# Single-Layered Phase-Change Metasurfaces Achieving Polarization- and Crystallinity-Dependent Wavefront Manipulation

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}Sb

_{2}Se

_{4}Te

_{1}(GSST) is proposed with average working amplitudes of 72.6% and 53% at different crystallization levels. The proposed metasurfaces could not only enable independent phase control at different crystallization levels but also introduced another polarization degree of freedom. As a proof of concept, we numerically demonstrate three kinds of metadevices in the infrared region achieving a multi-focus metalens with tunable foci, multistate vortex beam generator with adjustable topological charges and multi-channel meta-hologram with three independent information channels. It is believed that these multifunctional metasurfaces with both tunability and compactness are promising for various applications including information encryption, chiroptical spectroscopy, chiral imaging and wireless communication.

## 1. Introduction

_{2}S

_{3}[39,40], vanadium dioxide (VO

_{2}) [41,42] and many others [43,44], have been proposed and various promising applications such as switchable optical modulation [45,46], tunable wavefront control [47,48], active chirality [49] and dynamic color [50] display have been demonstrated. However, although the above mentioned works have further improved the tunability of phase-change metasurfaces, how to integrate more functionalities without the sacrifice of compactness is still challenging.

_{2}Sb

_{2}Se

_{4}Te

_{1}(hereinafter referred to as GSST) and combining multiple phase manipulation mechanisms, three independent information channels can be obtained with low cross talk. To further illustrate this issue, Figure 1 depicts the schematic of the proposed methodology. As shown in Figure 1a, when GSST is in the amorphous state (A-state), two different meta-holograms can be observed in the far field under right-handed circularly polarized (RCP) and left-handed circularly polarized (LCP) incidences. When varying the crystallinity of GSST to the crystalline state (C-state), as shown in Figure 1b, another meta-hologram can be observed and previous images in the A-state are perfectly hidden. Compared with previously reported works [37,38,39,40], the proposed metasurfaces could not only enable independent phase control at different crystallization levels but also introduce another polarization degree of freedom, which may pave a new way to realize active and multifunctional EM devices.

## 2. Design Principles and Simulation Results

_{2}) substrate. The optimized period for the meta atom is p = 5 μm and the thickness for all meta atoms is fixed at H = 7 μm. The working wavelength for the proposed meta atoms is designed for λ = 10.6 μm, which is the operation wavelength of commercial CO

_{2}lasers. By adjusting the length L and width W, six-levelled phase shift meta atoms are optimized to cover 0-2π both in the A- and C-states. As a result, a total number of 6 × 6 meta atoms are designed. The detailed geometric parameters and optical responses are shown in Figure S1 and Table S1. Figure 2c,d shows the simulated transmitted cross-polarized phase shift and amplitude, respectively, where i and j represent the number of the meta atom while the color of the pixel corresponds to the results in the A-state and the position of each pixel indicates the results in the C-state. It can be inferred from Figure 2c that for a given phase shift at A-state, six kinds of meta atoms can be chosen that can fully cover 0–2π at C-state. The average cross-polarized amplitude for the A- and C-states is 72.6% and 53%, respectively, which is sufficient for most wavefront manipulation applications. Finite element method in CST Microwave Studio is employed with unit cell boundaries in the xy directions and open boundary in the z direction. A fine tetrahedral mesh was applied with an adaptive mesh refinement to ensure the accuracy of the results. The optical constants data of the used materials are given in Figure S2 [51,52]. Here, the use of a BaF

_{2}substrate is due to its low permittivity in the infrared region that could reduce the reflectance at the bottom surface. Meanwhile, the choice of GSST as the PCM in the proposed design can be attributed to two main reasons. Firstly, GSST possesses high optical transparency with ultralow loss in both the A- and C-states in the simulated working wavelength, which is essential for wavefront manipulations [53]. Secondly, GSST exhibits a large optical contrast (Δn > 1.5) between the A- and C-states, which makes the optimization of 6 × 6 meta atoms accessible [52].

^{T}normally illuminating the meta atoms, the resulting transmitted EM wave can be described as [28]

_{A}± 2θ, where φ

_{A}is the propagation phase in A-state. In such case, if two independent phase distributions ψ

_{1}and ψ

_{2}are designed for opposite spin states, φ

_{A}and θ can be expressed by [54]

_{1}and n

_{2}are two arbitrary integers and are both chosen as zero in our case. Therefore, ψ

_{1}and ψ

_{2}can be calculated as

_{C}can be designed accordingly. Therefore, the implemented phase for the cross-polarized components under RCP and LCP incidences can be described as φ

_{C}± 2θ. It should be mentioned that since θ is fixed according to Equation (3), desired phase distributions ψ

_{3}can only be encoded to a certain circular polarization. For example, if ψ

_{3}is encoded for the RCP incidence, it can be written as

_{4}under the LCP incidence can be calculated as

_{4}cannot be designed arbitrarily and often results to meaningless far field results. Therefore, by properly choosing the sizes and arrangements of the meta atoms, three independent information channels denoted by ψ

_{1}, ψ

_{2}and ψ

_{3}can be obtained. To further demonstrate the versatility of the proposed design methodology, three kinds of multifunctional metasurfaces are simulated and characterized in the following part.

