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Abstract
Metalenses are a kind of flat optical device, which consist of an array of nanoantennas with subwavelength thickness that manipulates the incoming light wavefront in a precisely tailorable manner. In this work, we proposed a bifocal metalens that can realize switchable multiplane imaging, controlled by changing the polarization state of an incident light. The polarization-dependent metalens was designed and fabricated by arranging polysilicon nanobeam unit elements. We simulated and experimentally characterized the focus performance of the bifocal metalens. Under the light incidence with left-handed circular polarization, the focal length is 250 µm. By changing the polarization state to right-handed circular polarization, the focal length is tuned to 200 µm. Experimental results and numerical simulations are in good agreement. Moreover, when a linear polarization light is used, two focal spots will appear at the same time. Such a bifocal metalens is suitable for multiplane imaging applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, smart wearable devices, such as smart watch, virtual reality glasses, and smart phone have been developed rapidly. In these research and application fields, there have an increasingly urgent desire for thinner and lighter optical devices. To meet such a demand, metasurfaces have attracted much interest and been investigated extensively because they could offer the potential possibility for providing powerful alternatives of conventional refractive optical components [1–5]. Metasurfaces are composed of a set of subwavelength nanostructures, by which the amplitude, phase and polarization of an incident light beam are manipulated. The thickness of the nanostructures is usually uniform and it is smaller than the working wavelength. Therefore, metasurfaces are ultrathin and light-weight, and they can control light propagation in a precise way. In addition, multiple functions can be flexibly integrated into the same device. Owing to all these intrinsic advantages, many applications of metasurfaces have been demonstrated, such as anomalous reflection [6–8], polarization modulation [9–12], optical holography [13–15], structural color [16–18], biochemical sensing [19,20], and others [21].
For various optical components, lenses are among the most important ones in almost all the optical imaging systems. Compared with conventional bulky refractive lenses, which rely on the accumulation of optical path to alter the wave phase, metalenses make use of phase mutation occurred at the interface [22–30]. This is realized by the patterned nanoantennas, that is, meta-atoms. Through changing geometric parameters or rotation angles of such composing units, the required phase delay can be engineered flexibly. In numerous studies on the metalens, chromatic aberration [25,31,32], wide field of view [33,34] and adjustable focal length [35–37] have been paid much interest. For example, a broadband achromatic metalens by incorporating an integrated resonant unit element based on the Pancharatnam-Berry phase (PBP) principle has been proposed and demonstrated for full-color imaging [25]. For many practical applications, varifocusing or switchable focal length is also highly demanded. Combining metalenses and MEMS-based actuators can achieve controlled varifocal lens [36]. However, such an adjustable optical lens is commonly in form of a doublet, in which the focal length is tuned by altering the separation between two metasurfaces. Although the lens in this approach can exhibit tunable optical focus, the fabrication process is rather complicated due to the strict requirement in alignment. Another way to realize a variable focal length is to fabricate the metalens on a stretchable substrate [35]. When a certain strain is introduced, the unit element geometry and the gap between adjacent elements could be altered, which finally leads to a changeable focal length. However, the adjustable range may be limited because of the relatively small allowable strain. Recently, phase-change materials have been proposed as a promising way to construct reconfigurable nano-optical components including lenses [38]. In addition, epsilon-near-zero materials such as those based on indium tin oxide have also been demonstrated to achieve active light focusing by electro-optical control [39,40]. Despite all these progresses, further developments of the metalenses with switchable or variable focal lengths are still necessary.
In this study, we demonstrate a switchable bifocal metalens, which has different focal positions along with transformation of the incident light polarization. The semiconductor polysilicon having a high refractive index is used to construct the nanoantenna and to achieve waveguide-like resonant modes. Based on the PBP principle, we multiplex the metalens into two types of segment parts, which are arranged alternately in the radial direction. Each part corresponds to a circularly polarized light beam with different handedness and leads to different focal lengths. Finally, we carry out the focusing characterization and the double-plane imaging verification. The proposed bifocal metalens may find potential applications in fields such as tomography [41], multiplane imaging, and optical interconnections.
