Terahertz plasmonics: The rise of toroidal metadevices towards immunobiosensings

This work reviews fundamentals and the recent state-of-art achievements in the field of plasmonic biosensing based terahertz (THz) spectroscopy. Being nonpoisonous and nondestructive to the human tissues, THz signals offer promising, cost-effective, and real-time biodevices for practical pharmacological applications such as enzyme reaction analysis. Rapid developments in the field of THz plasmonics biosensors and immunosensors have brought many methodologies to employ the resonant subwavelength structures operating based on the fundamental physics of multipoles and asymmetric lineshape resonances. In the ongoing hunt for new and advanced THz plasmonic biosensors, the toroidal metasensors have emerged as excellent alternates and are introduced to be a very promising technology for THz immunosensing applications. Here, we provide examples of recently proposed THz plasmonic metasensors for the detection of thin films, chemical and biological substances. This review allows to compare the performance of various biosensing tools based on THz plasmonic approach and to understand the strategic role of toroidal metasensors in highly accurate and sensitive biosensors instrumentation. The possibility of using THz plasmonic biosensors based on toroidal technology in modern medical and clinical practices has been briefly discussed.

这项工作回顾了基于等离子生物感测的太赫兹（THz）光谱学领域的基础知识和最新技术成就。 THz信号对人体组织无毒无害，可为酶学分析等实用药理应用提供有前途，具有成本效益的实时生物设备。太赫兹等离子生物传感器和免疫传感器领域的飞速发展带来了许多方法来采用基于多极子和非对称线形共振的基本物理学原理工作的共振亚波长结构。在不断寻求新的和先进的THz等离子体生物传感器时，环形超传感器已经作为优秀的替代品出现，并被介绍为THz免疫传感应用中非常有前途的技术。在这里，我们提供了最近提出的用于检测薄膜，化学和生物物质的THz等离子体元传感器的示例。这项审查允许比较基于THz等离子体方法的各种生物传感工具的性能，并了解环形元传感器在高精度和灵敏的生物传感器仪器中的战略作用。简要讨论了在现代医学和临床实践中使用基于环形技术的THz等离子体生物传感器的可能性。

Introduction

Surface plasmon resonances (SPRs) are the coherent d-band electron oscillations, occurring at metal-dielectric interfaces, when exposed with intense light of certain frequencies [1,2]. As a promising counterpart of optical physics and nanophotonics for extreme light confinement and manipulation [3], plasmonics research field has been acknowledged as a motivating principle for developing advanced and practical photonics technologies, devices and applications [4–6]. Possessing a deep fundamental role in tailoring all-optical and optoelectronic devices, plasmonics has enabled designing of efficient photovoltaic devices [7–10], long-decay range hybrid waveguides [4,11,12], ultrafast modulators [13–15], photodetectors and transistors [16–20], polarization beam splitters [21–23], Mach-Zehnder interferometers [24–26], metamaterials [27–32], superlenses [33,34], nanolasers [35–37], quantum devices [38–40], solar water splitting [41,42], biodevices and clinical tools [43–45], etc. For the latter instance, plasmonics is a reliable technology with exquisite  benefits applicable in both in-vitro and in-vivo assays. The subwavelength plasmonic platforms have extensively been utilized for developing several types of label-free diseases diagnosing devices [46–55], cancer and tumor therapies [56–60], targeted drug delivery [61–64], nanowelding [65,66], hyperspectral nano-imaging [67–69], optoacoustic imaging [70,71], real-time pharmacology [72–74], vapor and micro-bubble generation [75– 77], laser nanosurgery [78–80], photothermal heat spectroscopy [81–85], photothermally controlled fluidics [86–89], heatassisted magnetic recording [90–93], and neuron stimulation [94,95]. Extreme localization of SPRs using subwavelength metallic objects leads to robust enhancement in the optical absorption, resulting in thermal heating of the free electron gas via electron– electron scattering in a hundreds of femtoseconds [96]. Of particular interests are the plasmonic biological and biochemical sensors, which possess a vital role in commercial and advanced clinical and pharmaceutical applications [43,44,97,98]. High accuracy, real-time response, being label-free, operating in room-temperature, cost-effective, and fast response, all these advantages prompted researchers to work on enhanced plasmonic biosensors for decades [99,100].

