Fano-resonant THz metamaterials for biological detection Theoretical details
用于生物检测的衰变太赫兹超材料理论细节
The possibility to couple EM radiation into subwavelength metamaterial structures has pronounced influence on light-matter interactions below the diffraction limit. In order to concentrate the incident intense radiation in planar metamaterials, they should be able to sustain sharp resonances with high Q-factors associated with high field concentrations. This type of metamaterials are optically thin, possessing modest Q-factors since they do not have an inner resonating volume for high EM field confinement. Moreover, their resonating units are usually strongly coupled to free space which in turn causes high radiation losses.
将EM辐射耦合到亚波长超材料结构中的可能性对低于衍射极限的光物质相互作用具有显着影响。 为了将入射的强辐射集中在平面超材料中，它们应该能够以与高场浓度相关的高Q因子维持尖锐的共振。 这种类型的超材料是光学薄的，具有适度的Q因子，因为它们不具有用于高EM场限制的内部共振体积。 此外，它们的谐振单元通常牢固地耦合到自由空间，这又导致高辐射损耗。
Several plasmonic metamaterials have been proposed to break the symmetry of multipixel unit cells and demonstrated sharp asymmetric Fano resonances along the THz to optical spectra [147–151]. In metallic subwavelength systems, Fano resonance can be successfully induced by a broad magnetic dipole and a narrow magnetic dark mode under intense beam illumination [152,153]. Multipixel antennas and coupled nanoparticles, can be tailored to sustain substantial absorption cross sections, with robust field enhancements in the capacitive openings and spacers of the structures. Conventionally, Fano resonance can be characterized as a narrow spectral transparency window where scattering is suppressed and absorption is enhanced [154–156]. Theoretically, in the multipixel THz unit cells, a Fano resonance is an asymmetric spectral feature, arising from the constructive and destructive interference of a narrow resonance with a broad spectral lineshape [149–158]. Although THz planar plasmonic metamaterials have a wide range of applications either in designing active and passive devices, these structures suffer from poor Q-factor Fano-lineshapes which limits their sensing capabilities and modulation performance. In the following subsections, we briefly review the recent advances in the use of Fano-resonant THz metamaterials for biosensing purposes.
已经提出了几种等离子体超材料，以打破多像素单位晶格的对称性，并证明沿着太赫兹对光谱具有尖锐的不对称Fano共振[147-151]。在金属亚波长系统中，在强光束照射下，宽磁偶极子和窄磁暗模可以成功地诱发Fano共振[152,153]。可以定制多像素天线和耦合的纳米颗粒，以维持相当大的吸收截面，并在结构的电容性开口和隔片中增强鲁棒的场强。按照惯例，Fano共振的特征是狭窄的光谱透明窗口，在该窗口中，散射得到抑制，吸收得到增强[154-156]。从理论上讲，在多像素THz晶胞中，Fano共振是不对称的光谱特征，这是由宽光谱线形的窄共振产生的相长干涉和相消干涉引起的[149-158]。尽管太赫兹平面等离子超材料在设计有源和无源器件方面都有广泛的应用，但这些结构的Q因子Fano线形较差，这限制了它们的传感能力和调制性能。在以下小节中，我们简要回顾了将Fano共振THz超材料用于生物传感的最新进展。
Thin-film sensing application 薄膜传感应用
Fano-resonant metamaterials have broadly been utilized for sensing applications from gas detection [159] and early stage cancer biomarker identification [160] to environmental RI perturbations sensing [149,161–163]. The interest to employ Fano-resonant platforms stems from the outstanding sensitivity of its narrow (high-quality) and asymmetric lineshape to minor variations in the dielectric permittivity of media. More precisely, of particular interest are Fano-resonant THz plasmonic metamaterials that have extensively been employed for various sensing principles such as detection of thin analyte layer and atomically-thin graphene monolayer. To evaluate the performance of inherently different resonances, Singh et al. [148] have studied and compared the sensing performance of two type of resonances (Quadrupolar and Fano modes) in a THz plasmonic metasystem. This was accomplished by introducing thin analyte layer with a thickness of 1 mm to the fabricated samples. It is verified that low loss, high-Q quadrupole, and Fano resonances can be successfully excited by breaking the symmetry of the metamaterial resonator structure, thus forming an asymmetric split ring resonator. The high-Q resonances support strong interaction between the incident THz wave and a specific analyte. The sharp resonances of a low-loss high-Q metamaterial enable the detection of very small spectral shifts that occurs from the low quantity of analyte interaction with the highly concentrated electric field (E-field) in the split gaps of the metamolecules. Fig. 6a represents the microscopic image of the metamaterial (Al resonators in 10 mm _ 10 mm arrays), where d represents the lower gap displacement from the center. Fig. 6b and c illustrate the schematics of the quadrupole and Fano resonance current distribution for incident E-field along the x-axis and y-axis, respectively and the corresponding excitation of resonances with high-Q factors. The plotted normalized transmission amplitudes in Fig. 6d and e demonstrate the formation of quadrupolar and Fano resonances with the Q-factor of 65 and 28, respectively. Taking advantage of narrow lineshapes, the planar metamaterial has strong potential for ultrasensitive sensing when an analyte layer is deposited on top of the metamaterial. The profiles in Fig. 6d and e illustrate shift in the position of the resonant modes for the presence of 16 mm of analyte layer.