2. Design and methods
The different focal lengths of the lens here are controlled by the light polarization. Figure 1 shows the schematic diagram of the transmissive bifocal metalens. When the right-handed circular polarization (RCP) and the left-handed circular polarization (LCP) lights pass through the metalens, two corresponding foci can be obtained. We independently design the focal lengths with the RCP and LCP parts because of the conformal peculiarity of the metalens. For an assigned focal length f, the required phase profile should satisfy the following equation,
where $\lambda $ is the working wavelength and $\rho = \sqrt {{x^2} + {y^2}} $ is the radial position. From Eq. (1), we can find that the demanded phase should vary along the radial direction and different phase profiles are required for different focal lengths. To obtain the bifocal metalens, we divide the lens area into a set of annuluses. The syncretic layout is schematically shown in Fig. 1(b). The green-shaded and blue-shaded parts represent the effective areas for the RCP and LCP lights, and their focal lengths are ${f_1}$ and ${f_2}$, respectively. The focal lengths are designed independently so that they could be switched by altering the handedness of the incident light. To maintain almost the same intensity of the two foci, the total effective areas of the RCP and LCP parts should be kept as close as possible in the structural optimization.
Fig. 1. Schematic illustration of the polarization-controlled bifocal metalens. (a) Different foci induced by different circularly polarized lights. Upon the RCP and LCP light illumination, two focal lengths can be obtained and they have a difference $\Delta f$. (b) Layout of the metalens structure. The lens pattern is multiplexed in the radial direction. The shaded green and blue parts represent the effective regions for the RCP and LCP incidence lights, respectively.
The phase at each location is satisfied by using the PBP in our design, which is a geometric phase induced by rotating the nanoantennas to cover the full 0-2π range [5]. Here, we use this conventional principle with the main design purpose of realizing the above bifocal metalens. The unit element in the metasurface is similar to a half-wave plate for which the orientation of the fast axis is spatially arranged and organized. When the fast axis of such a nanoantenna rotates an angle θ, a local phase change emerges, which is equal to $\varphi ={\pm} 2\theta $. Here, the sign depends on the circular polarization state of the incident light beam, that is, RCP or LCP. For an arbitrary incident plane wave $|{E_{in}}{\rangle }$ propagating through the metasurface, the transmitted light comprises of three polarization orders [5],
The schematic diagram of the basic building block is shown in Fig. 2(a). Polycrystalline silicon nanobeams with the thickness of 100 nm are patterned on a quartz substrate. Polycrystalline silicon is an optical material with a higher refractive index and it has a lower absorption coefficient in the visible wavelength range as compared with amorphous silicon. To enable a precise metalens design, the complex refractive index of the deposited polycrystalline silicon is experimentally characterized by a spectroscopic ellipsometer. The refractive index n and the extinction coefficient k at the working wavelength of 632.8 nm are determined to be 4.16 and 0.08, respectively. The geometric parameters t, w and p illustrated in the figure denote the thickness, the width and the period of the nanobeams, respectively. We first simulate the spectra of the phase retardation of a TE wave (x-polarization) with respect to a TM wave (y-polarization) at the wavelength ranging from 500 to 700 nm as shown in Fig. 2(b). Here, the nanobeam widths are 120 nm (black curve), 140 nm (red curve) and 160 nm (blue curve), respectively. The beam arrays have the same duty cycle of 60% and the thickness of 100 nm. The dashed green line shows the location where the phase retardation is equal to π. With the increase of nanobeam width, the peaks in phase-wavelength spectra within the simulated range will shift to a higher wavelength. Figure 2(c) demonstrates typical calculated phase maps. Here, the nanobeam width is 140 nm and the wavelength is 600 nm for the first two columns. They are 160 and 630 nm for the last two columns, respectively. The red wireframes denote the outlines of the silicon nanobeams. We can find that the wavefront for the TE-polarization light is delayed to a π-phase as compared with the TM-polarization light. The nanobeam is ascertained to be functionalized as a half-wave plate. Figure 2(d) presents the simulated polarization conversion efficiencies of the nanobeam arrays with different widths. The maximum conversion efficiency is 30.7% at the light wavelength of 640 nm and the nanobeam width of 160 nm. The efficiency peak also moves to a higher wavelength range when the width increases. With these fundamental studies, the underlying mechanism of the unit element in tailoring phase shift can be well understood and the metalens structure can be designed and optimized accordingly.