介绍

表面等离子体激元共振（SPR）是相干d波段电子振荡，当暴露于某些频率的强光下时，会发生在金属-电介质界面上[1,2]。作为极有可能的光学物理学和纳米光子学的极限光限制和操纵方法[3]，等离子子学研究领域被认为是开发先进和实用的光子学技术，设备和应用的动力原理[4-6]。 plasmonics在定制全光学和光电设备中具有深远的基础性作用，已使设计高效的光伏设备[7-10]，长衰减范围混合波导[4,11,12]，超快调制器[13-15]，光电探测器和晶体管[16–20]，偏振分束器[21–23]，马赫曾德尔干涉仪[24–26]，超材料[27–32]，超透镜[33,34]，纳米激光[35–37]，量子设备[38–40]，太阳能分水器[41,42]，生物设备和临床工具[43–45]等。对于后一种情况，等离子体技术是一种可靠的技术，在体外和体内均具有出色的益处。体内测定。亚波长等离激元平台已被广泛用于开发几种类型的无标记疾病诊断设备[46-55]，癌症和肿瘤疗法[56-60]，靶向药物输送[61-64]，纳米焊接[65,66] ，高光谱纳米成像[67–69]，光声成像[70,71]，实时药理学[72–74]，蒸汽和微气泡的产生[75–77]，激光纳米外科手术[78–80]，光热热光谱学[81-85]，光热控制流体学[86-89]，热辅助磁记录[90-93]和神经元刺激[94,95]。使用亚波长金属物体将SPR极端地定位会导致光吸收的强烈增强，从而导致自由电子气通过数百飞秒的电子-电子散射而热加热[96]。等离子体生化和生化传感器特别令人感兴趣，它们在商业和先进的临床和制药应用中具有至关重要的作用[43,44,97,98]。高精度，实时响应，无标签，可在室温下运行，具有成本效益和快速响应，所有这些优势促使研究人员致力于增强型等离激元生物传感器的研究已有数十年[99,100]。

Among all plasmonic biodevices, the terahertz (THz) plasmonic structures with the operating bandwidth between the world of transistors and lasers (0.1 THz < f < 10 THz) have received significant attention recently. It should be underlined that the plasmonic terminology has been used to distinguish the reviewed metallic metamaterials and metasensors from the classical nanophotonic platforms. As potential substitutes for traditional optical biosensors, THz spectroscopy has been acknowledged as a promising approach for advanced biological sensing applications with exotic features and advantages that have not been experienced in optical nanostructures [101]. THz plasmonic biodevices facilitate on-site detection, low-invasiveness, nondestructive, non-poisonous interaction with biological tissues, and high signal to noise (S/N) ratio [102]. In addition, the vibrational modes of various macro-molecules (i.e. proteins, DNA) are traced across the THz spectrum, which make this bandwidth interesting for biosensing purposes [101–105]. Furthermore, the development of micro-scale THz biosensing chips have successfully been realized by cost-effective and traditional single- or multi-step photolithography techniques. In recent years, THz plasmonic metamaterials composed of periodic arrays of artificially engineered building blocks with electromagnetic (EM) properties beyond natural materials have extensively been utilized for developing biosensing platforms [106–108]. Although current THz plasmonic metasensors are promising and provide substantial sensitivity and reasonable limit of detection (LOD), these technologies are still quite faraway from very early stage diagnosis of ultra-low weight infections and biomarkers at lowlevel densities. Generally, most of the THz plasmonic biosensors operating base on resonant-structures, and Fano-resonant metamaterials are highly popular in this field of sciences. However, due to the size of the THz plasmonic metamaterials, in most of assays, the nanoscopic molecules and microorganisms are transparent to the THz radiation and showing very low scattering cross-sections due to having sizes in the order of _k/100 [109].

