The Spoof Surface Plasmon (SSP) based on the metal microstructure-dielectric system, which has excellent sub-wavelength transverse resolution, interface near-field enhancement and other characteristics, is widely concerned in the fields of physics, chemistry and biology^[1], and shows great application potential in the field of super-resolution imaging and sensing^[2-3]. In order to excite SSP mode, the wave vector of electromagnetic wave in free space should match the wave vector of metal surface polarization wave. Generally, there is a certain phase difference between the two wave vectors, which requires grating coupling structure^[4], prism coupling structure^[5] and waveguide coupling structure^[6] to achieve wave vector compensation, thus generating terahertz SSP mode. The above structures have problems such as large volume, vertical reflection and decoupling effect, and the operating bandwidth of non-coplanar excitation structures such as gratings and waveguides are narrow, which makes it difficult to efficiently couple with SSP structures with high Q values^[7]. By using the tapered parallel plate waveguide as the coupling structure, Tang H H et al.. of Peking University effectively compressed and coupled the incident terahertz wave to a sub-wavelength gap to achieve ultra-wideband and efficient conversion from traditional electromagnetic wave to SSP^[8].

Meta-surface couplers with periodic scattering characteristics can introduce any additional wave vector, and have attracted more and more attention^[9-10]. Compared with traditional SSP coupler, the meta-surface dielectric coupler can not only realize the design and manufacture of sub-wavelength size and thickness, but also has greater advantages in constructing multi-channel and multi-functional SSP devices^[11-12]. In 2012, Sun S L et al.. first reported that the metal gradient meta-surface working in the reflection mode converts the Propagating Wave (PW) into the Surface Wave (SW), and the efficiency in the microwave region is close to 100%^[13]. The momentum mismatch between PW and SW is compensated by the reflection phase gradient of the meta-surface. For any incident angle greater than the critical value, a nearly perfect PW-SW conversion can occur. So far, most of the meta-surface couplers operating in reflection mode work in the microwave range, and the conversion efficiency of terahertz SSP meta-surface couplers is lower than 70%^[10]. In addition, the dispersion relationship of metal structural elements in these coupled structures limits the operating bandwidth. On the other hand, the currently reported couplers working in metallic cell structures have disadvantages such as complex multilayer structures and narrow operating band in the microwave range^[14].

Terahertz SSP sensor has the characteristics of real-time, label free, ultra-sensitive, etc., and is widely used in sensing, nondestructive testing and other related fields^[15]. Ng B et al.. used prism or scattering method to generate terahertz SSP mode on the metal surface of periodic grooves, further realizing detection and sensing of different fluid samples^[16-17]. Huang Y et al.. used a high resistivity silicon prism coupler with high refractive index to convert the incident terahertz wave into SSP mode, further realizing sensing research^[18]. By combining controllable plasma resonance and attenuated total reflection, they realized ultra-precise terahertz sensor with direct phase readout capability. The reflected THz phase showed two completely different jumping responses to the coupling gap with corresponding phase spectrum Q factor in the range of 9.7-43.4 for the liquid sensing. Sathukarn A et al.. reported a surface plasmon resonance refractive index sensor based on metal coating^[19]. A gold-plated grating with polydimethylsiloxane (PDMS) as a substrate was designed and measured for gasoline-toluene mixtures detection. The surface plasmon resonance frequency was matched to the operating frequency by varying the grating period. Most of the studies reported so far have used conventional structures as couplers. The use of prisms as couplers to excite SSP for sensing requires the selection of specific materials and design of prism structure parameters, and certain angular relationships need to be satisfied to excite the SSP mode. In addition, prismatic coupling structures are not easy to integrate in the system^[20].