泛音共振超材料已广泛用于从气体检测[159]和早期癌症生物标志物识别[160]到环境RI扰动传感[149,161–163]的传感应用。使用Fano谐振平台的原因在于其窄（高质量）和非对称线形的出色灵敏度，可应对介质介电常数的微小变化。更确切地说，特别感兴趣的是已广泛用于各种传感原理（例如薄分析物层和原子级石墨烯单层检测）的Fano共振THz等离子体超材料。为了评估固有不同共振的性能，Singh等人。 [148]已经研究和比较了在太赫兹等离子体元系统中两种类型的共振（四极和法诺模式）的传感性能。这是通过将厚度为1 mm的薄分析物层引入已制成样品中来实现的。可以证明，通过打破超材料谐振器结构的对称性，可以成功激发低损耗，高Q四极杆和Fano谐振，从而形成不对称的裂环谐振器。高Q共振支持入射的太赫兹波与特定分析物之间的强相互作用。低损耗高Q超材料的尖锐共振使得能够检测到非常小的光谱位移，该光谱位移是由于分析物与超分子的裂隙中的高浓度电场（电场）的相互作用较少而产生的。图6a表示超材料的微观图像（10 mm到10 mm阵列中的Al谐振器），其中d表示距中心的较小间隙位移。图6b和图6c分别示出了沿x轴和y轴入射的电场的四极和法诺共振电流分布的示意图，以及具有高Q因子的共振的相应激发。图6d和e中标绘的归一化传输幅度说明了Q因子分别为65和28的四极和Fano共振的形成。利用窄线形，当分析物层沉积在超材料的顶部时，平面超材料具有超敏感传感的强大潜力。图6d和e中的曲线说明了存在16毫米分析物层时共振模位置的变化。
In continue, they also studied the sensitivity of the induced resonant moments to the presence of an analyte layer. In Fig. 6f, the shift in the quadrupole resonance for a constant thickness of 4 mm with different RI of the analyte is demonstrated. The total shift in the quadrupole resonance frequency by changing the RI of analyte from n = 1 to 1.6 is found to be 15 GHz. The similar process has been repeated for the Fano resonance, as shown in Fig. 6g, and the total shift in this case is observed to be 22 GHz. The resonance shift as a function of RI variations of the analyte for a constant thickness of 4 mm is depicted in Fig. 6h. Accordingly, the quadrupole and Fano resonances sensitivities turned out to be 23.9 and 36.7 GHz/RIU, respectively. Proceeding down to thinner analyte layers (with a thickness of 1 mm), the metamaterial becomes extremely sensitive to both resonances below substrate thickness of 20 mm as shown in Fig. 6i. The sensitivity of Fano resonance gets enhanced by a factor of two and of the quadrupole resonance by a factor of three for 1 mm thick analyte. This experiment explicitly shows the substantial sensitivity of Fano lineshape to the presence of an analyte layer in comparison to the traditional quadrupolar mode.