在所有等离子生物设备中，具有晶体管与激光世界之间的工作带宽（0.1 THz <f <10 THz）的太赫兹（THz）等离子结构最近受到了广泛关注。应该强调的是，已经使用等离激元术语来区分已审查的金属超材料和超传感器与经典的纳米光子平台。作为传统光学生物传感器的潜在替代品，太赫兹光谱已被认为是具有先进的生物传感应用的有前途的方法，具有奇异的特征和在光学纳米结构中未曾经历过的优势[101]。太赫兹等离子体生物设备有助于现场检测，低侵入性，与生物组织的无损，无毒相互作用以及高信噪比（S / N）[102]。另外，在太赫兹频谱上可以追踪到各种大分子（即蛋白质，DNA）的振动模式，这使得该带宽对于生物传感而言很有趣[101-105]。此外，通过具有成本效益的传统单步或多步光刻技术已成功实现了微型THz生物传感芯片的开发。近年来，太赫兹等离子超材料由具有天然材料以外的电磁（EM）特性的人工工程构件的周期性阵列组成，已广泛用于开发生物传感平台[106-108]。尽管当前的THz等离子体元传感器前景广阔，并提供足够的灵敏度和合理的检测限（LOD），但这些技术与超低重量感染和低水平密度生物标志物的早期诊断仍相距甚远。通常，大多数基于共振结构的THz等离子体生物传感器和Fano共振超材料在该科学领域中非常受欢迎。但是，由于太赫兹等离子超材料的尺寸，在大多数测定中，纳米级分子和微生物对太赫兹辐射是透明的，并且由于其尺寸约为_k / 100，因此显示出非常低的散射截面[109]。 

To address this inherent limitation in THz metasensors, very recently, an alternative technology has been introduced and experimentally validated for the precise detection of extremely small amount of biomarkers at ultra-low concentrations [110,111]. Such sensitive metadevices have been developed based on toroidal resonances that provide unique spectral properties [112]. Theoretically, toroidal resonances have been introduced for the first time in 1957, in the context of nuclear, atomic, and molecular physics [113]. On the other hand, dynamic toroidal dipole has been excited successfully by either linear or vortex beams illuminations [114,115]. Toroidal dipoleresonant metamaterials and structures have received growing interest in the last decade [116–121]. Moreover, possessing narrow lineshape, and ultrahigh sensitivity of toroidal metamaterials to the environmental perturbations stimulated researches to employ these subwavelength technologies for developing advanced plasmonic tools [117,122–124].

为了解决太赫兹元传感器的固有局限性，最近，引入了一种替代技术，并进行了实验验证，可以精确检测超低浓度的极少量生物标志物[110,111]。已经基于提供独特光谱特性的环形共振开发了这种敏感的元设备[112]。从理论上讲，在核物理，原子物理和分子物理的背景下，环形共振于1957年首次引入[113]。另一方面，动态环形偶极子已被线性或涡旋光束照明成功激发[114,115]。在过去十年中，环形双极共振超材料和结构受到了越来越多的关注[116-121]。而且，具有超窄的线形和超材料的超环面材料对环境扰动的敏感性促使人们进行研究，以利用这些亚波长技术来开发先进的等离激元工具[117,122–124]。

The review article is organized as following: A detailed overview about various THz plasmonic metasensors based on perfect absorption techniques is presented in ‘THz plasmonic perfect absorbers for biological detection’. ‘Fano-resonant THz metamaterials for biological detection’ summarizes the recent advances in the field of label-free metasensors based on capacitive coupling in sub-microscale openings. The spectral properties and unique advantages of toroidal plasmonic metamaterials are demonstrated in ‘THz plasmonic biosensors based on extraordinary transparency’ with detailed key investigations about sensing performance of recently utilized biosensing tools. The use of toroidal plasmonics metadevices for biosensing that is explained in ‘Toroidal resonances for biosensing’, is a very novel aspect for both the plasmonics and biomedical technologies communities. Such a focused review reveals the recent advances in plasmonic biosensing aspects, and introduces the emergence of new technologies in the field for very broad interdisciplinary biomaterials community.