In recent years, the simultaneous coupling on a single meta-surface structure and the excitation structure of SSP have also attracted much attention. SSP mode is excited on the metal groove array by setting a phase gradient structure on part of the meta-surface. Yin L Z et al.. proposed a terahertz spin-decoupled dual function meta-surface coupler for SSP generation and beam deflection^[21]. The designed super-surface coupler consists of a coupling super-surface and a transmission super-surface. The former can anomalously reflect right-spin circularly polarized incident waves, as well as convert left-spin circularly polarized incident waves into SSP modes. The latter is used to propagate the excited SSP modes. When the frequency is 0.3 THz, the conversion efficiency of right- and left-spin circularly polarized incident waves can reach 82% and 70% respectively. In the recent work, our research group reported the terahertz SSP coupling structure based on gradient dielectric meta-surface and two-dimensional dielectric super-grating structure. These two structures can deflect the vertically incident terahertz wave to a specific angle in the substrate, which makes the power in the first order refraction direction increase significantly while attenuating the power of other reflection and refraction orders, thus realizing the compensation of SSP wave vector, and further generating SSP mode on the surface of the bottom metal groove array^[11-12]. Furthermore, the terahertz sensing performance with high sensitivity can be achieved by using these two structures in the detection of gas and liquid.

In this paper, SPP mode excitation and high Q sensing performance are achieved by using single-layer grating coupled meta-surface composite structure. Based on the principle of grating diffraction, the proposed meta-surface structure can take the wave vector of the diffraction wave at a specific angle as the compensation wave vector of THz SSP, thus generating surface plasmon resonance and high Q resonance peak in the transmission spectrum. Compared to the other sensors based on terahertz SSP, the structure designed in this paper has the following three main advantages:

(1) Using a simple single-layer grating meta-surface composite structure as a coupler, it can be used as a high Q sensor while exciting the SSP mode;

(2) The proposed grating meta-surface structure works in transmission mode, which overcomes the disadvantage of inconvenient reflection measurement when using dielectric coupler in practical applications;

(3) The Q value of the resonance peak generated by SSP excited by the designed meta-surface structure reaches 1923. When the meta-surface structure is used for sensing, the sensitivity is 67 GHz/RIU.

This work opens a new way for terahertz SSP to be used in many fields of ultra-thin and compact functional devices.

In this paper, an "E" - like metal meta-surface is designed to realize SSP mode excitation in terahertz band. Fig. 1 (a) shows the schematic diagram of the proposed grating structure, which is composed of a metal strip structure etched on the surface and a PDMS substrate. Terahertz wave is incident to the device perpendicular to the surface of the metal microstructure. Its electric field is parallel to the y-direction, and its magnetic field is parallel to the x-direction. The unit structure of the grating coupling meta-surface is shown in Fig. 1 (b). P_x and P_y represent the periods of the unit structure in the x- and y-directions respectively. The protruding metal bars are divided into two parts on average, with the length of w respectively. Three metal bars constitute a unit structure. The diffraction effect of the composite grating structure composed of three metal bars is equivalent to that of the grating shown in Fig. 2 (a), while three separate metal bars form the SSP structure. The conductivity of the selected metal material is 4.1 × 10⁷ s/m, the dielectric constant of PDMS is 2.34. The transmission characteristics of the proposed grating coupled meta-surface structure are studied by using the finite element analysis method, and the dispersion characteristics of a single metal bar structure with grating structure are analyzed. The simulation time is effectively reduced by setting periodic boundary conditions.

Based on the principle of grating diffraction, SSP mode can be excited by grating coupling. When THz wave in free space vertically incident on periodic meta-surface structure, electromagnetic wave diffraction can occur. Different diffraction angles of gratings indicate different diffraction orders. The wave vector of the diffraction wave at a specific angle can be used to compensate the wave vector of the SSP mode so that the diffraction electromagnetic wave vector corresponding to the diffraction angle matches with the SSP wave vector, then SSP resonance can be realized at this time. Externally, it shows that the diffracted electromagnetic wave is absorbed, and the corresponding resonance peak can be generated in the transmission spectrum. Compared with the traditional prism coupling mode, this structure reduces the number of used devices and can further realize miniaturization (Fig.2, color online).