接下来，他们还研究了感应共振矩对分析物层存在的敏感性。在图6f中，演示了在4 mm的恒定厚度下四极杆共振的位移，其中分析物的RI不同。通过将分析物的RI从n = 1更改为1.6，四极共振频率的总偏移为15 GHz。如图6g所示，对于Fano共振已经重复了类似的过程，在这种情况下，总偏移为22 GHz。对于6 mm的恒定厚度，共振位移是分析物RI变化的函数。因此，四极和Fano共振灵敏度分别为23.9和36.7 GHz / RIU。继续进行到更薄的分析物层（厚度为1 mm），超材料对基板厚度20 mm以下的两个共振都极为敏感，如图6i所示。对于1 mm厚的分析物，Fano共振的灵敏度提高了两倍，四极共振的灵敏度提高了3倍。该实验明确表明，与传统的四极模式相比，Fano线形对分析物层的存在具有相当大的敏感性。
For much thinner films (i.e. atomically thin graphene monolayer), in a recent work, Li and colleagues [160] have explored the possibility of thin-film sensing (here graphene monolayer) using high-Q Fano-resonant plasmonic metamaterials. Fig. 7a demonstrates schematic of the 200 nm-thick Al unit cell deposited on a 630 lm-thick p-type silicon substrate. The lateral dimension of the unit cell is L = 60 lm with a periodicity of P = 75 lm. The most sensitive region in the unit cells is the two gaps that behave as capacitors (gap width g = 3 lm, linewidth W= 6 lm), where the one of the capacitive gap at the center of the antenna has been fixed and the position of the other gap was shifted by a distance d in order to break the symmetry of the structure, as a golden rule for the excitation of a Fano resonance. In Fig. 7b, the microscopic image of the planar metamaterial after deposition of the graphene monolayer is exhibited. The measured transmission spectra of the planar metamaterial with and without the graphene layer on a set of different metamaterial samples are shown in Fig. 7c and d, in which the degree of asymmetry was varied from 0 to 20 lm. In the absence of the monolayer graphene, two distinct resonances induced at f_0.5 and _0.7 THz corresponding with the Fano lineshape and dipolar mode, respectively. Technically, by increasing the asymmetry parameter (d), the Fano mode strength (which defines by steepness of the slope between the dip and the peak) is remarkably enhanced with an almost stable resonance frequency. Fig. 7e and f demonstrate the E-field enhancement at the Fano dip frequency for varying asymmetry component in the absence and presence of graphene on top. As depicted, for the absence of graphene, the field concentrations in the gaps are all robust. By introducing the graphene monolayer on top of the metamaterial, the E-field is dramatically suppressed due to the recombination effect of the opposite charges at the two ends of the split gap, giving rise to the disappearance of the Fano resonance in the transmission amplitude spectra. As the capacitive gap increases, the field concentration in the samples enhances leading to distinct changes in the Fano resonance amplitude. RESEARCH: Review
Li和同事[160]对于许多更薄的薄膜（即原子上薄的石墨烯单层），在最近的工作中，探索了使用高Q费诺共振等离子超材料进行薄膜感测（此处为石墨烯单层）的可能性。图7a示出了沉积在630lm厚的p型硅衬底上的200nm厚的Al晶胞的示意图。晶胞的横向尺寸为L = 60 lm，周期为P = 75 lm。单位单元中最敏感的区域是充当电容器的两个间隙（间隙宽度g = 3 lm，线宽W = 6 lm），其中天线中心的电容性间隙之一已固定并且位置为了破坏结构的对称性，另一个间隙的最大位移偏移了距离d，这是激发Fano共振的黄金法则。在图7b中，显示了在沉积石墨烯单层之后的平面超材料的显微图像。图7c和d中显示了在一组不同的超材料上有和没有石墨烯层的平面超材料的透射光谱，图7c和d中的不对称度从0到20 lm变化。在不存在单层石墨烯的情况下，分别在f_0.5和_0.7 THz处诱导了两个不同的共振，分别对应于Fano线形和偶极模式。从技术上讲，通过增加不对称参数（d），可以以几乎稳定的谐振频率显着增强Fano模式强度（由凹陷和峰之间的斜率陡度定义）。图7e和f展示了在顶部不存在和存在石墨烯的情况下，对于变化的不对称分量，在Fano浸入频率下的电场增强。如所描绘的，对于不存在石墨烯的情况，间隙中的场浓度都非常稳定。通过在超材料的顶部引入石墨烯单层，由于裂隙两端的相反电荷的复合效应，电场得到了显着抑制，从而导致透射振幅谱中的Fano共振消失。 。随着电容间隙的增加，样品中的场集中会增强，从而导致Fano共振幅度发生明显变化。研究：评论
Ultimately, in order to evaluate the change in the overall transmission and compare the difference between the Fano dip and bright dipolar resonance, one can look at the variation in transmission (DT) as defined above at all frequencies in the spectra. The transmission variations (DT) of the Fano-resonant metamaterial at different levels of asymmetry is plotted in Fig. 7g. The strong variation of DT happens in three areas located at the Fano resonance minimum around _0.5 THz, the Fano resonance peak near 0.55 THz, and the bright dipolar mode near 0.7 THz. The value of DT at the Fano resonance is much larger than that of the dipolar mode, and with the increase in the distance d, the maximum DT amplified to 31% at the optimal asymmetric parameter of d = 15 lm.