这篇综述文章的组织方式如下：在“用于生物检测的THz等离子体完美吸收体”中，详细介绍了基于完美吸收技术的各种THz等离子体激元传感器。 “用于生物检测的共振FHz超材料”总结了基于亚微米级开口中电容耦合的无标记超传感器领域的最新进展。 “基于非凡透明性的THz等离子体生物传感器”展示了环形等离子体超材料的光谱特性和独特优势，并对最近使用的生物传感工具的传感性能进行了详细的关键研究。环形等离子体电子元设备在生物传感中的使用已在“用于生物传感的环形共振”中进行了说明，这对于等离子体和生物医学技术界都是一个非常新颖的方面。这样的重点综述揭示了等离激元生物传感方面的最新进展，并介绍了针对非常广泛的跨学科生物材料界的新技术的出现。

Thz plasmonic perfect absorbers for biological detection 用于生物检测的Thz等离子体完美吸收体

Fundamental theoretical aspects 基本理论方面

Perfect metamaterial absorbers are subwavelength structures consisting of well-engineered unit cells, offering advantages based on both the inherent lossy behavior of plasmons. By forming of a sub-wavelength resonant cavity in these structure, (where the reflected beam is trapped) thus, any losses-particularly in metals or dielectric spacer, substrate, superstrate, analyte, etc.- will be amplified to diminish the reflection and boost the absorption spectra [125,126]. The perfect and broadband absorption of the incident beam has successfully been obtained by tailoring wellengineered plasmonic meta-atoms and metamolecules [125– 130]. The presence of a metallic backed layer in the design of a perfect absorber leads to tremendous absorption of both components of the incident EM field by minimizing the reflectance response. Such a technology has been broadly employed to address the typical limitations associating with the biological sensing surfaces. Generally, in perfectly absorptive metamaterials, the optimal goal is achieving the maximum possible absorption (almost unity), where this feature can be obtained by dramatic decay of transmitted and reflected beam from a given metamaterial (A = 1-T-R, where T = 0). Multilayer structures consisting of metal-dielectric-metal interfaces are the traditional designs for developing perfect absorbers (Fig. 1). Such a sandwich-type structure allows for strong confinement of the incident light and hinders escaping of light. This results in the formation of circulating magnetic field at the metal-dielectric interfaces, and enhances the absorptance of the entire structure. In the upcoming sections, the recent advances in the use of perfect absorbers based on THz plasmonic technology for biochemical and biological immunosensing applications will be explained

完美的超材料吸收体是由精心设计的晶胞组成的亚波长结构，基于等离激元固有的损耗特性，它们具有优势。通过在这些结构中形成亚波长谐振腔（在其中捕获了反射光束），任何损耗（尤其是金属或介电垫片，基板，覆层，分析物等）中的任何损耗都会被放大，以减少反射和提高吸收光谱[125,126]。通过精心设计良好的等离激元亚原子和超分子，成功获得了入射光束的宽带吸收效果[125-130]。完美吸收体的设计中存在金属背衬层，可通过最小化反射响应来极大地吸收入射EM场的两个分量。这种技术已被广泛采用以解决与生物感测表面相关的典型限制。通常，在完全吸收的超材料中，最佳目标是实现最大可能的吸收（几乎统一），其中此特征可以通过给定超材料的透射和反射光束急剧衰减来获得（A = 1-TR，其中T = 0 ）。由金属-电介质-金属界面组成的多层结构是开发完美吸收体的传统设计（图1）。这样的夹心型结构允许入射光的强烈限制并且阻碍光的逸出。这导致在金属-电介质界面处形成循环磁场，并增强了整个结构的吸收率。在接下来的部分中，将解释基于太赫兹等离子技术的完美吸收体在生物化学和生物免疫传感应用中的最新进展。

