基于Fano共振的全介质超表面双参数传感器
Currently, the performance of refractive-index sensors based on metal metasurfaces is limited by their low quality factors, due to significant Ohmic losses in the metal material. Sensors based on all-dielectric metasurfaces can overcome these disadvantages. However, most dielectric refractive-index sensors neglect the impact of temperature fluctuations. Hence, they experience crosstalk between the refractive index and environmental temperature. In this study, we design a dual-parameter sensor based on the “θ” shaped all-dielectric silicon metasurface. Two Fano resonance peaks are generated by adding an empty hole to break the symmetry of the periodic units in the structure. The sensor can simultaneously measure both the refractive index and temperature by measuring the wavelengths of the two Fano resonances.
In this study, we use the commercial multiphysics simulation software COMSOL to numerically solve Maxwell equations for an all-dielectric dual-parameter metasurface sensor. We set periodic boundary conditions along the x- and y- directions and place two ports above and below the metasurface structure in the z-direction. An incident plane wave, polarized along the x-axis, is set at the upper port. The zeroth-order plane-wave transmittance is calculated at the lower port. To prevent undesirable reflections, perfectly matched layers (PMLs) are introduced outside each port. The maximum finite-element mesh size is set to 1/10 of the minimum incident wavelength. The scanned wavelength range is 1000?1200 nm. The relationship between the Fano resonance and quasi-bound state in the continuum (QBIC) is analyzed by varying the structural asymmetry parameter of the metasurface and calculating the corresponding quality factors.
The designed structure exhibits high values of sensitivity, quality factor (Q), and figure of merit (FOM). Two Fano resonances can be generated by breaking the symmetry of the periodic unit structure. The first Fano resonance peak is a QBIC with an ultrahigh Q in the near-infrared band (Fig.3). The near-field distributions at the resonance show the existence of electric quadrupole and toroidal dipole resonances in the two Fano resonances, indicating distinct formation mechanisms for each Fano resonance peak (Fig.5). We obtain the refractive index sensitivities of the two Fano resonance peaks, by fixing the temperature at room temperature and calculating the resonance wavelengths for different environmental refractive indices (Fig.7). Similarly, we set the environmental refractive index to 1.33 (the refractive index of water) and calculate the resonance wavelengths at different temperatures, to obtain the temperature sensitivities of the two Fano resonances (Fig.9). When the environmental refractive index and temperature change simultaneously, the two Fano resonance wavelengths shift. By calculating the product of the inverse sensitivity matrix (whose elements are the previously calculated refractive index and temperature sensitivities) and a column vector composed of the shifts of the two resonance wavelengths, the change in the environmental refractive index and temperature can be inferred. This approach enables dual-parameter sensing of both the refractive index and temperature. For six sets of randomly preset values of the change in the environmental refractive index and temperature, the matrix theory predictions exhibit small errors of less than ±5% relative to the preset values (Table 1), confirming the feasibility of dual-parameter sensing. Regarding the impact of the structural fabrication error, the simulation results show that for fabrication errors ranging from -2 nm to 2 nm, the resultant changes in the two resonance wavelengths remain within 5 nm (Fig.10).
In this study, we propose a dual-parameter sensor based on the “θ”-shaped dielectric silicon metasurface. The sensor design includes an empty hole, which introduces a structural asymmetry and generates two Fano resonances. This unique feature enables the simultaneous sensing of the environmental temperature and refractive index, eliminating any crosstalk between the two parameters. By conducting calculations to optimize the structural parameters such as hole radius and offset, we obtain refractive index sensitivities of 278.9 nm/RIU and 230.0 nm/RIU for the first and second Fano resonances, respectively. Additionally, we obtain temperature sensitivities of 18.86 pm/℃ and 42.71 pm/℃, respectively. The maximum figure of merit and Q are 9387 and 9735, respectively. The near-field analysis reveals the existence of electric quadrupole and toroidal dipole resonances in the two Fano resonances, indicating different formation mechanisms for each Fano resonance peak. When the environmental refractive index or temperature changes, the resonance wavelengths are shifted. These shifts follow different rules for the two Fano resonance peaks, enabling the dual-parameter sensing of the refractive index and temperature using a sensitivity matrix. The verification results show that the matrix theory predictions exhibit small errors (less than ±5%) relative to the preset values of the environmental refractive index and temperature change. The simulation results show that for fabrication errors ranging from -2 nm to 2 nm, the resultant changes in both the resonance wavelengths are within 5 nm.