The specific parameters of the designed structure are as follows: P_x=500 μm，P_y=400 μm，P=120 μm，L=3 × P，w=0.5 × P，a=40 μm，b=0.5 × P，d=60 μm, where P is the period of single metal bar small unit structure, a is the width of the first section of the protruding metal bar, b is the width of the second section of the protruding metal bar, and d is the distance between the protruding metal bar and the metal frame. In order to facilitate the device preparation in the subsequent work, the thickness of metal grating t=50 μm and the substrate thickness h=400 μm are selected. The transmission spectrum and dispersion curves are first analyzed by varying the width a of the first section of the metal bar, where the values of a are chosen as 30 μm, 50 μm, 70 μm, and 90 μm. The variation trend of transmission characteristics with width a is shown in Fig. 2 (c). It can be seen that with the increase of a, the resonant frequency shows a significant blue shift, and the bandwidth of the resonant peak is extremely narrow.

Secondly, the dispersion of grating structure and single metal bar structure is analyzed respectively, and the results are shown in Fig. 2 (d). The black solid line in Fig. 2 (d) represents the dispersion curve of the metal grating structure. Next, the dispersion analysis of the periodic metal bar structure is carried out, as shown in the dotted line in Fig. 2 (d), which can provide dispersion characteristics similar to those of the SSP mode. The analysis of the two dispersion curves shows that the dispersion of the grating structure and the SSP dispersion have an intersection point, and the wave vector compensation of the SSP mode can be achieved at this point by the grating coupling structure, which is numerically expressed as that the wave vector k₀ along the metal surface generated by the grating coupling structure matches with the wave vector k_SSP of the SSP mode. A comparative study reveals that the positions of the four intersections in Fig. 2(d) correspond to the positions of the four resonance peaks in the transmission spectrum in Fig. 2(c), and this result can indicate that the terahertz SSP mode is excited by the grating-coupled super-surface structure. The excited resonances exhibit surface plasmonic properties and form a field distribution along the metal surface, which greatly enhances the field confinement at the metal surface and allows the designed structure to have a relatively high Q factor, which can be used to realize ultra-sensitive sensors.

Furthermore, the influence of the geometric parameters of the meta-surface structure on the THz SSP mode excitation is studied. The control variable method is used to study by ① changing the width a of the first section of the protruding metal bar, ② changing the width b of the second section of the metal bar, ③ varying simultaneously a and b when making a=b, and ④ changing the spacing d between the metal bar and the metal outer frame, respectively, and obtain their transmission change curves as shown in Fig. 3 (color online). Firstly, the transmittance is analyzed when the width a is varied in the range of 30-90 μm in steps of 20 μm, and the other parameters constant are fixed. It can be seen from Fig. 3 (a) that the resonant frequency in the transmission spectrum shows a blue shift trend with the increase of width a. Then, when changing b, the same change interval and step size are used for analysis. It can be seen from Fig. 3 (b) that the resonant peaks in the transmission spectrum have an obvious tendency to redshift as b increases. When a=b, changing both a and b at the same time, it can be seen from Fig. 3 (c) that the resonant frequency in the transmission spectrum shows a slight blue shift. This is because the extent of the blue shift of the resonant frequency when changing a is greater than the extent of the red shift when changing b, so only a slight blue shift occurs when both are changed at the same time. Finally, the influence of different parameters d on the transmissivity of the meta-surface structure is studied, as shown in Fig. 3 (d). When d is changed, the resonance position in the transmission spectrum does not change significantly, so it can be judged that the SSP generated by this structure is insensitive to parameter d.

