Fano-resonant THz metamaterials for biological detection Theoretical details

用于生物檢測(cè)的衰變太赫茲超材料理論細(xì)節(jié)

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.

將EM輻射耦合到亞波長(zhǎng)超材料結(jié)構(gòu)中的可能性對(duì)低于衍射極限的光物質(zhì)相互作用具有顯著影響。 為了將入射的強(qiáng)輻射集中在平面超材料中弄诲，它們應(yīng)該能夠以與高場(chǎng)濃度相關(guān)的高Q因子維持尖銳的共振帽氓。 這種類(lèi)型的超材料是光學(xué)薄的，具有適度的Q因子床嫌，因?yàn)樗鼈儾痪哂杏糜诟逧M場(chǎng)限制的內(nèi)部共振體積。 此外，它們的諧振單元通常牢固地耦合到自由空間瘪菌，這又導(dǎo)致高輻射損耗皿桑。

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.

已經(jīng)提出了幾種等離子體超材料毫目，以打破多像素單位晶格的對(duì)稱(chēng)性，并證明沿著太赫茲對(duì)光譜具有尖銳的不對(duì)稱(chēng)Fano共振[147-151]诲侮。在金屬亞波長(zhǎng)系統(tǒng)中镀虐，在強(qiáng)光束照射下，寬磁偶極子和窄磁暗墓敌鳎可以成功地誘發(fā)Fano共振[152,153]刮便。可以定制多像素天線(xiàn)和耦合的納米顆粒绽慈，以維持相當(dāng)大的吸收截面恨旱，并在結(jié)構(gòu)的電容性開(kāi)口和隔片中增強(qiáng)魯棒的場(chǎng)強(qiáng)辈毯。按照慣例，F(xiàn)ano共振的特征是狹窄的光譜透明窗口搜贤，在該窗口中谆沃，散射得到抑制，吸收得到增強(qiáng)[154-156]仪芒。從理論上講唁影，在多像素THz晶胞中，F(xiàn)ano共振是不對(duì)稱(chēng)的光譜特征掂名，這是由寬光譜線(xiàn)形的窄共振產(chǎn)生的相長(zhǎng)干涉和相消干涉引起的[149-158]据沈。盡管太赫茲平面等離子超材料在設(shè)計(jì)有源和無(wú)源器件方面都有廣泛的應(yīng)用，但這些結(jié)構(gòu)的Q因子Fano線(xiàn)形較差饺蔑，這限制了它們的傳感能力和調(diào)制性能锌介。在以下小節(jié)中，我們簡(jiǎn)要回顧了將Fano共振THz超材料用于生物傳感的最新進(jìn)展猾警。

Thin-film sensing application?薄膜傳感應(yīng)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.

泛音共振超材料已廣泛用于從氣體檢測(cè)[159]和早期癌癥生物標(biāo)志物識(shí)別[160]到環(huán)境RI擾動(dòng)傳感[149,161–163]的傳感應(yīng)用掏湾。使用Fano諧振平臺(tái)的原因在于其窄（高質(zhì)量）和非對(duì)稱(chēng)線(xiàn)形的出色靈敏度，可應(yīng)對(duì)介質(zhì)介電常數(shù)的微小變化肿嘲。更確切地說(shuō)融击，特別感興趣的是已廣泛用于各種傳感原理（例如薄分析物層和原子級(jí)石墨烯單層檢測(cè)）的Fano共振THz等離子體超材料。為了評(píng)估固有不同共振的性能雳窟，Singh等人尊浪。 [148]已經(jīng)研究和比較了在太赫茲等離子體元系統(tǒng)中兩種類(lèi)型的共振（四極和法諾模式）的傳感性能。這是通過(guò)將厚度為1 mm的薄分析物層引入已制成樣品中來(lái)實(shí)現(xiàn)的封救∧吹樱可以證明，通過(guò)打破超材料諧振器結(jié)構(gòu)的對(duì)稱(chēng)性誉结，可以成功激發(fā)低損耗鹅士，高Q四極桿和Fano諧振，從而形成不對(duì)稱(chēng)的裂環(huán)諧振器惩坑。高Q共振支持入射的太赫茲波與特定分析物之間的強(qiáng)相互作用掉盅。低損耗高Q超材料的尖銳共振使得能夠檢測(cè)到非常小的光譜位移，該光譜位移是由于分析物與超分子的裂隙中的高濃度電場(chǎng)（電場(chǎng)）的相互作用較少而產(chǎn)生的以舒。圖6a表示超材料的微觀圖像（10 mm到10 mm陣列中的Al諧振器）趾痘，其中d表示距中心的較小間隙位移。圖6b和圖6c分別示出了沿x軸和y軸入射的電場(chǎng)的四極和法諾共振電流分布的示意圖蔓钟，以及具有高Q因子的共振的相應(yīng)激發(fā)永票。圖6d和e中標(biāo)繪的歸一化傳輸幅度說(shuō)明了Q因子分別為65和28的四極和Fano共振的形成。利用窄線(xiàn)形，當(dāng)分析物層沉積在超材料的頂部時(shí)侣集，平面超材料具有超敏感傳感的強(qiáng)大潛力键俱。圖6d和e中的曲線(xiàn)說(shuō)明了存在16毫米分析物層時(shí)共振模位置的變化。

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.