_{i}(i = 1, 2, 3) can be described by

_{i}, y

_{i}) is the lateral displacement of the focal points and f

_{i}is the designed focal lengths. In our case, (x

_{1}, y

_{1}) = (0,0), (x

_{2}, y

_{2}) = (0, −30 μm), (x

_{3}, y

_{3}) = (30 μm, 0) and f

_{i}is fixed at 60 μm as shown in Figure S3. The time domain solver of CST Microwave Studio was employed for the simulations with open boundaries in all directions. Figure 3 depicts the corresponding simulated electric field distributions at different observation planes obtained by the built-in electric field monitors in CST Microwave Studio at λ = 10.6 μm. It can be inferred that the simulated results agreed well with the designs based on Equation (6). Moreover, the observed results in Figure 3e,i also indicate that the cross talk between different information channels can be ignored. The slight distortion of the focus can be attributed to the limited sample size and can be further improved with a larger diameter. Compared with previously reported works with fixed or symmetrical focal performance [55,56], the proposed metalens had the capability to adjust the focus, which may find many exciting applications for imaging and sensing.

_{i}(i = 1, 2, 3) that can be described by

_{i}= −1, +2 and 0 for i = 1, 2 and 3. The simulated electric field distributions at z = f is shown in Figure 4a–c. As illustrated in Figure 4a,b, the donut-shaped patterns can be observed that demonstrate the generation of vortex beams. Moreover, the diameter of the donut-shaped pattern in Figure 4b was larger than those in Figure 4a,c indicating that the topological charge in this case was larger than the other cases, which is also a typical feature for vortex beams. The corresponding calculated results based on vectorial diffraction theory [58] are shown in Figure 4d–f. It can be inferred that the simulated results agreed quite well with their theoretical counterparts, which further demonstrates the validation of the proposed design method.

^{6}meta atoms with dimensions of 5 mm × 5 mm. To calculate the phase distributions for the meta-hologram, the Gerchberg–Saxton (GS) algorithm was used. Since the image plane is designed in the Fraunhofer region, the ideal phase distribution can be calculated after several iterations of Fourier transforms. Then, the implemented phase distributions ψ

_{i}(i = 1, 2, 3) can be obtained by discretizing the ideal phase distributions to six levels as shown in Figure 5d–f. Figure 5g–i shows the calculated far field intensity distributions under different polarized incidences and crystallization levels at λ = 10.6 μm, which was obtained by using the vectorial diffraction theory. The amplitude and phase at each location on the metasurface was retrieved from corresponding simulated results in Figure 2c,d. It can be inferred that when GSST is in the A-state, different information can be read out under opposite incident spin states. Then, when GSST changes to the C-state, the previous holographic images in the A-state can barely be observed and another new image can be observed, which confirms that the information coded in a certain crystallization level cannot be decoded in the other state.

## 3. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic diagram of the proposed metasurface at different crystallization levels. (

**a**) When GSST is in A-state, two different meta-holograms can be observed under RCP and LCP incidence. (

**b**) When GSST changes to C-state, another meta-hologram can be observed and previous images in A-state are perfectly hidden.

**Figure 2.**Simulated results for the meta atom. (

**a**) Three-dimensional and (

**b**) top view of the meta atom. (

**c**) The simulated transmitted cross-polarized phase shift at A- and C-state. (

**d**) The simulated transmitted cross-polarized amplitude at A- and C-state. i and j represent the number of the meta atom while the color of the pixel corresponds to the results at A-state and the position of each pixel indicates the results at C-state.

**Figure 3.**Simulated performance of the designed multi-focus metalens at different observation planes. (

**a**–

**c**) Electric field distributions when GSST is in A-state under RCP incidence. (

**d**–

**f**) Electric field distributions when GSST is in A-state under LCP incidence. (

**g**–

**i**) Electric field distributions when GSST is in C-state under RCP incidence. The upper row shows the E

_{xoy}results at z = 60 μm. The middle row shows the E

_{xoz}results at y = 0. The bottom row shows the E

_{yoz}results at x = 0.

**Figure 4.**Simulated and theoretical performance of the designed multistate vortex beam generator. (

**a**,

**b**) The simulated electric field distributions when GSST is in A-state under RCP (

**a**) and LCP (

**b**) incidences. (

**c**) The simulated electric field distributions when GSST is in C-state under RCP incidence. (

**d**–

**f**) The calculated results correspond to those in (

**a**–

**c**).

**Figure 5.**Multistate meta-hologram for information encryption. (

**a**–

**c**) Target images. (

**d**–

**f**) Calculated phase distributions based on GS algorithm. (

**g**–

**h**) Calculated far field results when GSST is in A-state under RCP (

**g**) and LCP (

**h**) incidences. (

**i**) Calculated far field results when GSST is in C-state under RCP incidence.

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**MDPI and ACS Style**

Hu, J.; Chen, Y.; Zhang, W.; Tang, Z.; Lan, X.; Deng, Q.; Cui, H.; Li, L.; Huang, Y.
Single-Layered Phase-Change Metasurfaces Achieving Polarization- and Crystallinity-Dependent Wavefront Manipulation. *Photonics* **2023**, *10*, 344.
https://doi.org/10.3390/photonics10030344

**AMA Style**

Hu J, Chen Y, Zhang W, Tang Z, Lan X, Deng Q, Cui H, Li L, Huang Y.
Single-Layered Phase-Change Metasurfaces Achieving Polarization- and Crystallinity-Dependent Wavefront Manipulation. *Photonics*. 2023; 10(3):344.
https://doi.org/10.3390/photonics10030344

**Chicago/Turabian Style**

Hu, Jie, Yujie Chen, Wenting Zhang, Ziyi Tang, Xiang Lan, Qinrong Deng, Hengyu Cui, Ling Li, and Yijia Huang.
2023. "Single-Layered Phase-Change Metasurfaces Achieving Polarization- and Crystallinity-Dependent Wavefront Manipulation" *Photonics* 10, no. 3: 344.
https://doi.org/10.3390/photonics10030344