# Design of Full Stokes Vector Polarimetry Based on Metasurfaces for Wide-Angle Incident Light

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Proposed Metasurface-Based Polarimetry

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_{3}substrate, as shown in Figure 2b. During the modeling process, the thickness of the substrate is set to 300 nm [27], the height of the nanopillar is set to 800 nm, and the center of the nanopillar is located on the center of substrate. The entire design region contains 20 × 40 × 3 unit lattice structures. The length, l, width, w, and rotation angle, $\psi $, of the nanopillar in each unit lattice determine the phase shift of the transmitted light.

## 3. Results and Discussion

#### 3.1. Stokes Vector Detection for Vertical Incident Light

^{T}, [−1, 0, 0]

^{T}, [0, 1, 0]

^{T}, [0, −1, 0]

^{T}, [0, 0, 1]

^{T}, and [0, 0, −1]

^{T}. The Full Width at Half Maximum (FWHM) method is used to determine the effective light spot area. The light intensity through the spot area in each Part is measured and normalized to calculate the Stokes parameters. The calculated Stokes parameters are shown in Figure 3b. The maximum error is less than 0.09, which is close to the result of article [29,32]. Notably, the maximum error is random, rather than fixed in a certain polarization state. The main reason for this is considered to be the approximate representation of the focus phase distribution, shown in Equation (5). Moreover, in the optical field simulation process, due to the inherent errors of the computer, these will lead to random differences in the optical field distribution. These results prove that our proposed structure has the ability to detect the polarization state of vertically incident light.

#### 3.2. Stokes Vector Detection for Oblique Incident Light

#### 3.3. Modified Coefficient for Oblique Incident Light

^{T}and (0.6, 0.693, −0.4)

^{T}, respectively. Figure 5c,d are the calculated normalized Stokes parameters with corresponding modified coefficients, respectively. The calculated Stokes parameters show good agreement with the original values. As the angle of incidence increases, the quality of the results decreases slightly. The average absolute value errors at −10°and −20° are, respectively, 0.035 and 0.047. The maximum error is 0.09 at −20° incidence. As in previous discussions in the case of vertical incident, the maximum error is randomly generated due to the approximate expression of the phase modulation and the margin of error of the computer. However, compared with Ref. [29], the proposed structure in this paper has almost the same measurement accuracy.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Schematic diagram of the metasurface unit; (

**b**) Schematic diagram of the principle of the polarimetry; (

**c**) Side view of the focusing effect of the polarimetry; (

**d**) The influence of the length, l, and width, w, of the nanopillars on the transmittance; (

**e**) The effect of the length, l, and width, w, of the nanopillars on the x-polarization phase shift; (

**f**) Phase values ${\phi}_{x}$ and ${\phi}_{y}$ corresponding to nanopillar dimensions.

**Figure 3.**(

**a**) The intensity distributions of the six vertically incident polarized lights (i.e., x-LP, y-LP, 45°-LP, 135°-LP, RCP, and LCP) on the focal plane with $f=6\text{}\mathsf{\mu}\mathrm{m}$; (

**b**) The calculated normalized Stokes parameters for different polarization states; (

**c**) The wavelength dependence of the structure transmittance; (

**d**) The y-polarized light intensity of Part I on the fixed focal plane with different wavelengths.

**Figure 4.**(

**a**) Schematic diagram of oblique incidence scenario; (

**b**,

**c**) Schematic diagrams of the inclination angle ±θ along the x-axis direction, respectively; (

**d**) The focal intensity distribution of y-polarized light of Part I on the focal plane with different incident angle (0°, −5°, −10°, −15°, and −20°); (

**e**) The relationship between the calculated incident angle and the actual incident angle, as well as the absolute value of the error. Intensity distributions of the transmitted light with the oblique incident angle of (

**f**,

**g**) −20° and 20° along the y-axis, (

**h**,

**i**) −20° and 20° along the x-axis, respectively.

**Figure 5.**The intensity distributions of different incident polarization states at (

**a**) −10° and (

**b**) −20°. The calculated normalized modified Stokes parameters of different polarization states at incident angles of (

**c**) −10° and (

**d**) −20°.

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**MDPI and ACS Style**

Liu, S.; Zhang, Z.; Cheng, J.; Wang, X.; Sun, S.; Xu, J. Design of Full Stokes Vector Polarimetry Based on Metasurfaces for Wide-Angle Incident Light. *Photonics* **2023**, *10*, 382.
https://doi.org/10.3390/photonics10040382

**AMA Style**

Liu S, Zhang Z, Cheng J, Wang X, Sun S, Xu J. Design of Full Stokes Vector Polarimetry Based on Metasurfaces for Wide-Angle Incident Light. *Photonics*. 2023; 10(4):382.
https://doi.org/10.3390/photonics10040382

**Chicago/Turabian Style**

Liu, Songjie, Zejun Zhang, Jingxuan Cheng, Xiyin Wang, Shixiao Sun, and Jing Xu. 2023. "Design of Full Stokes Vector Polarimetry Based on Metasurfaces for Wide-Angle Incident Light" *Photonics* 10, no. 4: 382.
https://doi.org/10.3390/photonics10040382