Fig. 2. Illustration of the silicon nanoantennas and structural parameter optimization. (a) Sketch of the silicon nanobeam with thickness t, width w and period p. TE and TM polarized waves are along the x- and y-axes, respectively. (b) Simulated spectra of the phase retardation of a TE wave with respect to a TM wave. The wavelength range is from 500 to 700 nm. (c) Simulated phase maps. Here, the nanobeam width is 140 nm and the wavelength is 600 nm for the first two columns. They are 160 and 630 nm for the last two columns, respectively. The wavefront for the TE wave is delayed to a π-phase as compared with the TM wave. (d) Corresponding polarization conversion efficiencies of these nanobeam arrays.
Subsequently, we design a bifocal metalens working at the central wavelength of 632.8 nm. The nanobeam thickness is 100 nm and the width is 160 nm. The beam period is 267 nm. The lens has a 100 µm focal length upon a RCP light beam and a 125 µm focal length upon a LCP light. To verify the functional performances of the metalens, we simulate the focal properties based on the finite-difference time-domain (FDTD) method, which is performed by solving the Maxwell’s equations. Owing to the computing time-cost, the metalens in FDTD simulations is assigned to have a diameter of 56 µm. Note that the fabricated metalens in the followed experiments can have magnified parameters as compared with these simulation settings including the focal lengths. Figure 3 shows the numerical results when an incident light with circular polarization passes through the metalens. Evidently, the two focal lengths are in close agreement with the design objectives. The full width at half maximum (FWHM) of the focus is 1.44 µm for the RCP incidence and 1.46 µm for the LCP incidence, respectively, approximating the theoretical diffraction limit. In addition, the focusing efficiencies are evaluated to be around 7.0% and 8.7% for the LCP and RCP incidence, respectively. We define the efficiency here as the ratio of the optical power in the focal area with a radius of three times of the FWHM to the incident power. The focusing efficiency can be further improved by using other materials with even lower absorption to enhance the polarization conversion efficiency.
Fig. 3. Simulated focusing characteristics of the bifocal metalens. The intensity maps in the xz-plane are presented for the RCP (a) and the LCP (c) light illumination. (b) and (d) The corresponding normalized sectional profiles along the x-axis at the focus. The dashed lines denote the profiles calculated from the ideal Airy disks.
3. Lens fabrication
After design, we fabricate the bifocal metalenses and the fabrication processes are briefly described as follows. First, a 100-nm-thick polycrystalline silicon film is deposited onto a clean quartz substrate using low-pressure chemical vapor deposition (LPCVD) at 620 °C. The complex refractive index of the polycrystalline silicon film is characterized by a spectroscopic ellipsometer (SOPRA, GES5E). The analyzed wavelength range is from 300 to 1000 nm. The intrinsic absorption coefficient of the polysilicon is calculated from the refractive index n and the extinction coefficient k. The absorption is very small when the wavelength is over 600 nm. At the working wavelength of 632.8 nm, parameters n and k are 4.16 and 0.08, respectively. Then, an about 200 nm thick electron-beam resist layer (ARP6200.04) is spin coated on the polysilicon layer at 2000 rpm for 30 s and baked at 90 °C for 60 s. After that, the resist is patterned by using an electron beam lithography (EBL) system (JEOL, JBX-6300FS) with the beam current of 500 pA and developed in a solution of AR600-546 for 60 s. The rudimental resist is removed by reactive ion etching (RIE) for 5 s. Next, standard dry etching of silicon materials is applied in the SF6 and C4F8 plasma environment with a ratio of 45: 100 at 10 °C. Finally, the remaining resist is removed with a resist-dispenser (EKC) for 7 min at 80 °C.
