Meta-lens based on multi-level phase-change

Lenses have a broader range of utilizations, like drones, webcams, and telescopes. Conventional lenses modify the phase of light by accumulating phase throughout the optical route, with their shape and material determining the phase of light. Such methods have some limitations, such as fixed focal lengths. Combining multiple lenses and employing specialized design techniques can overcome these limitations, but this approach increases volume. Compared to traditional lenses, meta-lenses are thinner and more compact, offering functionalities surpassing conventional lenses,^1–4 such as achromatic meta-lens,^5,6 high-dimensional quantum source,⁷ etc. Through the interaction of light with subwavelength-antennas, they provide control over the phase,⁸ amplitude,⁹ polarization state,^10–12 etc., of the wavefront passing or reflecting through the metasurface.^13–16 As a revolutionary technology in optics,^17–19 they hold the potential to completely revolutionize cumbersome lens arrangements in traditional optical systems, making products such as smartphones, cameras, and surveillance cameras smaller, thinner, and lighter. Although passive metasurfaces are highly useful in many scenarios, a strong desire remains to expand their capability to manipulate the light.

Tunable meta-lens with multiple responses and functionalities can dynamically manipulate electromagnetic responses and fulfill the complex requirements in practical operations.^20–23 Different methods, like using electricity,²⁴ strain,^25–27 and various materials such as phase-change materials^28–30 and liquid crystals,³¹ have been created to make meta-lenses tunable for better performances and advanced functions, such as optical sectioning fluorescence microscopy^32–34 and 6G communications.³⁵ However, most of them can only work in two modes. Other mechanisms like stretchable substrates³⁶ and rotary metasurfaces^35,37 can continuously tune the focal lengths. However, mechanical control of meta-devices by external force is unstable and not easily integrated into various application platforms. There is a growing interest in non-mechanical modulation approaches to overcome such limitations. A theoretical study was conducted on the thermo-optical effects in resonant silicon nano-resonators to develop tunable meta-lens capable of continuous focal length adjustment.³⁸ The maximum phase compensation is 100°, and the efficiency is relative low duo to the loss of silicon in the visible. All-optical modulation³⁹ is a promising candidate for tunable meta-lens with continuously adjustable focal length. Compared to other technologies based on thermal, magnetic, acoustic, mechanical, and electrical effects, all-optical modulation enables the highest modulation bandwidths up to terahertz.⁴⁰ Phase-change materials are highly suitable for all-optical modulation devices, yet their full potential has not been fully realized. For instance, multi-level phase-change memory devices have been extensively researched and applied in non-volatile semiconductor memory.^41,42 At present, the use of phase-change materials in meta-devices is largely limited to exploiting their crystalline and amorphous states, with at most one additional hybrid state being utilized.⁴³ 

In this work, a tunable phase-change materials-based meta-lens is demonstrated. The working wavelength is 1550 nm. The focal length can be continuously manipulated from 35 to 55 μm. Calculating the phase differences between the meta-lens’ minimum and maximum focal lengths can provide maximum phase compensation. The nano-antenna is a rectangle of different sizes and orientations, and the phase is from two parts, i.e., the Pancharatnam–Berry phase and the propagation phase. The compensation method is based on manipulating the refractive index of the nano-antenna made of phase-change materials (Sb₂S₃)³⁰ to tune the propagation phase. Sb₂S₃ is a promising option due to its losses and relatively wide range in refractive index. As the material's refractive index changes from 2.8 to 3.4, the phase compensation will gradually increase from 0 to its maximum value, and the corresponding focal length will increase progressively as designed. The tunable Airy beam, Bessel beam, and meta-lens with static focal length but tunable deflections based on Sb₂S₃, and tunable meta-lens based on Ge₂Sb₂Te₅ are also demonstrated to show the universality of the proposed design. The proposed phase-change materials-based tunable meta-lenses provide an affordable and straightforward approach for tunable infrared components.

Figure 1(b) shows the difference of the phase profile of the meta-lenses working at various focal lengths from 45 to 90 μm. The diameter of the designed meta-lens is 30 μm, and the working wavelength is 1550 nm. The calculated curves show that the phase differences range from 0 to 4.5 rad, covering the whole lens. Thus, different nano-antennas with specific phase differences in this scope should be crafted under the refractive index range from 2.8 to 3.4. When these nano-antennas are placed at suitable positions in the metasurface, the proposed function can be performed smoothly.