最终，为了评估整体透射率的变化并比较Fano倾斜和明亮的偶极共振之间的差异，我们可以查看光谱在所有频率下的透射率（DT）的变化。 图7g绘制了在不同不对称度下的Fano共振超材料的传输变化（DT）。 DT的强烈变化发生在三个区域，分别位于_0.5 THz附近的Fano共振最小值，Fano共振峰值在0.55 THz附近和明亮的偶极子模式在0.7 THz附近。 在Fano谐振下的DT值比偶极模式大得多，并且随着距离d的增加，在最佳非对称参数d = 15 lm时，最大DT放大到31％。
FIGURE 6 (a) Microscopic image of the terahertz asymmetric split-ring metamaterial array with the detailed geometric dimensions. (b) The unit cell where the quadrupole resonance is excited and the analyte photoresist layer is deposited on top of the metamaterial. (c) The unit cell where the Fano resonance is being excited. (d) and (e) The normalized transmission spectra of the quadrupole and Fano resonances with and without the analyte layer, respectively. Numerically obtained amplitude transmission spectra of (f) quadrupole resonance and (g) Fano resonances when 4 mm constant thickness analyte with different RIs is coated on the metamaterial. (h) Quadrupole and Fano resonances shift with the change in RIs. i) Simulated sensitivities of Fano and quadrupole resonances with 1 mm thick analyte of varying RIs at decreasing thicknesses of Si substrate [148]. Copyright 2014, American Institute of Physics.
图6（a）具有详细几何尺寸的太赫兹不对称开环超材料阵列的显微图像。 （b）激发四极共振并将分析物光刻胶层沉积在超材料顶部的晶胞。 （c）激发Fano共振的晶胞。 （d）和（e）分别具有和不具有分析物层的四极和法诺共振的归一化透射光谱。 当将具有不同RI的4 mm恒定厚度分析物涂覆在超材料上时，通过数值获得的（f）四极共振和（g）Fano共振的振幅透射光谱。 （h）四极和Fano共振随RI的变化而变化。 i）在硅衬底厚度减小的情况下，用1 mm厚的变化RI的分析物模拟的Fano和四极共振灵敏度[148]。 美国物理研究所2014年版权所有。
FIGURE 7 (a) Artistic image of the unit cell. (b) Microscopic image of the metamaterial with d = 20 lm after the graphene deposition. The scale bar is 75 lm. Measured (c) and simulated (d) amplitude transmission spectra of the plasmonic metamaterial with various values of “d” as a function of the frequency before (red curve) and after (blue curve) the graphene deposition with the incident E-field oriented along the x-axis (shown in the insets). (e), (f) Simulated E-field enhancement at the Fano mode frequency before and after the graphene deposition, respectively. (g) Simulated transmission variation DT of the THz metamaterial as a function of the asymmetry parameter d [160]. Copyright 2016, Royal Society of Chemistry.
图7（a）晶胞的艺术形象。 （b）石墨烯沉积后d = 20 lm的超材料的显微图像。 比例尺为75流明。 带有“ d”的各种值的等离子超材料的测量（c）和模拟（d）振幅透射光谱，其为入射电场定向的石墨烯沉积之前（红色曲线）和之后（蓝色曲线）频率的函数 沿x轴（如插图所示）。 （e），（f）分别在石墨烯沉积之前和之后以Fano模式频率模拟的电场增强。 （g）太赫兹超材料的模拟透射率变化DT作为不对称参数d的函数[160]。 皇家化学学会2016年版权所有。
FIGURE 8 (a) Schematic image and geometry of bilayer THz metamaterial with following dimensions l = 60 lm, w = 6 lm, and g = 3 lm. The periodicity for the array is fixed at 75 lm and the spacing is denoted as t. (b) The transmission spectra of a bilayer SRR for different refractive index of analyte. (c) The frequency shifts of x_ and x+ versus refractive index of analyte [158]. Copyright 2017, American Optical Society (OSA). (d), (e) Schematic illustration of sensing from the top and bottom surfaces of the flexible metasensor using a plasmonic unit cell, respectively. (f) Microscopic image of the fabricated resonator array with geometric parameters of the unit cell shown in the inset as follows: d = 20, w = 6, l = 60, g = 3, and a square period of 75 lm (g), (h) Simulated Fano resonance frequency shift with a 100 nm thick analyte film on the top and bottom surfaces of the sample, respectively. The thickness of the metallic resonators is 200 nm. (i) Images of the fabricated sample showing flexibility and robustness [162]. Copyright 2017, American Institute of Physics (APS).