接下來(lái)世分，他們還研究了感應(yīng)共振矩對(duì)分析物層存在的敏感性方妖。在圖6f中，演示了在4 mm的恒定厚度下四極桿共振的位移罚攀，其中分析物的RI不同。通過(guò)將分析物的RI從n = 1更改為1.6雌澄，四極共振頻率的總偏移為15 GHz斋泄。如圖6g所示，對(duì)于Fano共振已經(jīng)重復(fù)了類(lèi)似的過(guò)程镐牺，在這種情況下炫掐，總偏移為22 GHz。對(duì)于6 mm的恒定厚度睬涧，共振位移是分析物RI變化的函數(shù)募胃。因此，四極和Fano共振靈敏度分別為23.9和36.7 GHz / RIU畦浓。繼續(xù)進(jìn)行到更薄的分析物層（厚度為1 mm）痹束，超材料對(duì)基板厚度20 mm以下的兩個(gè)共振都極為敏感，如圖6i所示讶请。對(duì)于1 mm厚的分析物祷嘶，F(xiàn)ano共振的靈敏度提高了兩倍，四極共振的靈敏度提高了3倍夺溢。該實(shí)驗(yàn)明確表明论巍，與傳統(tǒng)的四極模式相比，F(xiàn)ano線(xiàn)形對(duì)分析物層的存在具有相當(dāng)大的敏感性风响。

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]對(duì)于許多更薄的薄膜（即原子上薄的石墨烯單層）嘉汰，在最近的工作中，探索了使用高Q費(fèi)諾共振等離子超材料進(jìn)行薄膜感測(cè)（此處為石墨烯單層）的可能性状勤。圖7a示出了沉積在630lm厚的p型硅襯底上的200nm厚的Al晶胞的示意圖鞋怀。晶胞的橫向尺寸為L(zhǎng) = 60 lm，周期為P = 75 lm持搜。單位單元中最敏感的區(qū)域是充當(dāng)電容器的兩個(gè)間隙（間隙寬度g = 3 lm接箫，線(xiàn)寬W = 6 lm），其中天線(xiàn)中心的電容性間隙之一已固定并且位置為了破壞結(jié)構(gòu)的對(duì)稱(chēng)性朵诫，另一個(gè)間隙的最大位移偏移了距離d辛友，這是激發(fā)Fano共振的黃金法則。在圖7b中，顯示了在沉積石墨烯單層之后的平面超材料的顯微圖像废累。圖7c和d中顯示了在一組不同的超材料上有和沒(méi)有石墨烯層的平面超材料的透射光譜邓梅，圖7c和d中的不對(duì)稱(chēng)度從0到20 lm變化。在不存在單層石墨烯的情況下邑滨，分別在f_0.5和_0.7 THz處誘導(dǎo)了兩個(gè)不同的共振日缨，分別對(duì)應(yīng)于Fano線(xiàn)形和偶極模式。從技術(shù)上講掖看，通過(guò)增加不對(duì)稱(chēng)參數(shù)（d）匣距，可以以幾乎穩(wěn)定的諧振頻率顯著增強(qiáng)Fano模式強(qiáng)度（由凹陷和峰之間的斜率陡度定義）。圖7e和f展示了在頂部不存在和存在石墨烯的情況下哎壳，對(duì)于變化的不對(duì)稱(chēng)分量毅待，在Fano浸入頻率下的電場(chǎng)增強(qiáng)。如所描繪的归榕，對(duì)于不存在石墨烯的情況尸红，間隙中的場(chǎng)濃度都非常穩(wěn)定。通過(guò)在超材料的頂部引入石墨烯單層刹泄，由于裂隙兩端的相反電荷的復(fù)合效應(yīng)外里，電場(chǎng)得到了顯著抑制，從而導(dǎo)致透射振幅譜中的Fano共振消失特石。 盅蝗。隨著電容間隙的增加，樣品中的場(chǎng)集中會(huì)增強(qiáng)姆蘸，從而導(dǎo)致Fano共振幅度發(fā)生明顯變化风科。研究：評(píng)論

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.