Biochemical sensing application 生化感测应用

Here, we consider the optical and sensing properties of several multiresonant THz metamaterials with the perfect absorption feature [131]. Using both numerical and experimental studies, Yahiaoui and co-workers demonstrated the detection performance of the tailored perfect beam absorber by variations in the thickness and refractive index (RI) of an analyte layer. Fig. 2a illustrates the scanning electron microscope (SEM) image of the fabricated metamaterial, and the insets are the crosssectional schematic and description for geometrical components of a single metamolecule. In the experiments, the aluminum (Al) unit cells are deposited on a multilayer substrate consists of 50 mm dielectric spacer and an Al mirror. The multilayer geometry of the perfect absorber can be described in the way that antiparallel currents are excited in the top layer and the bottom metallic layer [132,133]. Actually, this is known a magnetic resonance due to the fluxing currents result in a magnetic mode which can strongly interact with the magnetic field of the incident beam [132–134]. At the resonance frequency, a strong enhancement of the localized EM field is established between the two layers. Thus, the EM energy can be efficiently confined in the intermediate dielectric spacer and hence no light is reflected back. This leads to a pronounced reflectance dip in the spectrum with nearly zero intensity, therefore giving rise to around _100% absorbance. Fig. 2b shows the experimentally and numerically defined reflection (R) amplitude as a function of frequency, confirming the excitation of multiple resonances around fR1 = 0.22 THz, fR2 = 0.48 THz, and fR3 = 0.76 THz. Perturbing the RI of the medium is a traditional method to demonstrate the sensing performance of the perfect absorber metamaterial. It is well-accepted that increasing the RI of the media gives rise to red-shifts in the position of the excited modes to the shorter frequencies [135]. In this work [131], the plasmonic metamaterial absorber is loaded by a thin analyte layer with the RI of n = 1.73. Fig. 2b exhibits red-shifts in the position of all reflection dips. The reason for this shift can be explained by the changes in the entire capacitance across the structure. Once the surface of the metamaterial is loaded with small amount of dielectric material, the capacitance value increases and the resonances shift towards the lower frequencies. The frequency shift (Df) of the metasensor is shown as a function of RI of the analyte in Fig. 2c(i). Obviously, the frequency shift of the resonances continuously increases linearly with the increase of the RI of the thin analyte layer. The amplitude modulation of the reflectivity (DR) is also demonstrated numerically in Fig. 2c(ii). Upon increasing the RI of the analyte and depending on the excited resonant mode, their amplitude variations as a function of the RI could be very different with a mutual nonlinear evolution. To define the sensitivity of the perfect metamaterial absorber, Yahiauoui and teammates artificially changed the thickness and RI of the analyte layer. The thickness of the overlayer is altered numerically in the range 1–50 mm in order to evaluate the frequency sensitivity of the sensor as a function of the analyte thickness. By increasing the analyte thickness, a distinct red shift of the resonances is observed by the authors. Based on the frequency shift with the change in analyte thicknesses, the frequency sensitivity of the sensor is estimated explicitly, as shown in Fig. 2d(i). Here, the third resonant mode is more sensitive than the first and the second resonances, since it induces remarkably larger frequency sensitivity and eventually reaches almost 140 GHz/RIU for an overlayer thickness of 50 mm. In this work, the researchers also performed further simulations to evaluate the effect of the dielectric spacer on the characteristic of the sensor. The results for the sensitivity variations based on reducing the thickness of the dielectric substrate to 15 mm are reported in Fig. 2d(ii), for the third resonant mode of the metamaterial absorber. Thus, when the thickness of the overlayer is less than 20 mm, the sensitivity of the sensor is not dramatically enhanced as compared to the nominal case (50 mm). 