图8（a）具有以下尺寸的双层太赫兹超材料的示意图和几何形状：l = 60 lm，w = 6 lm，g = 3 lm。阵列的周期固定为75 lm，间隔表示为t。 （b）双层SRR对不同分析物折射率的透射光谱。 （c）x_和x +的频移与分析物的折射率的关系[158]。美国光学学会（OSA）版权所有2017。 （d），（e）分别使用等离激元晶胞从柔性元传感器的顶面和底面进行感应的示意图。 （f）制造的谐振器阵列的显微图像，插图中显示了单位晶胞的几何参数，如下所示：d = 20，w = 6，l = 60，g = 3，平方周期为75 lm（g） ，（h）在样品的顶部和底部分别有100 nm厚的分析物膜的模拟的Fano共振频率偏移。金属谐振器的厚度为200 nm。 （i）制成样品的图像显示出柔韧性和坚固性[162]。美国物理研究所（APS）版权所有2017。
Biochemical sensing application 生化感测应用
In this subsection, we focus on the sensitivity of Fano-resonant plasmonic THz metamaterial to the environmental perturbations. Driven by the need, several plasmonic subwavelength platforms have been examined and introduced to enhance the Q-factor and narrowness of the induced Fano lineshapes. Similar to Ref. 164, the engineered split ring resonators in various orientations have been considered as fundamental platforms for THz plasmonic metasensor technology. Very recently, Du et al. [165] have analyzed the sensing properties of a high-Q metamaterial for RI label-free sensing purpose. Fig. 8a illustrates the designed bilayer metamaterial, in which each square singlepixel element has a side length of l = 60 mm, a width of w = 6 mm, a capacitive gap of g = 3 mm, and the periodicity of unit cell array is fixed at p = 75 mm. The planar metamolecule arrays are patterned as 200 nm Al layers on both sides of a polyimide spacer layer (with the RI of 1.6 + 0.02i) [166] with thickness of 10 mm. Each unit cell consists of two vertically spatially separated resonators with identical geometry (same constitution) as well as the same orientation (same configuration). In this study, Du and co-workers qualitatively understood the spectral properties of the tailored Fano-resonant metamaterial. Using the Fano formula given by:
公式
在本小节中，我们将重点关注Fano共振等离子体激元THz超材料对环境扰动的敏感性。在需要的驱使下，已经研究并引入了几种等离激元亚波长平台，以增强Q因子和感应Fano线形的窄度。类似于参考号。 164，在各种方向上设计的裂环谐振器已被视为太赫兹等离子体元传感器技术的基本平台。最近，Du等人。 [165]已经分析了高Q超材料的无RI标签感测特性。图8a展示了设计的双层超材料，其中每个方形单像素元素的边长为l = 60 mm，宽度为w = 6 mm，电容间隙为g = 3 mm，单位晶胞阵列的周期为固定在p = 75毫米。平面超分子阵列在厚度为10 mm的聚酰亚胺间隔层（RI为1.6 + 0.02i）[166]的两侧图案化为200 nm Al层。每个单元由两个垂直空间分隔的谐振器组成，这些谐振器具有相同的几何形状（相同的构造）和相同的方向（相同的配置）。在这项研究中，Du和同事从质上了解了定制的Fano共振超材料的光谱特性。使用以下公式给出的Fano公式：
公式
, the researchers fitted the transmission spectra, as plotted in Fig. 8b. Two pronounced modes are induced correlating with the dark Fano dip (x_) and bright mode (x+). This graph also shows the formation of a Fano dip around 1.1 THz in the S-parameter profile (|S21|) for alterations in the RI of the surrounding environment. One can see a general and continuous red-shift in the position of Fano dip by increasing the index of the media. The standard sensitivities in Fig. 8c of both resonances are obtained using the following formula:
公式
，研究人员拟合了透射光谱，如图8b所示。诱导出两个明显的模式，分别与暗法诺倾角（x_）和亮模式（x +）相关。该图还显示了在S参数曲线（| S21 |）中约1.1 THz的Fano凹陷的形成，用于改变周围环境的RI。通过增加介质的索引，可以看到Fano浸入位置发生普遍且连续的红移。使用下式获得两个共振的图8c中的标准灵敏度：
公式
in which c is the velocity of light in vacuum, f0 is the resonance frequency, and n represents the RI of the deposited analyte on the surface of the metachip. In terms of standard sensitivity, the corresponding sensitivities for 4 mm thick analyte of the lower (x_) and higher (x+) resonance frequencies are 2.49 _ 104 nm/RIU and 3.26 _ 104 nm/RIU, respectively. For the practical sensing application, as mentioned in prior sections, the traditional FOM is usually applied to evaluate the performance of the tailored optical sensor. Fig. 8d demonstrates the FOM of the targeted modes (x_ and x+) for different analyte thicknesses. Interestingly, although the sensitivity of x_ is slightly smaller than that of x+, the FOM of x_ about ten times larger. The superior performance in terms of FOM for x_ resonance lies in the fact that the linewidth (Dk) of this dark resonance is much narrower thank the classical bright mode.