最終，為了評(píng)估整體透射率的變化并比較Fano傾斜和明亮的偶極共振之間的差異乞旦，我們可以查看光譜在所有頻率下的透射率（DT）的變化贼穆。 圖7g繪制了在不同不對(duì)稱(chēng)度下的Fano共振超材料的傳輸變化（DT）。 DT的強(qiáng)烈變化發(fā)生在三個(gè)區(qū)域兰粉，分別位于_0.5 THz附近的Fano共振最小值故痊，F(xiàn)ano共振峰值在0.55 THz附近和明亮的偶極子模式在0.7 THz附近。 在Fano諧振下的DT值比偶極模式大得多玖姑，并且隨著距離d的增加愕秫，在最佳非對(duì)稱(chēng)參數(shù)d = 15 lm時(shí)，最大DT放大到31％焰络。

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.

圖6（a）具有詳細(xì)幾何尺寸的太赫茲不對(duì)稱(chēng)開(kāi)環(huán)超材料陣列的顯微圖像戴甩。 （b）激發(fā)四極共振并將分析物光刻膠層沉積在超材料頂部的晶胞。 （c）激發(fā)Fano共振的晶胞闪彼。 （d）和（e）分別具有和不具有分析物層的四極和法諾共振的歸一化透射光譜甜孤。 當(dāng)將具有不同RI的4 mm恒定厚度分析物涂覆在超材料上時(shí)协饲，通過(guò)數(shù)值獲得的（f）四極共振和（g）Fano共振的振幅透射光譜。 （h）四極和Fano共振隨RI的變化而變化缴川。 i）在硅襯底厚度減小的情況下茉稠，用1 mm厚的變化RI的分析物模擬的Fano和四極共振靈敏度[148]。 美國(guó)物理研究所2014年版權(quán)所有把夸。

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.

圖7（a）晶胞的藝術(shù)形象而线。 （b）石墨烯沉積后d = 20 lm的超材料的顯微圖像。 比例尺為75流明恋日。 帶有“ d”的各種值的等離子超材料的測(cè)量（c）和模擬（d）振幅透射光譜膀篮，其為入射電場(chǎng)定向的石墨烯沉積之前（紅色曲線(xiàn)）和之后（藍(lán)色曲線(xiàn)）頻率的函數(shù) 沿x軸（如插圖所示）。 （e）岂膳，（f）分別在石墨烯沉積之前和之后以Fano模式頻率模擬的電場(chǎng)增強(qiáng)誓竿。 （g）太赫茲超材料的模擬透射率變化DT作為不對(duì)稱(chēng)參數(shù)d的函數(shù)[160]。 皇家化學(xué)學(xué)會(huì)2016年版權(quán)所有闷营。

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).

圖8（a）具有以下尺寸的雙層太赫茲超材料的示意圖和幾何形狀：l = 60 lm，w = 6 lm知市，g = 3 lm傻盟。陣列的周期固定為75 lm，間隔表示為t嫂丙。 （b）雙層SRR對(duì)不同分析物折射率的透射光譜娘赴。 （c）x_和x +的頻移與分析物的折射率的關(guān)系[158]。美國(guó)光學(xué)學(xué)會(huì)（OSA）版權(quán)所有2017跟啤。 （d）诽表，（e）分別使用等離激元晶胞從柔性元傳感器的頂面和底面進(jìn)行感應(yīng)的示意圖。 （f）制造的諧振器陣列的顯微圖像隅肥，插圖中顯示了單位晶胞的幾何參數(shù)竿奏，如下所示：d = 20，w = 6腥放，l = 60泛啸，g = 3，平方周期為75 lm（g） 秃症，（h）在樣品的頂部和底部分別有100 nm厚的分析物膜的模擬的Fano共振頻率偏移候址。金屬諧振器的厚度為200 nm。 （i）制成樣品的圖像顯示出柔韌性和堅(jiān)固性[162]种柑。美國(guó)物理研究所（APS）版權(quán)所有2017岗仑。

Biochemical sensing application?生化感測(cè)應(yīng)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