1 引言
由近场中离散态和连续态之间干涉引起的Fano共振可以有效抑制系统的辐射衰减[1],并且可以引起更强的场增强,获得更精细的光谱,因此Fano共振可用于设计高灵敏度的光学传感器。近些年,研究人员在不同领域提出了众多基于超表面的光学器件,包括光学滤波器[2]和折射率传感器[3]等。目前,大多数基于金属超表面的折射率传感器,由于金属材料会产生较大的欧姆损耗,其品质因子一般较低[4-5],而基于全介质超表面的折射率传感器,恰恰能够克服上述缺点。
2018年,Liu等[6]提出了一种基于硅裂环的超表面,在透射谱中只有一个Fano共振峰,无法同时实现高精度的双参数测量。2019年,Liu等[7]提出一种双Fano共振峰的偏振不敏感折射率传感器,其灵敏度为186.96 nm·RIU-1。2020年,王梦梦等[8]提出一种等离子体折射率纳米传感器,由直波导耦合开口方环谐振器组成,其灵敏度为1125.7 nm·RIU-1,品质因子为30.01。2021年,Qi等[9]提出了一种由沉积在金对称分裂环中的金纳米棒构成的等离子体纳米腔,通过改变纳米棒的旋转角度或长度,可以优化纳米棒的辐射损耗,其灵敏度达到1090 nm·RIU-1,但其优值(FOM)只有60。2022年,Song等[10]提出了一种全介质空心超表面,其灵敏度达到160 nm·RIU-1。Samadi等[11]提出了一种基于互补裂环谐振器的双Fano共振峰折射率传感超表面,通过破坏结构对称性,可以在近红外窗口中激发具有超高品质因子的连续域中的准束缚态(QBIC),具有超高优值(FOM大于105),其灵敏度达到155 nm·RIU-1。陈颖等[12]提出基于硅缺口盘单谐振器的全介质超表面微流体折射率传感器,灵敏度达到400.36 nm·RIU-1,品质因子为1252.3。但上述传感器大多忽略了温度波动的影响,不能应对环境中折射率和温度之间的串扰。
利用连续域中的束缚态(BIC)可以实现高品质因子(Q)的共振。BIC最初的概念起源于量子力学[13],之后在流体力学、声学和光学[14]中被观察到。BIC只存在于没有辐射损失的理想结构中,它的特征是谐振线宽为零,Q无穷大,因此BIC与远场辐射之间不存在耦合,无法由外部激励源激励产生。对于对称保护型BIC,其存在于具有空间对称性(例如镜像对称)的结构中,通过打破对称性,对称保护型BIC能够转化为QBIC[15],其具有有限大的Q,因此能够由外部激励源激励产生。QBIC的优势在于,通过减小不对称参数,在理论上能够可控地获得任意大的Q。可见,BIC模式是理想化的状态,它只有转化为QBIC模式才具有现实意义,从而实现光与物质相互作用的增强。
本文提出了一种基于双Fano共振的“θ”形全介质超表面双参数传感器,通过破坏周期性单元结构的对称性,产生了光谱对比度分别为71.4%和99.4%的两个独立的Fano共振峰,其中第一个Fano峰为近红外波段具有超高品质因子的QBIC。基于这两个Fano共振峰的传感器可实现液体、气体折射率以及周围环境温度的双参数测量。利用商用多物理场仿真软件COMSOL对该传感器进行了折射率和温度的双参数测量的模拟仿真,结果显示,该传感器在波长1036.5 nm和1155.8 nm处可分别达到278.9 nm·RIU-1和230.0 nm·RIU-1的折射率灵敏度,对温度的灵敏度分别为18.86 pm·℃-1和42.71 pm·℃-1,可以实现对折射率和温度的同时测量。
2 超表面共振特性的分析和结构参数的确定
图 1. “θ”形折射率、温度双参数传感器结构示意图。(a)超表面的整体示意图;(b)超表面周期的示意图;(c)超表面周期的俯视图
Fig. 1. Structural diagram of “θ”-shape refractive index and temperature dual-parameter sensor. (a) Overall diagram of metasurface; (b) schematic of metasurface period; (c) top view of metasurface period
文献[16]指出环形偶极子(TD)共振可以明显减小辐射损耗,从而形成一种高Q的光学共振,能极大增强光与物质的相互作用。后文的分析表明,本文所提出的“θ”形全介质硅超表面周期结构能够形成TD共振。同时,通过引入空孔破坏周期单元结构的对称性,能够形成QBIC。上述TD共振与QBIC形成了双Fano共振峰,其中Fano共振是由离散态和连续态之间的干涉形成的,其光谱曲线具有非对称的线型。
光谱对比度(
式中:
式中:
当r=60 nm,d=50 nm时,对传感器进行波长扫描仿真,
图 2. 超表面加入不对称空孔前(虚线)、后(实线)的透射光谱对比
Fig. 2. Comparison of transmission spectrum of metasurface with (solid line) and without (dotted line) asymmetric air hole
从
改变空孔半径r(分别取50、60、70 nm)和偏移量d(分别取20、30、40、50 nm),透射率谱的计算结果如
图 4. 超表面结构的透射率曲线。(a)r=50 nm;(b)r=60 nm;(c)r=70 nm