在这里，我们考虑几种具有完美吸收特性的多共振太赫兹超材料的光学和传感特性[131]。 Yahiaoui及其同事使用数值研究和实验研究，通过分析物层的厚度和折射率（RI）的变化，证明了量身定制的完美光束吸收器的检测性能。图2a示出了所制造的超材料的扫描电子显微镜（SEM）图像，插图是单个超分子的几何成分的横截面示意图和描述。在实验中，铝（Al）晶胞沉积在由50 mm介电垫片和Al镜组成的多层基板上。可以通过在顶层和底层金属层[132,133]中激发反平行电流的方式描述完美吸收体的多层几何形状。实际上，由于通量电流导致的磁模式会与入射光束的磁场发生强烈相互作用，从而导致磁共振[132-134]。在共振频率处，在两层之间建立了局部电磁场的强烈增强。因此，可以将EM能量有效地限制在中间电介质间隔物中，并且因此没有光被反射回去。这会导致光谱的反射率下降，强度几乎为零，因此吸收率约为_100％。图2b显示了实验和数字定义的反射（R）幅度随频率变化的情况，确认了在fR1 = 0.22 THz，fR2 = 0.48 THz和fR3 = 0.76 THz附近的多个共振的激发。扰动介质的RI是证明完美吸收体超材料的传感性能的传统方法。广为接受的是，增加介质的RI会导致激发模式位置向较短频率的红移[135]。在这项工作[131]中，等离子超材料吸收体由薄的分析物层加载，RI为n = 1.73。图2b显示了所有反射倾角位置的红移。这种偏移的原因可以通过整个结构上整个电容的变化来解释。一旦超材料的表面负载了少量的介电材料，电容值就会增加，并且谐振会朝着更低的频率移动。图2c（i）中显示了元传感器的频移（Df）与分析物的RI的函数关系。显然，共振的频移随着薄分析物层的RI的增加而线性地连续增加。反射率（DR）的幅度调制也在图2c（ii）中进行了数值演示。在增加分析物的RI并取决于激发的共振模式时，它们的幅度变化作为RI的函数可能会随着相互非线性演化而非常不同。为了定义完美的超材料吸收体的灵敏度，Yahioauoui及其队友人为地改变了分析物层的厚度和RI。为了评估传感器的频率灵敏度与分析物厚度的函数关系，覆盖层的厚度会在1-50 mm范围内进行数字更改。通过增加分析物的厚度，作者观察到了共振的明显红移。如图2d（i）所示，基于随分析物厚度变化而产生的频率偏移，显式估计传感器的频率灵敏度。在此，第三谐振模式比第一和第二谐振更敏感，因为它引起明显更大的频率灵敏度，并最终在50 mm的覆盖层厚度下达到近140 GHz / RIU。在这项工作中，研究人员还进行了进一步的仿真，以评估介电垫片对传感器特性的影响。对于超材料吸收器的第三共振模式，在图2d（ii）中报告了基于将介电基片的厚度减小到15 mm而引起的灵敏度变化的结果。因此，当覆盖层的厚度小于20mm时，与标称情况（50mm）相比，传感器的灵敏度没有显着提高。

FIGURE 1 Schematic representation of a perfect absorber unit cell consisting of metal-dielectric-metal interfaces, where the transmittance (T) and reflectance (R) spectra suppress and the absorption (A) cross-section enhances.