在本小節(jié)中，我們將重點(diǎn)關(guān)注Fano共振等離子體激元THz超材料對(duì)環(huán)境擾動(dòng)的敏感性聚请。在需要的驅(qū)使下荠雕，已經(jīng)研究并引入了幾種等離激元亞波長(zhǎng)平臺(tái)，以增強(qiáng)Q因子和感應(yīng)Fano線(xiàn)形的窄度。類(lèi)似于參考號(hào)舞虱。 164欢际，在各種方向上設(shè)計(jì)的裂環(huán)諧振器已被視為太赫茲等離子體元傳感器技術(shù)的基本平臺(tái)。最近矾兜，Du等人损趋。 [165]已經(jīng)分析了高Q超材料的無(wú)RI標(biāo)簽感測(cè)特性。圖8a展示了設(shè)計(jì)的雙層超材料椅寺，其中每個(gè)方形單像素元素的邊長(zhǎng)為l = 60 mm浑槽，寬度為w = 6 mm，電容間隙為g = 3 mm返帕，單位晶胞陣列的周期為固定在p = 75毫米桐玻。平面超分子陣列在厚度為10 mm的聚酰亞胺間隔層（RI為1.6 + 0.02i）[166]的兩側(cè)圖案化為200 nm Al層。每個(gè)單元由兩個(gè)垂直空間分隔的諧振器組成荆萤，這些諧振器具有相同的幾何形狀（相同的構(gòu)造）和相同的方向（相同的配置）镊靴。在這項(xiàng)研究中，Du和同事從質(zhì)上了解了定制的Fano共振超材料的光譜特性链韭。使用以下公式給出的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

偏竟，研究人員擬合了透射光譜，如圖8b所示敞峭。誘導(dǎo)出兩個(gè)明顯的模式踊谋，分別與暗法諾傾角（x_）和亮模式（x +）相關(guān)。該圖還顯示了在S參數(shù)曲線(xiàn)（| S21 |）中約1.1 THz的Fano凹陷的形成旋讹，用于改變周?chē)h(huán)境的RI殖蚕。通過(guò)增加介質(zhì)的索引，可以看到Fano浸入位置發(fā)生普遍且連續(xù)的紅移沉迹。使用下式獲得兩個(gè)共振的圖8c中的標(biāo)準(zhǔn)靈敏度：

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是真空中的光速睦疫，f0是共振頻率，n表示在元芯片表面上沉積的分析物的RI鞭呕。就標(biāo)準(zhǔn)靈敏度而言笼痛，較低（x_）和較高（x +）共振頻率的4毫米厚分析物的相應(yīng)靈敏度分別為2.49_104 nm / RIU和3.26_104 nm / RIU。對(duì)于實(shí)際的傳感應(yīng)用琅拌，如先前部分所述缨伊，傳統(tǒng)的FOM通常用于評(píng)估定制光學(xué)傳感器的性能。圖8d展示了針對(duì)不同分析物厚度的目標(biāo)模式（x_和x +）的FOM进宝。有趣的是刻坊，盡管x_的靈敏度略小于x +的靈敏度，但x_的FOM卻大了大約十倍党晋。在FOM方面谭胚，x_共振的卓越性能在于徐块，由于經(jīng)典的明亮模式，該黑暗共振的線(xiàn)寬（Dk）窄得多灾而。

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.

在不斷尋求先進(jìn)且精確的等離激元生物傳感器的過(guò)程中胡控，最近，針對(duì)新型生物傳感應(yīng)用引入了靈活的Fano共振THz元傳感器旁趟。 Srivastava等昼激。 [167]利用裂環(huán)諧振器單元電池，它位于RI = 1.72锡搜，厚度為25 mm的柔性聚酰亞胺基板上（見(jiàn)圖8e）橙困。錯(cuò)開(kāi)開(kāi)口環(huán)諧振器中的電容性開(kāi)口會(huì)破壞幾何對(duì)稱(chēng)性，從而導(dǎo)致明顯的Fano傾斜角的激發(fā)耕餐，從而強(qiáng)烈耦合到y(tǒng)極化輻射凡傅。 Fano共振的激發(fā)對(duì)電容間隙位置的強(qiáng)烈依賴(lài)性已在本綜述的前一部分中進(jìn)行了解釋。電場(chǎng)在諧振器電容間隙附近的限制為傳感應(yīng)用提供了一個(gè)極好的平臺(tái)肠缔。作為概念證明夏跷，研究人員在給定的RI下沉積了分析物層，并在柔性超材料的兩側(cè)均存在高折射率物質(zhì)的情況下測(cè)量了感應(yīng)共振的位移（圖8e和f）明未。圖8g是超材料的顯微圖像槽华。 Srivastava和他的隊(duì)友在兩種情況下僅用100 nm厚的分析物觀察到了Fano共振位置的明顯光譜偏移，表現(xiàn)出雙表面感應(yīng)（圖8h和i）亚隅。在圖8j中示出了所制造的柔性結(jié)構(gòu)硼莽。實(shí)驗(yàn)和數(shù)值驗(yàn)證表明庶溶，該柔性超材料具有很大的潛力煮纵，可用于折射傳感目的，并且所測(cè)得的最大靈敏度分別報(bào)告為頂表面和底表面分別約為84 GHz / RIU和6 GHz / RIU偏螺。