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基于连续域束缚态(bound states in the continuum, BIC)的全介质超表面因其具有超高品质因子(quality factor, Q), 能有效地增强光与物质的相互作用, 而被广泛应用于微纳生物传感领域. 本文提出了一种基于BIC的矩形全介质双聚体超表面, 并采用有限元方法进行仿真模拟以及使用时域耦合模进行理论分析. 针对超表面中两长方对的角度、折射率、宽度和高度等参数, 分别设计了4种系统破缺方式, 均实现了对称保护型BIC(symmetry-protected BIC, SP-BIC)向准BIC(quasi-BIC, QBIC)模式的转变, 获得的最大Q因子高达1.75 × 104. 引入相同的不对称参数后, 4种调控方式下的超表面灵敏度几乎处于同一水平, 而传感品质因数(figure of merit, FOM)的差异可达103数量级. 在同一调控方式下, 当破缺参数绝对值相等时, 正向破缺的超表面的灵敏度和FOM都高于负向破缺. 经优化调节后, 超表面的灵敏度和FOM分别达到了395 nm/RIU和3502 RIU–1, 其综合性能指标已优于大部分现有研究. 该超表面为生物、医疗领域的传感检测提供了有效手段, 同时该研究为基于BIC的折射率传感器的设计提供了新思路.All-dielectric metasurfaces based on bound states in the continuum (BIC) are widely used in the field of micro-nano biosensors due to their ultra-high quality factor (Q), which can effectively enhance the interaction between light and matter. In this paper, a rectangular all-dielectric dimer metasurface based on BIC is proposed. The finite element method is used for simulation, and time-domain coupled mode theory is employed for theoretical analysis. For the parameters of the two rectangular components in the metasurface, such as their angles, refractive indices, widths, and heights, four different symmetry-breaking modes are designed (
Fig. 1 ). All of these modes realize the transformation from symmetry-protected BIC (SP-BIC) to quasi-BIC (QBIC), with the maximum Q factor reaching 1.75 × 104 (Fig. 2 ). These four breaking methods cover the current common SP-BIC breaking methods and provide choice for designing devices. After introducing the same asymmetric parameters, the QBIC resonance excited by the metasurface under the four control modes is dominated by magnetic dipoles (Fig. 6 ). The sensitivity of the designed sensor device is almost at the same level, while the difference in figure of merit (FOM) can reach three orders of magnitude (Fig. 7 ). In addition, under the same control mode, the sensitivity and FOM of the metasurface with positive breaking are higher than those with negative breaking when the absolute values of the breaking parameters are equal (Fig. 8 ). After optimization and adjustment, the sensitivity and FOM of the metasurface reach 395 nm/RIU and 3502 RIU–1, respectively, and its comprehensive performance index is better than those in most of existing studies (Table 1 ). The metasurface provides an effective means for sensing detection in the biological and medical fields. At the same time, this research offers a new insight into the design of refractive index sensors based on BIC.
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Keywords:
- all-dielectric metasurface /
- bound states in the continuum /
- refractive index sensing /
- sensitivity
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图 1 矩形全介质超表面 (a) 阵列结构示意图; (b) 元胞xy二维平面图; (c) 4种破缺方式下的元胞结构; (d) 时域耦合模式理论模型示意图
Fig. 1. Rectangular all-dielectric metasurface: (a) Schematic diagram of the array structure; (b) two-dimensional planar graph of the unit cell in the xy-plane; (c) cell structures under four types of breaking modes; (d) schematic diagram of the time-coupled model theory.
图 2 Mode Ⅰ调谐下超表面的仿真结果与理论分析 (a) 元胞的xy二维平面图; (b) 不同对称破缺角度θ下的仿真透射光谱与拟合曲线; (c) Q因子和共振波长随旋转角度θ的变化关系; (d) Q因子与不对称参数α的关系; (e), (f) θ = 6°, θ = 12°时QBIC共振处硅棒中心xz截面电场分布
Fig. 2. Simulation results and theoretical analysis of the metasurface tuned by Mode I: (a) Two-dimensional planar graph of the unit cell in the xy-plane; (b) the simulated transmission spectra and fitting curves at different symmetry breaking angles θ; (c) relationship between the Q factor and the resonance wavelength as a function of the rotation angle θ; (d) relationship between the Q factor and the asymmetric parameter α; (e)–(f) when θ = 6° and θ = 12°, the electric field distribution in the xz section at the center of the silicon rod at QBIC resonance.
图 3 Mode Ⅱ调谐下超表面的仿真结果与理论分析 (a) 元胞的xy二维平面图; (b) 不同对称破缺折射率Δn下的仿真透射光谱与拟合曲线; (c) Q因子和共振波长随折射率Δn的变化关系; (d) Q因子与不对称参数α的关系; (e)—(h) Δn = ±0.3, Δn = ±0.4时QBIC共振处硅棒中心xz截面电场分布
Fig. 3. Simulation results and theoretical analysis of the metasurface tuned by Mode II: (a) Two-dimensional plane graph of the unit cell in the xy-plane; (b) simulated transmission spectra and fitting curves under different symmetry-breaking refractive index Δn; (c) relationship between the Q factor and the resonance wavelength as a function of the refractive index Δn; (d) relationship between the Q factor and the asymmetric parameter α; (e)–(h) when Δn = ±0.3 and Δn = ±0.4, the electric field distribution in the xz cross section at the center of the silicon rod at QBIC resonance.
