# Design of Narrow-Band Absorber Based on Symmetric Silicon Grating and Research on Its Sensing Performance

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{1}is the height of the Si gate. h

_{2}is the thickness of the Au thin layer. w is the thickness of the Si gate. After systematic optimization, the optimal parameters of the absorber are as follows: A1 = 3100 nm, h

_{1}= 630 nm, h

_{2}= 90 nm, w = 260 nm, A2 = 700 nm. For simulating the optical performance of the perfect absorber, we use the FDTD method [49,50,51]. The incident light source is TM (The direction of the electric field is along the X-axis) plane light wave, and the direction of the light source is perpendicular to the grating surface. The X-axis and Y-axis directions are periodic boundary conditions; the Z-axis direction is a perfectly matched layer boundary condition.

## 3. Results

_{0}sinα + 2πi/A1. In which k

_{0}and k(i) are the wave vectors of incident light and order, i = 0, ±1, ±2... ±n, α is the incident angle. With proper parameters, the order (+1, −1) can connect the plane propagating surface plasmon waves. It can be seen that the coupling resonance between the surface plasmon mode and the incident light leads to strong absorption. Through the wave vector matching condition [52], the coupling process can be expressed as Equations (1) and (2):

_{eff}represents the effective refractive index of the surface plasmon model. λ(+1) and the λ(−1) all mean resonance wavelength. In the case of vertical incidence, α = 0 and λ(+1) = λ(−1), so only one absorption peak occurs. As shown in Figure 3, it is the wave vector matching diagram of the structure.

_{eff}. The influence of the change in the spacing width of the Si grating on the redshift of the peak wavelength is much smaller than that of the period length (In Figure 5B). Similarly, the absorption peak first increases and then decreases with the change of the spacing between the two secondary gratings. The half-height and half-width of the absorption peak decrease with the increase of the Si grating spacing width, which is because the smaller the Si grating spacing is, the stronger the excited electric field is and the greater the displacement current is generated, thus widening the half-height and half-width. In addition, we also note that the absorbance of the absorption peak does not decrease significantly (about 2%) when the Si grating spacing is 540 nm because the Si grating spacing corresponding to the maximum absorbance changed within a certain range, which would not have a great impact on the absorbance.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**A**) Three-dimensional diagram of symmetrical Si grating structure and (

**B**) section diagram of element structure.

**Figure 2.**Spectrogram of reflectance (R), transmittance (T), and absorbance (A) under the normal incidence of symmetrical Si grating.

**Figure 4.**The distribution of electric field (

**A**) and magnetic field (

**B**) on the XOZ section at λ = 3750 nm of the symmetric Si grating. The grating is outlined with white lines.

**Figure 5.**Periodic parameters of symmetrical Si grating (

**A**) and spacing parameters of the two secondary gratings (

**B**).

**Figure 6.**Parameters of the width of symmetrical Si grating (

**A**) and thickness of symmetrical Si grating (

**B**).

**Figure 8.**(

**A**) Absorbance spectrogram and (

**B**) relationship between RI and the corresponding peak wavelength of symmetrical Si grating under RI change. K and S represent the slope of the straight line and the sensitivity of the structure, respectively.

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**MDPI and ACS Style**

Pan, M.; Huang, H.; Chen, W.; Li, S.; Xie, Q.; Xu, F.; Wei, D.; Fang, J.; Fan, B.; Cai, L. Design of Narrow-Band Absorber Based on Symmetric Silicon Grating and Research on Its Sensing Performance. *Coatings* **2021**, *11*, 553.
https://doi.org/10.3390/coatings11050553

**AMA Style**

Pan M, Huang H, Chen W, Li S, Xie Q, Xu F, Wei D, Fang J, Fan B, Cai L. Design of Narrow-Band Absorber Based on Symmetric Silicon Grating and Research on Its Sensing Performance. *Coatings*. 2021; 11(5):553.
https://doi.org/10.3390/coatings11050553

**Chicago/Turabian Style**

Pan, Miao, Huazhu Huang, Wenzhi Chen, Shuai Li, Qinglai Xie, Feng Xu, Dongwei Wei, Jun Fang, Baodian Fan, and Lihan Cai. 2021. "Design of Narrow-Band Absorber Based on Symmetric Silicon Grating and Research on Its Sensing Performance" *Coatings* 11, no. 5: 553.
https://doi.org/10.3390/coatings11050553