Fig. 4. Transmissivity curves of metasurface structures. (a) r=50 nm; (b) r=60 nm; (c) r=70 nm
为了进一步研究两个Fano共振峰的形成机理,接下来利用近场分布讨论共振模式的特性。定义归一化电场强度和归一化磁场强度分别为|
图 5. 谐振波长处的电磁场分布。(a)λ=1036.5 nm,z=t/2;(b)λ=1155.8 nm,z=t/2;(c)λ=1036.5 nm,z=t/2;(d)λ=1155.8 nm, x=0
Fig. 5. Electromagnetic field distributions at resonant wavelengths. (a) λ=1036.5 nm, z=t/2; (b) λ=1155.8 nm, z=t/2; (c) λ=1036.5 nm, z=t/2; (d) λ=1155.8 nm, x=0
3 超表面传感性能的分析
当超表面结构上方环境中被测物质的折射率和温度同时发生变化时,通过测量两个Fano共振峰的波长,可实现对折射率和温度的双参数传感,有效避免环境中折射率和温度之间的串扰,下面具体分析。
图 6. 不同n下的透射率曲线。(a)Dip 1;(b)dip 2
Fig. 6. Transmissivity curves under different n. (a) Dip 1; (b) dip 2
图 7. 当n从1.33变为1.40时dip 1和dip 2的共振波长与折射率依赖关系的线性拟合。(a)Dip 1;(b)dip 2
Fig. 7. Linear fitting of resonance wavelength as a function of refractive index for dip 1 and dip 2 when n changes from 1.33 to 1.40. (a) Dip 1; (b) dip 2
表 1. 折射率和温度双参数传感的矩阵理论预测结果( 和 )和设定值( 和 )之间的对比
Table 1. Comparison among matrix-theory prediction results ( and ) and preset values ( and ) for refractive index and temperature dual-parameter sensing
|
表 2. 不同超表面结构传感性能的对比
Table 2. Comparison of sensing performance of different metasurface structures
|
当传感器用于环境温度传感时,以
图 8. 不同温度下的透射率曲线。(a)Dip 1;(b)dip 2
Fig. 8. Transmissivity curves under different temperatures. (a) Dip 1; (b) dip 2
图 9. 共振波长随温度变化的线性拟合。(a)Dip 1;(b)dip 2
Fig. 9. Linear fitting of resonant wavelength as a function of temperature. (a) Dip 1; (b) dip 2
基于上述结果,利用两个Fano共振峰的共振波长与待测物质的折射率和周围环境温度的线性依赖特性,可以实现折射率和温度的双参数传感测量。
双参数传感器可以用灵敏度矩阵(
式中:
式中:
根据
利用
接下来验证双参数传感器能够同时测量环境折射率和温度,本文展示了6组随机数据的计算结果,如
本文提出的“θ”形全介质硅超表面的双参数传感器,考虑其在实际加工中不可避免地会产生加工尺寸误差。在原尺寸大小w=150 nm,R1=300 nm,r=60 nm的基础上,同时改变上述三个变量的大小,仿真其在-2~2 nm误差范围内对双重Fano共振峰位置的影响。仿真结果如
图 10. 谐振波长随结构尺寸绝对误差变化的曲线
Fig. 10. Resonance wavelength versus absolute error of structure size
4 结论
提出了一种“θ”形全介质硅超表面双参数传感器,通过增加空孔破坏结构的对称性,获得了两个Fano共振峰,实现了温度和折射率的同时传感测量,有效避免了环境中折射率和温度的串扰问题。通过仿真计算选择优化空孔半径和偏移量等结构参数,最终得到两个Fano共振峰的折射率传感灵敏度S分别为278.9 nm·RIU-1和230.0 nm·RIU-1,温度传感灵敏度分别为18.86 pm·℃-1和42.71 pm·℃-1,FOM值最大为9387,Q最大为9735。此外,近场分析结果表明,这两个Fano共振中分别存在电四极子共振和环形偶极子共振,表明这两个Fano共振峰的形成机理不同。通过改变被测物质的折射率或温度,均可以改变Fano共振峰的波长,并且共振波长的改变对于两个Fano共振峰呈现不同的规律,从而可实现折射率和温度的双参数传感。所提超表面结构为高品质因子双参数传感器的设计提供了参考。
[1] Limonov M F, Rybin M V, Poddubny A N, et al. Fano resonances in photonics[J]. Nature Photonics, 2017, 11(9): 543-554.
