The double-notched circular disk multifunctional metasurface sensor based on the theory of bound states in the continuum
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摘要:
本文提出并制备了一种基于石英基底的双缺口圆盘硅阵列全介质多功能超表面光学传感器。通过引入呈45°分布的双非对称缺口打破结构对称性，成功将无辐射的理想连续域束缚态（BIC）态转化为极强光局域场的高Q值准BIC态，并于
1617 nm处激发了超窄线宽Fano传感谐振峰。仿真结果表明，谐振峰的主要贡献极子为磁偶（MD）极子，品质因子（Q ）理论最高可达1.6×105，FOM最高可达36350 ；其具有363.5 nm/RIU的折射率传感与51.96 pm/ °C的温度传感性能。此外，可通过改变入射光的偏振态对超表面谐振峰的调制深度进行调控。由传感实验可得，其不同折射率液体的灵敏度为268.7 nm/RIU。本结构可广泛应用于环境监测、生物医学检测及偏振型光开关控制等领域，并为多参数超表面传感器设计提供参考，扩展了超表面在实际传感应用中的多功能性。Abstract:The integration of metasurfaces with optical sensors can effectively reduce the sensor volume and enhance its capability for electromagnetic field manipulation. This paper proposes and fabricates an all-dielectric multifunctional metasurface optical sensor based on a double-notched circular disk silicon array on a quartz substrate. By introducing two asymmetrically arranged gaps oriented at 45° to break the structural symmetry successfully converted the non-radiative ideal bound state in the continuum (BIC) is into a high-Q quasi-BIC state with strongly localized optical fields, and an ultra-narrow linewidth Fano resonance peak at
1617 nm is excited. Simulation results indicate that the resonance peak is predominantly contributed by the magnetic dipole (MD) mode, with a theoretically maximum quality factor (Q) of up to1.6 ×105 and a figure of merit (FOM) reaching36350 . The sensor exhibits a refractive index sensitivity of 363.5 nm/RIU and a temperature sensitivity of 51.96 pm/°C. Furthermore, the modulation depth of the metasurface resonance peak can be controlled by varying the polarization state of the incident light. Experimental analysis demonstrates a sensitivity of 268.7 nm/RIU for liquids with different refractive indices. This structure holds promise for applications in environmental monitoring, biomedical detection, polarization-controlled optical switching, and provides a reference for multi-parameter metasurface sensors, extending the multifunctionality of metasurfaces in practical sensing applications. -
图 1 圆盘双缺口超表面结构。(a) 超表面结构示意图；(b) 单个周期的结构图；(c) 单个周期结构的俯视图
Figure 1. Metasurface structure of the double-notched circular disk. (a) Schematic diagram of the metasurface structure; (b) unit cell geometry; (c) top-view representation of the unit cell
图 2 (a) 所设计超表面的透射光谱；(b) 超表面透射光谱仿真结果（黑色）与Fano拟合曲线（红色）
Figure 2. (a) Transmission spectrum of the designed metasurface; (b) simulated transmission spectrum (black curve) and corresponding Fano fitting curves (red curve)
图 3 不同非对称下的超表面光谱响应与品质因子拟态。(a) 不同非对称δ下超表面的透射光谱；(b) 透射光谱的2D-map；(c)
$\varDelta $ 与品质因子Q之间关系的仿真与拟合结果Figure 3. The spectra response of metasurfaces under different asymmetries and quality factor fitting. (a) Transmission spectra of the metasurface under different asymmetry parameters (δ); (b) two-dimensional map of the transmission spectra as a function of δ; (c) simulated and fitted relationship between spectral shift (
$\varDelta $ ) and quality factor Q
图 4 (a) 对称结构及(b) 非对称结构的多极子分解情况
Figure 4. Multipole decomposition results (a) symmetric metasurface structure and (b) asymmetric metasurface structure
图 5 超表面电磁场分布（白色箭头指示局域场矢量方向；黑色箭头指示等效偶极矩或总场环流方向）。(a) 对称结构x-y平面电场；(b) 对称结构z-x平面磁场；(c) 结构中x-y平面（z=100 nm，蓝色）以及z-x平面（x=0 nm，粉色）的示意图；(d) 非对称结构MD极子示意图；(e) 非对称结构x-y平面电场分布（位移电流环）；(f) 非对称结构z-x平面磁场分布