图1是由金属-电介质-金属界面组成的理想吸收器单元电池的示意图，其中透射率（T）和反射率（R）光谱受到抑制，吸收率（A）横截面增强。

In recent years, several alternative and promising platforms have been introduced for RI sensing purpose by taking advantage of remarkable absorption cross-section in spoof plasmon metamaterials [136], and multilayer metamaterials combined with microfluidic channels for liquid sensing [137]. Focusing on these mechanisms, Ng et al. [136] developed a spoof plasmon metamaterial integrated with an Otto prism setup to utilize its surface sensitivity for RI sensing of various fluids. Prism coupling systems have previously been used to excite surface resonant modes on semiconductor and metallic arrays in the THz spectrum [138,139]. As plotted in Fig. 3a, the developed spoof plasmon-resonant system consists of a linear array of grooves based on 600 nm of gold (Au) layer deposited on a layer of photoresist. The optical microscope image of the fabricated groove array is exhibited in Fig. 3b and the employed geometries are specified in the caption of the figure. In this study, the researchers coupled to THz spoof plasmons via a wax prism and as a proof of principle, experimentally demonstrated RI sensing of different fluids by monitoring significant changes in both amplitude and phase of the THz radiation. A wax prism in the traditional Otto prism configuration has been used for (1) phase-matching, (2) coupling to the spoof plasmon mode evanescently at the base of the prism with a coupling gap (g), and (3) between the spoof plasmons and prism base (see Fig. 3c). Then the changes in the reflectivity (R) has been monitored, and phase change spectra were studied as the grooves are filled with different fluids: nitrogen (n = 1.00), gasoline (n = 1.41), liquid paraffin (n = 1.49), glycerin (n = 1.82) and water (n = 2.1). This led to a perfect spread of RI values, enabling to investigate the efficacy of THz spoof plasmon sensing with various sample fluids. As can be seen in Fig. 3d, there is a remarkable red-shift in the reflection dip as the RI of the fluid filling the grooves increases. The resonance points for nitrogen, gasoline, liquid paraffin, glycerin and water are 1.71, 1.53, 1.48, 1.30, and 1.17 THz, respectively. For lowloss fluids (e.g. gasoline and liquid paraffin), the width of the resonances are 90 GHz and 50 GHz, respectively, while for high-loss fluid (e.g. glycerin), the reflection dip broadens significantly to 280 GHz, giving rise to a Quality-factor (Q-factor) of approximately 4.6. Conversely, for a very high-loss fluid (e.g. water), the resonance lineshape further broadens to approximately 390 GHz. This implies that RI sensing with amplitude measurements is not suitable for highly absorbing fluids, since a larger RI change would be required to properly discern any spectral shifts in the resonance lineshape. These results were achieved in spite of dramatic attenuation on the radiated THz signal through the high-loss fluid layer. The profile in Fig. 3e demonstrates the resonance frequencies of the different fluids as a function of respective RIs. The blue solid line is a linear fit given by fsp = _0.49n + 2.21. This graph shows a sensitivity of 0.49 THz/ RIU with the corresponding LOD of 0.02 RIU at a detection resolution of 10 GHz. The insets are the electric-field density maps for the lowest and highest RIs at the plasmon resonance frequency. The computed figure of merit (FOM) values for nitrogen, gasoline, liquid paraffin and glycerin are 49, 15, 25, and 7, respectively. The relationship between resonance frequency (fsp) and n of an idealized spoof plasmonic sensor consisting of a linear array of square grooves with effective groove width weff (weff = wt = wb), is analytically given by: 

equation

 where c is the speed of light, n is the RI of the dielectric substance filling the grooves, h = 74_ is the angle of the incident beam, and np is the RI of the prism (1.44). This equation defines the spoof plasmon dispersion of the metamaterial with the prism light line and is solved for weff = wt = 37 lm and weff = wb = 25 lm with the RI variations between 1 and 2.1. Thus, the minimum sensitivity over the range of sampled values of n, quantified by taking the numerical gradient of the analytical curves, are 0.40 THz/RIU and 0.47 THz/RIU for weff = 37 lm and weff = 25 lm, respectively. Although the reported LOD and FOM values in this work are remarkable, it is shown that the performance and accuracy of plasmonic THz absorber sensors can be boosted [133].

近年来，通过利用欺骗性等离激元超材料[136]中的显着吸收截面以及多层超材料与微流体通道相结合进行液体感测[137]，已经引入了几种替代且有前途的平台用于RI感测。 Ng等人着眼于这些机制。 [136]开发了一种与奥托棱镜装置集成在一起的欺骗性等离激元超材料，以利用其表面灵敏度对各种流体进行RI感测。棱镜耦合系统以前曾被用来在THz频谱中激发半导体和金属阵列上的表面共振模式[138,139]。如图3a所示，已开发的欺骗型等离子体激元共振系统由基于600 nm沉积在光刻胶层上的金（Au）层的沟槽的线性阵列组成。制成的凹槽阵列的光学显微镜图像如图3b所示，所用的几何形状在图的标题中指定。在这项研究中，研究人员通过蜡棱镜与太赫兹欺骗等离子激元耦合，并作为原理证明，通过监测太赫兹辐射的振幅和相位的显着变化，实验证明了RI对不同流体的传感。传统的Otto棱镜配置的蜡棱镜已用于（1）相位匹配，（2）在棱镜的底部以耦合间隙（g）短暂耦合到欺骗的等离振子模式，以及（3）欺骗的等离激元和棱镜底座（见图3c）。然后，对反射率（R）的变化进行了监测，并研究了沟槽填充不同流体时的相变光谱：氮气（n = 1.00），汽油（n = 1.41），液体石蜡（n = 1.49），甘油（n = 1.82）和水（n = 2.1）。这导致RI值的完美散布，从而能够研究THz欺骗等离子体激元在各种样品流体中的感应功效。从图3d中可以看出，随着填充凹槽的流体的RI的增加，反射倾角会出现明显的红移。氮气，汽油，液体石蜡，甘油和水的共振点分别为1.71、1.53、1.48、1.30和1.17 THz。对于低损耗流体（例如汽油和液体石蜡），谐振的宽度分别为90 GHz和50 GHz，而对于高损耗流体（例如甘油），反射倾角显着扩展至280 GHz，从而提高了质量。因子（Q因子）约为4.6。相反，对于损耗极高的流体（例如水），谐振线形会进一步加宽到大约390 GHz。这意味着具有振幅测量值的RI传感不适用于高吸收性流体，因为需要较大的RI变化才能正确识别共振线形中的任何频谱偏移。尽管通过高损耗流体层的辐射太赫兹信号发生了显着衰减，但仍获得了这些结果。图3e中的曲线显示了不同流体的共振频率与相应RI的关系。蓝色实线是由fsp = _0.49n + 2.21给出的线性拟合。该图显示了在10 GHz的检测分辨率下灵敏度为0.49 THz / RIU，相应的LOD为0.02 RIU。插图是等离激元共振频率下最低和最高RI的电场密度图。氮气，汽油，液体石蜡和甘油的品质因数（FOM）值分别为49、15、25和7。理想频率的欺骗性等离子体传感器的谐振频率（fsp）与n之间的关系由具有有效沟槽宽度weff（weff = wt = wb）的方形沟槽的线性阵列组成，解析式为：