The scanning electron microscopy (SEM) image of a part of one fabricated metalens is shown in Fig. 4. The green and blue sections are shaded to represent the effective regions for the RCP and LCP lights, respectively. The inset shows a zoomed view. From the SEM imaging, the fabricated metalens is in close agreement with the design patterns and the fabrication accuracy is satisfactory in general. The diameter of the metalens is 107 µm, which has almost a two-fold magnification as compared with the FDTD simulation setting. The numerical aperture of the lens is approximately NA = 0.27 for RCP and NA = 0.21 for LCP.
Fig. 4. SEM images of the bifocal metalens. (a) The lens region near the center. The shaded green and blue parts represent the effective regions for the RCP and LCP lights, respectively. (b) The lens region near the edge and a partial zoomed view of the fabricated nanobeam arrays.
4. Results and discussion
To demonstrate the practical focal performance of the fabricated metalens, we build an optical characterization system. The laser’s wavelength is 632.8 nm. A linear polarizer and a quarter-wave plate are used to generate the LCP or RCP polarization state. The focal spot at the transmitted side of the metalens is magnified by an objective lens (40X) and captured by a CMOS camera (pco. panda 4.2, PCO AG, Germany) with the pixel size of 6.5 µm × 6.5 µm. The fabricated metalens is fixed on a precise three-axis translation station with a resolution of 1 µm for optical alignment and position scanning along the optical axis.
The experimental results of the metalens focusing upon three polarization states of RCP, LCP and LP at the normal incidence are presented in Fig. 5. In order to generate a RCP light beam, we first adjust the polarizer and the fast axis of the quarter-wave plate to 45°. Then, the position of the metalens is moved along the longitudinal direction in a step of 5 µm. The intensity in each step is recorded by the CMOS camera to generate a three-dimensional spatial distribution and to determine the focal spot unambiguously. The constructed intensity in the xz-plane under the RCP light incidence is shown in Fig. 5(a). The white dotted line denotes the determined focal plane and the corresponding intensity distribution in the xy-plane is provided in Fig. 5(e). The FWHM of the focal spot is evaluated to be 1.42 µm (see Fig. 5(i)).
Fig. 5. Experimental focusing characterizations of the bifocal metalens at the laser wavelength of 632.8 nm. Reconstructed intensity maps in the xz-plane for the RCP incidence (a), LCP incidence (b), and LP incidence (c). (d) The sectional intensity profile along the central z-axis for the LP incidence. (e-h) Corresponding focal spots. (i-l) Sectional profiles of the focal spots along the x-axis. The respective intensity is normalized.
We then change the incident light from RCP to LCP by rotating the quarter-wave plate to an angle of −45° and repeat the measurements. Similarly, the constructed intensity distribution in the xz-plane, the intensity map in the focal plane and the intensity sectional profile in the x-direction at the focus are shown in Figs. 5(b), 5(f) and 5(j), respectively. The focal length is measured to be approximately 50 µm longer under the LCP light incidence than the RCP incidence and it agrees well with the theoretical expectation. The FWHM of the focal spot is 1.50 µm upon the LCP light incidence. Such a value is very close to the theoretical diffraction-limited FWHM of 1.51 µm, which is evaluated as $\lambda /({2 \times \textrm{NA}} )$. Evidently, the experimental and simulated results are in good agreement and the minor deviation is mainly resulted from the metalens fabrication error and the measurement accuracy.