[2] Nguyen V A, Ngo Q M, Le K Q. Efficient color filters based on Fano-like guided-mode resonances in photonic crystal slabs[J]. IEEE Photonics Journal, 2018, 10(2): 2700208.
[3] He Z H, Xue W W, Cui W, et al. Tunable Fano resonance and enhanced sensing in a simple Au/TiO2 hybrid metasurface[J]. Nanomaterials, 2020, 10(4): 687.
[4] Chen X, Fan W H, Yan H. Toroidal dipole bound states in the continuum metasurfaces for terahertz nanofilm sensing[J]. Optics Express, 2020, 28(11): 17102-17112.
[5] Cheng R J, Xu L, Yu X, et al. High-sensitivity biosensor for identification of protein based on terahertz Fano resonance metasurfaces[J]. Optics Communications, 2020, 473: 125850.
[6] Liu G D, Zhai X, Wang L L, et al. A high-performance refractive index sensor based on Fano resonance in Si split-ring metasurface[J]. Plasmonics, 2018, 13(1): 15-19.
[7] Liu H G, Zheng L, Ma P Z, et al. Metasurface generated polarization insensitive Fano resonance for high-performance refractive index sensing[J]. Optics Express, 2019, 27(9): 13252-13262.
[8] 王梦梦, 韵力宇, 王一飞, 等. 基于Fano共振的等离子体折射率纳米传感器[J]. 激光与光电子学进展, 2020, 57(5): 052401.
[9] Qi Z P, Hu G H, Liu B, et al. Plasmonic nanocavity for obtaining bound state in the continuum in silicon waveguides[J]. Optics Express, 2021, 29(6): 9312-9323.
[10] Song S Z, Yu S L, Li H, et al. Ultra-high Q-factor toroidal dipole resonance and magnetic dipole quasi-bound state in the continuum in an all-dielectric hollow metasurface[J]. Laser Physics, 2022, 32(2): 025403.
[11] Samadi M, Abshari F, Algorri J F, et al. All-dielectric metasurface based on complementary split-ring resonators for refractive index sensing[J]. Photonics, 2022, 9(3): 130.
[12] 陈颖, 张敏, 丁志欣, 等. 基于全介质超表面的微流体折射率传感器[J]. 中国激光, 2022, 49(6): 0613001.
[13] von NeumannJ, WignerE P. Über das verhalten von eigenwerten bei adiabatischen prozessen[M]∥Wightman A S. The collected works of Eugene Paul Wigner. Berlin, Heidelberg: Springer, 1993: 294-297.
[14] Plotnik Y, Peleg O, Dreisow F, et al. Experimental observation of optical bound states in the continuum[J]. Physical Review Letters, 2011, 107(18): 183901.
[15] Koshelev K, Lepeshov S, Liu M K, et al. Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum[J]. Physical Review Letters, 2018, 121(19): 193903.
[16] Papasimakis N, Fedotov V A, Savinov V, et al. Electromagnetic toroidal excitations in matter and free space[J]. Nature Materials, 2016, 15(3): 263-271.
[17] Modi K S, Kaur J, Singh S P, et al. Extremely high figure of merit in all-dielectric split asymmetric arc metasurface for refractive index sensing[J]. Optics Communications, 2020, 462: 125327.
[18] Savinov V, Fedotov V A, Zheludev N I. Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials[J]. Physical Review B, 2014, 89(20): 205112.
[19] ZhaoL, WangJ Y, LiH Y, et al. Simultaneous sensing of refractive index and temperature using a symmetry-breaking silicon metasurface with multiple Fano peaks[C]∥2021 IEEE 16th International Conference on Nano/Micro Engineered and Molecular Systems (NEMS), April 25-29, 2021, Xiamen, China. New York: IEEE Press, 2021: 1441-1446.
[20] Chen J, Yuan J, Zhang Q A, et al. Dielectric waveguide-enhanced localized surface plasmon resonance refractive index sensing[J]. Optical Materials Express, 2018, 8(2): 342-347.
[21] 刘海, 任紫燕, 陈聪, 等. 基于Fano共振超表面的多功能传感器设计[J]. 中国激光, 2023, 50(10): 1010001.
Article Outline
南雪莹, 刘会刚, 刘海涛. 基于Fano共振的全介质超表面双参数传感器[J]. 中国激光, 2024, 51(2): 0210002. Xueying Nan, Huigang Liu, Haitao Liu. All‑Dielectric Metasurface Dual‑Parameter Sensor Based on Fano Resonance[J]. Chinese Journal of Lasers, 2024, 51(2): 0210002.