In the above research, the influence of four variables on transmission characteristics is analyzed. In order to further explain the performance of THz SSP mode excited by the designed grating coupled meta-surface structure, the influence of these four structural parameters on dispersion characteristics is further studied. Similarly, with the fixed parameters b and d and varied parameter a from 30 μm increasing to 90 μm in steps of 20 μm, as shown in Fig. 4 (a)(color online), the asymptotic frequency of its dispersion characteristics shows a significant blue shift trend, which is consistent with the blue shift trend of the resonant frequency in the transmission spectrum corresponding to changing a in Fig. 3 (a), further demonstrating that the resonant peak is the resonance formed after the excitation of the SSP mode. Next, with the fixed other parameters and varied parameter b from 30 μm to 90 μm in the same step of 20 μm, as shown in Fig. 4 (b)(color online), its asymptotic frequency has red shift. Then, it is analyzed with parameter a=b and both changing in the same step and range, and the fixed parameter d. The results are shown in Fig. 4 (c)(color online). It can be seen that the asymptotic frequency of dispersion has a slight blue shift. Finally, with the fixed parameters a and b, the influence of the parameter d on the dispersion characteristics is analyzed. As shown in Fig. 4 (d)(color online), the asymptotic frequency of the dispersion curve does not shift significantly, which is consistent with the influence of the above analysis parameters on the transmissivity. From the above analysis, it can be determined that the resonance in the transmission spectrum is formed by the SPP mode excited by the grating coupled metal meta-surface.

Through the analysis of parameters a and b, it can be judged that the asymptotic frequency of the dispersion of this structure is proportional to the width a of the first section of metal bar (the smaller the a, the lower the asymptotic frequency), and inversely proportional to the width b of the second section of metal bar (the larger the b, the lower the asymptotic frequency). When a=b and the width of the both metal bars are changed at the same time, the influence of parameter a and parameter b on the dispersion asymptotic frequency is mutual cancellation, and the influence of parameter a on the frequency shift is slightly greater than that of parameter b, resulting in a slight blue shift of the asymptotic frequency. Finally, when the distance d between the metal bar and the metal frame is changed, it is found that the dispersion characteristics do not change significantly. To sum up, the stimulated THz SSP can be regulated by changing parameter a or parameter b. Because SSP has strong field limiting ability and high Q value at resonance frequency, SSP resonance can be used for highly sensitive sensing.

Fig. 5 (color online) shows the electric field distribution when the resonant frequency is 0.22 THz. In the electric field distribution in the x-z cross section, there is a terahertz SSP mode propagating along the metal surface on the metal microstructure surface. The surface wave generated by the structure surface is very sensitive to the transformation of the surrounding environment. When this is used as a sensor, the object to be measured can be placed on the structure surface to sense the change of the surface electric field distribution caused by the change of the object to be measured. Since refractive index is one of the important properties of sample materials, different materials have their own specific refractive index, so it is possible to distinguish and identify different materials or material properties by detecting different refractive indexes. Therefore, in the sensing research, it is assumed that different refractive indexes are used to analyze the performance of the sensor.

Q can represent the structure's ability to limit electromagnetic waves. The higher the Q, the greater the ability to limit electromagnetic waves. Changes in the surrounding environment have an impact on the structure field distribution, and sensing can be realized by detecting the changes. Therefore, the structure with higher Q value has stronger sensing performance. In order to improve the sensitivity, one of the key factors is to design a structure with high Q value. Generally, if SSP is used to achieve high sensitivity, its structure needs to have a high Q value. The calculation formula of Q value is Q=f₀/(|f₁-f₂|), where f₀ is the resonant center frequency,f₁ and f₂ are the corresponding frequencies when the resonant peak amplitude is half of the maximum value. The analysis of the resonant peak of the transmission spectrum shown in Fig. 2 shows that the Q value reaches 1923, indicating that the structure has strong field limiting ability, which is conducive to practical applications in many fields. There are several reasons for the high Q value. Firstly, because the resonance is closer to the asymptotic frequency, the SSP mode near the resonance point is more confined to the metal structure. As can be seen from Fig. 5 (a), the local field is effectively enhanced, resulting in a very sharp resonance peak^[22]; secondly, the periodic grating structure excites resonance and couples with the SSP structure. The electromagnetic wave forms FP resonance in the three-metal bar structure, which is conducive to generating high Q resonance; finally, as shown in Fig. 5 (b), the sharp resonant peak has a reverse parallel current distribution in the adjacent grooves, which ensures very low radiation loss of the incident wave and greater current density, forming a higher-order mode resonance and generating a high Q value.