图 4 Mode Ⅲ调谐下超表面的仿真结果与理论分析 (a) 元胞的xy二维平面图; (b) 不同对称破缺宽度Δw下的仿真透射光谱与拟合曲线; (c) Q因子和共振波长随宽度Δw的变化关系; (d) Q因子与不对称参数α的关系; (e)—(h) Δw = ±30 nm, Δw = ±40 nm时QBIC共振处硅棒中心xz截面电场分布
Fig. 4. Simulation results and theoretical analysis of the metasurface tuned by Mode III: (a) Two-dimensional planar graph of the unit cell in the xy-plane; (b) simulated transmission spectra and fitting curves under different symmetry-breaking widths Δw; (c) relationship between the Q factor and the resonance wavelength as a function of the width Δw; (d) relationship between the Q factor and the asymmetric parameter α; (e)–(h) when Δw = ±30 nm and Δw = ±40 nm, the electric field distribution in the xz cross section at the center of the silicon rod at QBIC resonance.
图 5 Mode Ⅳ调控下超表面的仿真结果与理论分析 (a) 元胞的xy二维平面图; (b) 不同对称破缺高度Δh下的仿真透射光谱与拟合曲线; (c) Q因子和共振波长随宽度Δh的变化关系; (d) Q因子与不对称参数α的关系; (e)—(h) Δh = ±30 nm, Δh = ±40 nm时QBIC共振处硅棒中心xz截面电场分布
Fig. 5. Simulation results and theoretical analysis of the metasurface under the control of Mode IV: (a) Two-dimensional planar graph of the unit cell in the xy-plane; (b) simulated transmission spectra and fitting curves at different symmetry-breaking heights Δh; (c) variation of the Q factor and the resonance wavelength as a function of the width Δh; (d) relationship between the Q factor and the asymmetric parameter α; (e)–(h) when Δh = ±30 nm and Δh = ±40 nm, the electric field distribution in the xz section at the center of the silicon rod at QBIC resonance.
图 6 多极子分解对QBIC机理的分析. Mode Ⅰ调控 (a) 不同极矩散射功率; (b) 元胞内部xy截面下电场分布情况; (c) 不对称参数为0.1时, 4种破缺方式下的多极矩贡献情况
Fig. 6. Multipole decomposition analysis of the QBIC mechanism. Mode I control: (a) Different polar scattering powers; (b) the electric field distribution in the xy section of the cell; (c) when the asymmetry parameter is 0.1, the multipole moment contributions under the four breaking modes.
图 7 当α = 0.1时, 对4种破缺方式下超表面的传感性能进行研究 (a) 4种破缺方式下QBIC共振的透射光谱; (b) Mode Ⅰ破缺模式下, 超表面在不同折射率传感介质中的透射谱; (c) 4种破缺模式下的QBIC共振波长与环境折射率的关系; (d) 4种破缺模式下的灵敏度; (e) 4种破缺模式下的FOM
Fig. 7. When the asymmetry parameter α = 0.1, the sensing performance of the metasurface under four damage modes is studied: (a) Transmission spectra of QBIC resonance under four different breaking modes; (b) transmission spectra of the metasurface in different refractive index sensing media in Mode I broken mode; (c) relationship between the QBIC resonance wavelength and the ambient refractive index in four broken modes; (d) sensitivity under four breaking modes; (e) FOM values under four breaking modes.
图 8 正、负向破缺对超表面传感性能的影响. Mode Ⅲ调控 (a) 传感性能与破缺程度Δw的关系; (b)—(e) Δw = ±40 nm时, QBIC共振处柱体内部的xy平面和表面的xz端面的电场分布. Mode Ⅳ调控 (f) 传感性能与破缺程度Δh的关系; (g)—(j) Δh = ±40 nm时, QBIC共振处柱体内部的xy平面和表面的xz端面的电场分布
Fig. 8. Effect of positive and negative breaks on the sensing performance of the metasurface. Mode III regulation: (a) Relationship between sensing performance and Δw; (b)—(e) when Δw = ±40 nm, the electric field distribution in the xy plane inside the cylinder and on the xz end face of the surface at QBIC resonance. Mode IV regulation: (f) Relationship between sensing performance and Δh; (g)—(j) when Δh = ±40 nm, the electric field distribution in the xy plane inside the cylinder and on the xz end face of the surface at QBIC resonance.
表 1 矩形全介质双聚体超表面传感性能与前期研究的对比
Table 1. Comparison of sensing performance of the rectangular all-dielectric dimer metasurface with previous studies.
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