Furthermore, we characterize the focal performance of the metalens for an incident light with the linear polarization through removing the quarter-wave plate. Under such a condition, the correlated LCP and RCP lights illuminate the fabricated lens at the same time. Figure 5(c) shows the experimental intensity distribution map in the xz-plane and two discrete focal spots are clearly observed along the longitudinal z-direction. The two focal spots have an experimental separation of approximately 60 µm. The marked positions I and II denote the focal spots contributed by the RCP and LCP components, respectively. The intensity profiles taking at positions I and II are shown in Figs. 5(g) and 5(h). The corresponding FWHMs are 1.30 and 1.44 µm, respectively, as depicted in Figs. 5(k) and 5(l). The intensity profile along the optical axis is illustrated in Fig. 5(d). The peak intensities of the two focal spots have a slight discrepancy, which is possibly owing to the different numerical apertures for RCP and LCP parts. However, we can make the intensity much more consistent through finely optimizing the effective areas for RCP and LCP parts of the metalens if it is required. In addition, the measured focal length at position II is larger than the expected value. This deviation is mainly caused by the positional error because a large z-scan interval of 5 µm is used in the measurement.
To demonstrate the imaging capability of the bifocal lens, we prepare a target object, which consists three line patterns with the width of 5 µm and a separation of 5 µm. The imaging setup is shown in Fig. 6(a). Again, a linear polarizer and a quarter-wave plate are used to create a circular polarized light beam. The target pattern can move along the optical axis to introduce different object planes. With the incidence of a LCP light having the wavelength of 632.8 nm, an unambiguous image can be observed on the CMOS camera screen when the target is moving to position I. In imaging, we actually fix the image distance of 400 µm while the object position is gradually adjusted to fit the corresponding object-image relation. The object distance here is determined to be approximately 667 µm and the theoretical magnification factor equals to 0.6. However, the image is not so clear because of the limited lens diameter and the small numerical aperture. Then, we translate the incident light from LCP to RCP by rotating the quarter-wave plate. The image on the screen appears to be quite blurry owing to the inconsistent image plane for RCP light incidence. When the target is further moved to a proper position II where the object distance is roughly 400 µm, the image becomes clearer again. Compared with the image at position I (Fig. 6(b)), the image at position II is a little bigger due to the increased magnification factor, which is resulted from the two different focal lengths. The image is blurry again when the incident light turns to the opposite handedness. These experimental results indicate that the bifocal metalens can image the objects at different distances by switching the handedness of the incident light. Such characteristics are demanded in tomographic volume imaging because they could add an additional degree of freedom in the slice sectioning. As a proof-of-concept, the lens aperture in this work is a little small for easier fabrication. This leads to relatively poor practical imaging. When a lens with a much larger diameter is fabricated, the numerical aperture and field of view can be increased accordingly, which will lead to better imaging quality. Our metalens here has not been designed for correcting the chromatic aberration. However, dispersion engineered approaches should be also implementable to realize an achromatic metalens [25,31,32].
Fig. 6. Imaging results of the bifocal metalens at 632.8 nm. QWP: quarter-wave plate; Obj: objective lens. (a) Schematic illustration of the imaging setup. The target contains three line patterns with both the width and the separation of 5 µm. (b) The image at the position I under the LCP light or (c) the RCP light. (d) The image at the position II under the RCP light or (e) the LCP light. These two different positions have different object distances. The inset in image (b) shows the optical microscopy image of the object and the scale bar is 10 µm.
5. Conclusions
In conclusion, we have experimentally demonstrated a bifocal metalens, which can realize double-plane or even multi-plane imaging controlled by the polarization of incident light. The polysilicon nanobeams with specified spatial orientations are used to realize the desired phase profile based on the PBP principle. For the flexible design, the metalens is divided into a set of rings, which are arranged alternatively and effective for the LCP and RCP lights, respectively. As a consequence, two different focal lengths with a separation distance of 50 µm along the optical axis are obtained. The focusing characteristics are in good agreement with the theoretical expectations. In addition, if a LP light is used as the illumination source, two foci emerge simultaneously. Therefore, focal spots can be flexibly switched. In addition, we have demonstrated double-depth imaging upon the circularly polarized light beam with the opposite handedness by using the bifocal metalens. Such a switchable metalens may have potential applications in multiplane imaging.
Funding
National Natural Science Foundation of China (51675504, 52075517).
Acknowledgments
We acknowledge for the support of this work by allocating us resources of the USTC Center for Micro- and Nanoscale Research and Fabrication.
Disclosures
The authors declare no conflicts of interest.
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