公式

其中c是光速， n是填充凹槽的电介质的RI，h = 74_是入射光束的角度，np是棱镜的RI（1.44）。该方程式定义了超材料在棱镜光线下的欺骗性等离激元色散，对于RI = 1至2.1的weff = wt = 37 lm和weff = wb = 25 lm求解。因此，通过取分析曲线的数值梯度来量化的n采样值范围内的最小灵敏度分别对于weff = 37 lm和weff = 25 lm为0.40 THz / RIU和0.47 THz / RIU。尽管在这项工作中报告的LOD和FOM值非常可观，但已表明可以提高等离子体THz吸收器传感器的性能和准确性[133]。

FIGURE 2 (a) Scanning electron microscope (SEM) image of the fabricated metamaterial absorber with a schematic cross-section of the sample (top right) and the polarization of the incident plane wave (bottom left). The inset is a representation of a single unit cell with the relevant geometrical dimensions: a = b = 250 mm, c = d = g = 50 mm, e = 25 mm, and l = 155 mm. The unit cells are arranged in the periods of px = py = 300 mm. (b) Simulated and measured reflection spectra of the metamaterial absorber versus frequency without analyte and with 50-mm-thick analyte (n = 1.73). (c) Frequency shift (i) and amplitude modulation (ii) against analyte RI for the different resonant modes of the metamaterial absorber-based sensor device. (d) Frequency sensitivity of the resonant modes as a function of the analyte thickness (i), and frequency sensitivity of the third resonant mode as a function of the analyte thickness at dielectric spacer thicknesses of 50 mm and 15 mm, respectively (ii). The symbols represent the exact values, while the solid lines are the fitting functions [131]. Copyright 2015, American Institute of Physics (AIP).

图2（a）所制造的超材料吸收体的扫描电子显微镜（SEM）图像，其样品的横截面示意图（右上方）和入射平面波的偏振态（左下方）。插图表示具有相关几何尺寸的单个晶胞：a = b = 250 mm，c = d = g = 50 mm，e = 25 mm，l = 155 mm。单位晶格的排列周期为px = py = 300 mm。 （b）模拟和测量的超材料吸收体的反射光谱与不带分析物和使用50毫米厚分析物时的频率的关系（n = 1.73）。 （c）针对基于超材料吸收体的传感器设备的不同共振模式，针对分析物RI的频移（i）和幅度调制（ii）。 （d）介电间隔层厚度分别为50 mm和15 mm时，共振模式的频率灵敏度与分析物厚度（i）的函数关系以及第三共振模式的频率灵敏度与分析物厚度的函数关系（ii） 。符号代表精确值，而实线是拟合函数[131]。美国物理研究所（AIP）版权所有2015。