其中c是真空中的光速，f0是共振频率，n表示在元芯片表面上沉积的分析物的RI。就标准灵敏度而言，较低（x_）和较高（x +）共振频率的4毫米厚分析物的相应灵敏度分别为2.49_104 nm / RIU和3.26_104 nm / RIU。对于实际的传感应用，如先前部分所述，传统的FOM通常用于评估定制光学传感器的性能。图8d展示了针对不同分析物厚度的目标模式（x_和x +）的FOM。有趣的是，尽管x_的灵敏度略小于x +的灵敏度，但x_的FOM却大了大约十倍。在FOM方面，x_共振的卓越性能在于，由于经典的明亮模式，该黑暗共振的线宽（Dk）窄得多。
In the ongoing search for advanced and accurate plasmonic biosensors, recently, flexible Fano-resonant THz metasensors have been introduced for novel biosensing applications. Srivastava et al. [167] utilized split-ring resonator unit cell residing on a flexible polyimide substrate with the RI of n = 1.72 and thickness of 25 mm (see Fig. 8e). Dislocating the capacitive openings in the split-ring resonator breaks the geometrical symmetry, resulting in the excitation of a pronounced Fano dip, which strongly couples to the y-polarized radiation. The strong dependency of the excitation of Fano resonances to the capacitive gaps position was explained in previous section of this review. The confinement of the E-field in the vicinity of the capacitive gaps of resonators provides an excellent platform for sensing applications. As a proof of concept, the researchers deposited an analyte layer with a given RI and measured the shifts in the induced resonances in the presence of high-index substance on both sides of the flexible metamaterial (Fig. 8e and f). Fig. 8g is the microscopic image for the metamaterial. Srivastava and teammates observed a distinct spectral shift in the Fano resonance position in both scenarios with only a 100 nm thick analyte, exhibiting the dualsurface sensing (Fig. 8h and i). The fabricated flexible structure is shown in Fig. 8j. It is experimentally and numerically verified that the flexible metamaterial has a great potential to be employed for refractometric sensing purposes, and the measured maximum sensitivity is reported around 84 GHz/RIU and 6 GHz/ RIU for top and bottom surfaces, respectively.
在不断寻求先进且精确的等离激元生物传感器的过程中，最近，针对新型生物传感应用引入了灵活的Fano共振THz元传感器。 Srivastava等。 [167]利用裂环谐振器单元电池，它位于RI = 1.72，厚度为25 mm的柔性聚酰亚胺基板上（见图8e）。错开开口环谐振器中的电容性开口会破坏几何对称性，从而导致明显的Fano倾斜角的激发，从而强烈耦合到y极化辐射。 Fano共振的激发对电容间隙位置的强烈依赖性已在本综述的前一部分中进行了解释。电场在谐振器电容间隙附近的限制为传感应用提供了一个极好的平台。作为概念证明，研究人员在给定的RI下沉积了分析物层，并在柔性超材料的两侧均存在高折射率物质的情况下测量了感应共振的位移（图8e和f）。图8g是超材料的显微图像。 Srivastava和他的队友在两种情况下仅用100 nm厚的分析物观察到了Fano共振位置的明显光谱偏移，表现出双表面感应（图8h和i）。在图8j中示出了所制造的柔性结构。实验和数值验证表明，该柔性超材料具有很大的潜力，可用于折射传感目的，并且所测得的最大灵敏度分别报告为顶表面和底表面分别约为84 GHz / RIU和6 GHz / RIU。