental measurements. Using the Wiener filtering algorithm, clear coaxial zoom images with two different magnifications were achieved with the CBM. The experimental results showed that the imaging resolutions of the CBM at the two focal lengths were 164 lp/mm (f1 = 4 mm) and 117 lp/mm (f2 = 8 mm), which are comparable to those of monofocal metalenses at the corresponding focal lengths. Furthermore, clear zoom images of the vein patterns of dragonfly wings were obtained with the CBM without additional optics or modulations. Such a strategy for zoom metalenses paves the way for the applications of bifocal metalenses in integrated optics and advanced optical devices.

Funding

Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province (KJS2268); Natural Science Foundation of Jiangsu Province (BK20220293).

Acknowledgments

The authors are grateful for the technical support for Nano-X from Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences (SINANO). The authors acknowledge financial support from the Natural Science Foundation of Jiangsu Province (No. BK20220293). This study was funded by the Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province (KJS2268).

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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Supplementary Material (1)

NameDescription
Supplement 1       Additional information for simulation and experiments

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 (6)
Fig. 1.
Fig. 1. Schematic of the design and working principle of a circular-target-style bifocal metalens (CBM). (a) CBM structure. The CBM comprises a circular sub-aperture with a diameter of D1 and a focal length of f1 as well as an annular sub-aperture with an inner diameter of D1, an outer diameter of D2, and a focal length of f2. (b) Coaxial zoom imaging of the CBM. The image displays magnifications of 1× and 2×. The CBM has no requirements for the polarization state of the light source. (c) Schematic of the image restoration. Clear images can be restored from the direct imaging in (b) using the Wiener filtering algorithm.

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Fig. 2.
Fig. 2. The complex pupil functions of the CBM imaging at (a) f1 and (b) f2. The simulated modulation transfer functions (MTFs) of the CBM imaging at (c) f1 and (d) f2. (e) Comparison of the MTF of a circular monofocal metalens (CMM, red dashed line) with that of the CBM at f1 (blue solid line) denoted by a white dashed line in (c). (f) Comparison of the MTF of an annular monofocal metalens (AMM, red dashed line) with that of the CBM at f2 (blue solid line) denoted by a white dashed line in (d).

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Fig. 3.
Fig. 3. SEM images of the fabricated GaN metalenses. (a) CMM with dimeter of 460 µm and focal length of 4 mm. (b) AMM with inner dimeter of 460 µm, outer dimeter of 650 µm, and focal length of 8 mm. (c) CBM with focal lengths of 4 and 8 mm. The (d) top and (e), (f) oblique views of the CBM.

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Fig. 4.
Fig. 4. (a), (b) Simulated point spread functions (PSFs) of the CMM and CBM at f1. (c), (d) Simulated PSFs of the AMM and CBM at f2. (e), (f) Measured PSFs of the fabricated CMM and CBM at f1. (g), (h) Measured PSFs of the fabricated AMM and CBM at f2. (i), (j) Comparison of the calculated and measured PSFs of the CMM and CBM at f1. (k), (l) Comparison of the calculated and measured PSFs of the AMM and CBM at f2.

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Fig. 5.
Fig. 5. Simulated and measured images of the 1951 USAF resolution test chart. (a) Schematic of the optical imaging setup for the metalenses. (b), (c) Simulated images directly obtained by the CMM and CBM at f1. (d), (e) Simulated images directly obtained by the AMM and CBM at f2. (f) – (i) Images restored from (b) – (e), respectively, by the Wiener filtering algorithm using the simulated the PSFs. (j) – (m) Images enlarged from the red dash line in (f) – (i), respectively. (n), (o) Measured images directly obtained by the CMM and CBM at f1. (p), (q) Measured images directly obtained by the AMM and CBM at f2. (r) – (u) Images restored from (n) – (q), respectively, by the Wiener filtering algorithm using the measured PSFs.

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Fig. 6.
Fig. 6. Zoom imaging of a dragonfly wing vein pattern by the CBM. (a) Photograph of the dragonfly specimen. The inset displays an enlargement of the black dotted box, and the red dashed box denotes the imaging position for the CBM. (b), (c) Directly obtained and restored images of the dragonfly wing pattern with the CBM focal length of 4 mm. (d), (e) Directly obtained and restored images of the dragonfly wing pattern with the CBM focal length of 8 mm.

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Equations (6)

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φ ( ξ , η ) = 2 π λ ( f 1 − ξ 2 + η 2 + f 1 ) , w h i l e ξ 2 + η 2 < D 1 2
φ ( ξ , η ) = 2 π λ ( f 2 − ξ 2 + η 2 + f 2 ) , w h i l e D 1 2 < ξ 2 + η 2 < D 2 2 .
g 1 ( x i , y i ) = f 1 ( x i , y i ) ⊗ PS F 1 ( x i , y i ) + n 1 ( x i , y i )
g 2 ( x i , y i ) = f 2 ( x i , y i ) ⊗ PS F 2 ( x i , y i ) + n 2 ( x i , y i )
P i n f o c u s ( ξ , η ) = A ( ξ , η )
P d e f o c u s ( ξ , η ) = A ( ξ , η ) exp ⁡ [ i k 2 ( 1 z i − 1 z a ) ( ξ 2 + η 2 ) ]
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