# A Single-Celled Metasurface for Multipolarization Generation and Wavefront Manipulation

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Working Principle and Unit Cell Design

_{LL}and R

_{RR}; here, the first and second subscripts represent the handedness of the reflected and incident light, respectively) [9]. The optical properties of the meta-atoms were simulated based on the finite element method (FEM). Detailed information about the simulation method is described in the Appendix A, and a discussion on the efficiency of the designed meta-atom (see Figure S1) can be found in Supplementary Materials. The umbrella-shaped nanostructure on the top introduced a spin-dependent response due to the chiral configuration, and our previous study showed LCP and RCP incident light mainly interact with the left and right parts of the nanostructure, respectively. Moreover, different from normal anisotropic structures like nanobrick, the principal axis of the umbrella-shaped structure was determined by the lengths of the left and right arms. These features provided an effective approach to generate spin-independent rotation of the polarization ellipse without rotating the structure. As shown in Figure 1b,c, when the value of β is fixed, the increase of α will bring an evolution of φ

_{LL}(the phase of R

_{LL}) varying from 0° to 360° while φ

_{RR}(the phase of R

_{RR}) remains nearly constant at the same wavelength. A similar phenomenon can be observed when α is fixed and β changes, except that φ

_{LL}and φ

_{RR}are interchanged. Moreover, for structures with the same α and β, the phase retardation δ is stable in the whole operation band. In the other words, when an x-LP (i.e., LP polarization with polarization direction along the x-axis) incident interacts with the meta-atom, an achromatic phase retardation δ will introduce the two spin-flipped reflection components. Meanwhile, the intensity difference between the two components (R

_{LL}and R

_{RR}) is small enough to be ignored. Thus, these two components are coupled in the near-field and contribute to broadband and achromatic optical activity effects. By synchronously controlling φ

_{LL}, φ

_{RR,}and δ, it is possible to independently control the wavefront as well as the polarization state of reflection in a single-celled metasurface.

## 3. Metasurface for Vectorial Holography

_{g1}, Φ

_{g2}, Φ

_{g3}, and Φ

_{g4}of the four target images were calculated. Phase gradient Φ

_{d}along the x-axis providing a 20° deflection was introduced to avoid the influence of the spin-preserving components. Then, the four-phase distributions were respectively encoded onto the single-celled metasurfaces M

_{1}, M

_{2}, M

_{3}, and M

_{4}, and interleaved to form the final sample. Herein, in the design of M

_{1}, M

_{2}, and M

_{3}, the value of φ

_{RR}at each pixel was modulated by changing the central angle β of each unit cell, and φ

_{RR}= Φ

_{gi}+ Φ

_{d}(i = 1,2,3). In addition, the value of φ

_{LL}was modulated by changing the central angle α, and φ

_{LL}= Φ

_{gi}+ Φ

_{d}+ 2δ (i = 1, 2, 3), where δ is the polarization rotation angle regarding the polarization direction of the incident light; the values are 90, 0, and 45, respectively. As for M

_{4}, central angle α was fixed at 60° while φ

_{RR}= Φ

_{g4}+ Φ

_{d}was encoded in each central angle β of the metasurface.

_{1}–M

_{4}) for different target reconstructions were simulated separately, and the dimension of the arrays was chosen as 50 × 50. As shown in Figure 3a, the simulated results verify the broadband working ability, as similar reconstructed images of the targets can be observed from 1.2 µm to 2 µm. In the process of diffraction, the size of the reconstructed image is proportional to the wavelength; thus, it can be found that the reconstructed image size gradually increases from 1.2 to 2 µm. Then, the feature of spatially varying polarizations was verified by an experimental polarization-sorting test. Upon rotation of polarizer P

_{2}, the reconstructed image of circularly polarized targets T

_{4}was almost unchanged while the linearly polarized targets (T

_{1}, T

_{2}, and T

_{3}) showed obvious polarization characteristics. Specifically, as shown in Figure 3b, when the angle between polarizer P

_{1}and P

_{2}changed from 45° to −45°, the reconstructed image of T

_{3}changed from clear to nearly disappeared. After adding a quarter waveplate before P

_{2}and rotating P

_{2}, it can be observed that the reconstructed image of T

_{1}-T

_{3}was almost unchanged while the reconstructed image of T

_{4}sequentially changed from dimmed to clearly as the polarization state of the analyzer changed from RCP to LCP. Here, the phenomenon that the reconstructed image cannot completely disappear may mainly be caused by the fabrication error. The errors in structure parameters not only influence the phase but also bring a bigger difference between the R

_{LL}and R

_{RR}of each atom, which finally changes the combined reflection from quasilinear to elliptical polarized, and such a problem can be improved by optimizing the fabrication processes.