Besides the phase provided by the nano-antennas, the polarization conversion efficiency also needs consideration because the Pancharatnam–Berry phase is based on the circular polarization transformation. To conjointly consider the phase compensation and the efficiency, we first sweep the length (L) and the width (W) of the nano-antennas with fixed height (H, 2000 nm) and fixed period (P, 600 nm) to calculate the phase and efficiency maps and select the parameters to appreciate both for the phase compensation and the polarization conversion efficiency. The commercial software COMSOL^® Multiphysics was employed to simulate the response of the nano-antennas. The periodic boundary conditions are applied in the x and y directions, and perfectly matched layers are used in the z-direction. The database of the selected nano-antennas is shown in Fig. 2. The inset of Fig. 2(a) shows the schematic of the nano-antenna. There are nine nano-antennas with phase compensations ranging from 0.5 to 4.5 rad, with intervals of 0.5 rad, and the polarization conversion efficiencies are all above 50% when the refractive index is increased gradually from 2.8 to 3.4. From Fig. 2(a) to 2(i), the parameters of the widths and lengths are (70 nm, 480 nm), (100 nm, 490 nm), (160 nm, 410 nm), (210 nm, 360 nm), (370 nm, 230 nm), (400 nm, 240 nm), (400 nm, 260 nm), (390 nm, 275 nm), and (430 nm, 305 nm), respectively.

We will provide a detailed guide on how to accurately integrate nano-antennas of suitable dimensions into the layout of meta-lens along with determining their rotational angles. First, as depicted in Fig. 2, it is evident that the propagation phase of the nine selected nano-antennas linearly increases with the refractive index. Hence, by determining the phase profile required for the maximum and minimum focal lengths of the meta-lens, we can accurately establish the dimensions and orientations of each nano-antenna. Thus, intuitively, one may utilize the Pancharatnam–Berry phase to provide the focusing phase at lower refractive indices while leveraging the additional propagation phase induced by the increase in refractive index as phase compensation to adjust the focal lengths corresponding to the respective refractive indices. At this point, it is crucial to note that simply calculating the rotation angles based on a phase difference of 1/2 is inaccurate. This is because the nine nano-antennas have different dimensions, and the variation in their propagation phases will disrupt the focusing phase. Therefore, applying an additional rotation angle to each nano-antenna is necessary to compensate for the differences in propagation phase caused by their dimensions. In summary, the dimensions of each nano-antenna are determined by the phase difference corresponding to the maximum and minimum refractive indices. Additionally, the orientation of the nano-antennas is jointly determined by the focusing phase at the minimum refractive index and the difference between the propagation phases of each nano-antenna at the minimum refractive index.

By placing the selected nano-antennas with specific phase and phase differences into the layout of the meta-lens, the tunable focal lengths can be verified by full-wave simulations through the commercial software Lumerical^® FDTD solutions. Figure 3(a) shows the xz-plane intensity distributions of the proposed tunable meta-lens where the focus properties can be viewed. The focal length can be manipulated from 35 to 55 μm, as seen in Fig. 3(b). The difference between the intended and simulated focal lengths primarily arises from the variations in undersized meta-lens and individual nano-antenna efficiencies. Figure 3(c) presents the calculated polarization conversion and focusing efficiency. The polarization conversion efficiency is defined as the output of the right circular polarization light over the input of the left circular polarization light. The focusing efficiency is defined as the intensity sum of 1.5 times full width at half maximum of the focal spot (only the right circular polarization components) over the input of the left circular polarization light. The results show about 70% polarization conversion efficiency and about 50% focusing efficiency among the different refractive indices of the nano-antennas, respectively, which achieve a trade-off between these critical efficiencies. The efficiency can be further enhanced by increasing the height of the nano-antennas or adding a matching layer to decrease the reflection, for instance.