Figure 5. Electromagnetic field distribution of the metasurface (white arrows indicate the direction of the local field vector; black arrows indicate the direction of the equivalent dipole moment or the total field circulation). Electric field distributions in the x-y plane of (a) symmetric structure and (e) asymmtric structure. Magnetic field in the z-x plane of (b) symmetric structure and (f) asymmetric structure. (c) Schematic illustration showing the x-y plane (z = 100 nm, in blue) and z-x plane (x = 0 nm, in pink) within the metasurface structure. (d) Schematic diagram of MD polaritons in the asymmetric structure Electric field in the x-y plane (displacement current loop) in the asymmetric structure
图 6 超表面透射光谱几何依赖性。(a)~(d) 保持其他参数不变，分别只改变Px、Py、R、h时透射光谱以及超表面传感的性能。（S为折射率传感灵敏度）
Figure 6. Geometric dependence of the transmission spectrum of metasurfaces. (a)-(d) Influence of geometric parameter variations—Px, Py, R, and h—on the transmission spectra and refractive index sensing sensitivity (S), with all other parameters held constant
图 7 超表面折射率传感性能。(a) 改变背景折射率n透射光谱的变化；(b) n对共振峰位置的线性拟合结果
Figure 7. Metasurface refractive index sensing performance. (a) Transmission spectra as a function of background refractive index (n). (b) Linear fitting results of the resonance peak wavelength versus refractive index (n)
图 8 超表面温度传感特性。(a) 不同温度下的透射光谱曲线；(b) 温度传感灵敏度拟合
Figure 8. Temperature sensing characteristics of metasurfaces. (a) Transmission spectra measured at different temperatures. (b) Linear fitting results of temperature sensing sensitivity
图 9 超表面透射光谱偏振特性。(a) 不同偏振角度下超表面的透射光谱曲线；(b) 不同偏振角度下的2D-color map；(c) 不同偏振角度下的电场情况（x-y平面，z=100 nm处）
Figure 9. Polarization characteristics of the transmission spectrum of metasurfaces. (a) Transmission spectra of the metasurface under varying polarization angles. (b) Two-dimensional color map of spectral response as a function of polarization angle. (c) Electric field distribution in the x-y plane at z = 100 nm for different polarization angles
图 10 (a) 超表面工艺流程图及(b) 制备超表面芯片的SEM图像
Figure 10. (a) Process flow chart and SEM images of the fabricated metasurfaces
图 11 折射率传感及偏振敏感实验结果
Figure 11. Experimental results of refractive index sensing and polarization sensitivity
表 1 同类型超表面传感器仿真性能对比
Table 1. Simulation performance comparison of metasurface sensors of the same type
材料 n范围 共振峰位置(nm) Sn(nm/RIU) T范围 ST Qmax FOMmax 偏振可调 参考文献 Si/SiO2 1.33~1.40 1023.65 ,1095.52 ,232 5~50K 63 pm/K 2.6×104 3980 Yes [14] Si/Si3N4 1.33~1.40 2409.3 ,2667.0 746 0~100 °C 54 pm/ °C 54757 18650 None [16] LiNbO3/SiO2 1.0~1.40 1230.19 241 None None 105 3×105 None [19] TiO2/SiO2 1.31~1.35 936, 1013 ,1010 ,1052 288 None None 6900 888 Yes [20] Si/SiO2 1.0~1.08 1038.75 ,1168.44 325 None None 34176 10156 None [27] Si/SiO2 1.0~2.0 1617 363.5 20~80 °C 51.96 pm/ °C 1.6×105 36350 Yes This work 
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表 2 实验测试中使用的不同类型待测溶液及其折射率标准值
Table 2. The different types of test solutions used in the experimental tests and their standard refractive index values
Solute
typeDeionized
waterAnhydrous
ethanol50% Ethanol 6% Sucrose 10% Sucrose 20% Sucrose 5% NaCl 10% NaCl 20% NaCl n 1.33 1.3618 1.3584 1.3452 1.3532 1.3727 1.3377 1.3487 1.3707
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