## 4. Metasurface for Spatially Varying Foci and Polarization States

_{2}. The full-width at half-maximum (FWHM) was 1.57 μm, indicating the designed metalenses have pretty good focusing performance.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{2}was set as 1.5. The structure parameters were p = 700 nm, r = 120 nm, w = 80 nm, t

_{1}= 200 nm, t

_{2}= 180 nm, t

_{3}= 100 nm.

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**Figure 1.**(

**a**) Schematic diagram of the unit cell (

**b**,

**c**) phase of spin-flipped reflection. (

**b**) φ

_{LL}and (

**c**) φ

_{RR}varies with central angle α (

**d**) phase retardation between φ

_{LL}and φ

_{RR}in the range of 1–2 µm when α = 40° and β = 60°. (

**e**) Reflection difference between spin-flipped reflection R

_{LL}and R

_{RR}varies with central angle α. In these simulations, p = 700 nm, r = 120 nm, w = 80 nm, t

_{1}= 200 nm, t

_{2}= 180 nm, t

_{3}= 100 nm. Specifically, in (

**b**,

**c**,

**e**), α varies from 30° to 150° and β = 60°.

**Figure 2.**(

**a**) Schematic diagram of vectorial holography with spatially varying polarization. (

**b**) The design process of the metasurface for vectorial metaholography. (

**c**) SEM photo of the fabricated sample. (

**d**) Experimental setup for vectorial hologram polarization-sorting process (P

_{1}–polarizer 1, P

_{2}–polarizer 2, L

_{1}–objective lens, L

_{2}–lens 2, L

_{3}–lens 3, QWP–quarter waveplate. In the test, QWP is only used for the sorting of circular polarization).

**Figure 3.**(

**a**) Simulated results of reconstructed images at different wavelengths. (

**b**) Experimental results of sorting spatially varying polarizations (λ = 1.55 µm).

**Figure 4.**(

**a**) Schematic diagram of metasurface with spatially varying focal spots and polarization states. The right two inserts show the two design schemes for obtaining spatially varying focal spots. (

**b**) Schematic diagram of the designed metalens array. (

**c**) Simulated x and y components of the focal spot intensity on the x–y plane (z = 33 μm); the generated polarization states are designed as 0°, 45°, 90°, and 120° for L

_{1}, L

_{2}, L

_{3}, and L

_{4}, respectively. (

**d**) The intensity distribution of focal spot (L

_{2}, 1.55 μm) along the y-axis (x = 0 μm, z = 33 μm).

**Figure 5.**Intensity distributions of the designed lenses under incidence with different wavelengths.

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**MDPI and ACS Style**

Ji, R.; Guo, X.; Liu, Z.; Wu, X.; Jin, C.; Liu, F.; Zheng, X.; Sun, Y.; Wang, S.
A Single-Celled Metasurface for Multipolarization Generation and Wavefront Manipulation. *Nanomaterials* **2022**, *12*, 4336.
https://doi.org/10.3390/nano12234336

**AMA Style**

Ji R, Guo X, Liu Z, Wu X, Jin C, Liu F, Zheng X, Sun Y, Wang S.
A Single-Celled Metasurface for Multipolarization Generation and Wavefront Manipulation. *Nanomaterials*. 2022; 12(23):4336.
https://doi.org/10.3390/nano12234336

**Chicago/Turabian Style**

Ji, Ruonan, Xin Guo, Zhichao Liu, Xianfeng Wu, Chuan Jin, Feng Liu, Xinru Zheng, Yang Sun, and Shaowei Wang.
2022. "A Single-Celled Metasurface for Multipolarization Generation and Wavefront Manipulation" *Nanomaterials* 12, no. 23: 4336.
https://doi.org/10.3390/nano12234336