Besides meta-lens, we also demonstrate the tunable Airy beam and Bessel beam to show the universality of the proposed design. The phase distribution on the metasurface to generate the Airy beam and the Bessel beam are 2 × π × a³ × (x³ + y³)/3³⁵ and –(2 × π/λ) × sqrt(x²+ y²)  × b,⁴⁴ respectively. Here, a and b are constants, λ is the working wavelength, and x and y are the Cartesian coordinates on the metasurface. By tuning the refractive index of the nano-antennas, the constant a can be manipulated from 0.108 to 0.118, and b can be changed from 0.2 to 0.28, leading to the intensity distributions in the x–z plane shown in Figs. 4(a) and 4(b), respectively.

The phase difference between the adjustable meta-lens of the minimum (0°) and maximum deflection angles (5°) is presented in Fig. 5(b). The maximum phase difference is 4.34 rad, which the selected nine nano-antennas can also achieve. Figure 5(c) presents the intensity distributions of the xz-plane of the refractive index-based tunable meta-lens, demonstrating the effectiveness of the design.

Besides Sb₂S₃, our design method also applies to other phase-change materials, and here, we take Ge₂Sb₂Te₅ as another example.^29,45 The advantage of Ge₂Sb₂Te₅ is quite evident in the mid-IR range due to the low loss and the large refractive index difference between the phase states (from 3.7 to 5) to cover more phase compensation. Following the design flow mentioned above, we select ten nano-antennas whose lengths and widths are (400 nm, 140 nm), (390 nm, 180 nm), (420 nm, 200 nm) (460 nm, 200 nm), (480 nm, 200 nm), (520 nm, 280 nm), (600 nm, 280 nm), (600 nm, 290 nm), (600 nm, 300 nm), and (600 nm, 310 nm), respectively, working at 2500 nm. The height and period are 1400 and 700 nm, respectively. Figure 6 shows the performance of the meta-lens based on Ge₂Sb₂Te₅ when continuously varying the refractive index of the Ge₂Sb₂Te₅. Figure 6(a) shows the xz-plane intensity distributions of the proposed tunable meta-lens. The focal length can be tuned from 22 to 30 μm, as seen in Fig. 6(b). Figure 6(c) presents the calculated polarization conversion and focusing efficiency.

In conclusion, the working principle of the phase-change materials-based tunable meta-lens working at 1550 nm with continuous adjustable focal lengths or deflection angles is proposed. We can acquire the phase differences covering the whole mate-lens by evaluating the phase profiles of the tunable meta-lenses of various focal lengths or deflection angles. Nine nano-antennas are optimized and selected to cover phase differences from 0.5 to 4.5 rad and maintain high polarization efficiencies simultaneously. Two kinds of meta-lens are showcased. The focal length of the tunable meta-lens can be modified from 35 to 55 μm, and the other can work in deflection mode with steering angle from 0° to 5° continuously. The design approach applies to other tunable meta-devices to generate dynamic Airy beams, Bessel beams, etc. and to different phase-change materials. The proposed meta-lens can dynamically adjust its focal length and focusing properties through optical laser manipulation, enabling seamless adaptation to diverse application scenarios without requiring complex configurations. Our design seamlessly transitions to these operational ranges, delivering substantial utility and value by leveraging a phase-change material without losses across near-infrared to mid-infrared wavelengths. This study innovates approaches for harnessing the continuous modulation capabilities of tunable meta-devices based on phase-change materials, thereby enhancing their integration within multifunctional infrared systems.

This work was supported by the University Grants Committee/Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. AoE/P-502/20, CRF Project Nos. C1015-21E and C5031-22G, GRF Project Nos. CityU15303521; CityU11305223; CityU11310522; and CityU11300123, and Germany/Hong Kong Joint Research Scheme No. G-CityU 101/22], City University of Hong Kong (Project Nos. 9380131, 9610628, and 7005867), and National Natural Science Foundation of China (NNSFC) (Grant No. 62375232).

The authors have no conflicts to disclose.

Jing Cheng Zhang: Investigation (lead); Methodology (lead); Software (lead); Visualization (lead); Writing – original draft (lead). Jin Yao: Software (supporting); Visualization (supporting); Writing – original draft (supporting). Din Ping Tsai: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (lead); Resources (lead); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.