The sensing sensitivity of the designed structure is analyzed by varying the refractive index of the environment surrounding the metal surface to simulate different substances. It is assumed that the refractive index is varied in the interval of 1-1.5 with a step of 0.1 and the dimensions of the structure are a=b=60 μm and d=60 μm. Fig. 6 (color online) shows the transmissivity of the grating coupling meta-surface with different environmental refractive indexes and the corresponding sensing sensitivity calculation results. It can be seen from Fig. 6(a) that the resonant peak in the transmission spectrum shows a red shift trend when the refractive index of the object to be measured gradually increases. The difference in the positions of the resonance peaks in the transmission spectra corresponding to different refractive indices is used to differentiate the substances for sensing purposes. The sensing performance of the structure is characterized by the change of resonance position with different refractive indexes, as shown in Fig. 6(b). When the refractive index changes to a certain extent, the greater the shift of the resonance position, the more sensitive the sensor perceives changes in the external environment. In the sensing sensitivity analysis, the formula S=Δf/Δn can be used to express the shift of the resonance peak frequency caused by the change of refractive index per unit of the object to be measured, i.e., the sensitivity, which is measured in RIU (Refractive Index Unit). The sensing sensitivity of the designed structure is 67 GHz/RIU calculated by fitting.

In this paper, a composite structure based on an "E"-shaped grating coupled with a meta-surface is designed to realize terahertz SSP excitation and high Q sensing. The meta-surface structure takes the wave vector of the diffracted wave at a specific angle as the compensation wave vector of the terahertz SSP mode, so that the diffracted electromagnetic wave vector corresponding to the diffracted angle matches the wave vector of the SSP mode, thus achieving surface plasmon resonance and generating a high Q resonant peak in the transmission spectrum with a Q value of 1923. Since the structure works in transmission mode, its sensing performance can be characterized by varying the refractive index of the surrounding materials. The results show that the sensitivity is 67 GHz/RIU when the meta-surface structure is used for sensing. The proposed grating coupled meta-surface structure does not require additional couplers when exciting THz SSP modes, and its high Q resonance can be widely applied in many fields.

基于金属微结构-介质系统的人工表面等离子体激元（SSP）具有优异的亚波长横向分辨率和界面近场增强等特性，在物理学、化学和生物学领域受到广泛关注^[1]，并且在超分辨率成像和传感领域展现出巨大的应用潜力^[2-3]。为了激发SSP模式，需要使自由空间中的电磁波波矢和金属表面极化波波矢相匹配。然而，通常二者之间存在着一定的相位差，需要采用光栅耦合结构^[4]、棱镜耦合结构^[5]以及波导耦合结构^[6]等进行波矢补偿，从而产生太赫兹SSP模式。上述几种结构具有体积庞大、需要垂直反射以及存在解耦合效应等问题，且光栅和波导等非共面激发结构的工作带宽较窄，不容易和具有高Q值的SSP结构高效耦合^[7]。北京大学的Tang H H等人通过使用锥形平行板波导作为耦合结构，使得入射太赫兹波能够被有效压缩并耦合到一个亚波长间隙，实现从传统电磁波到SSP的超宽带和高效转换^[8]。

具有周期性散射特性的超表面耦合器能够引入任意附加的波矢，受到越来越广泛的关注^[9-10]。与传统的SSP耦合器相比，超表面介质耦合器不仅可以实现亚波长尺寸的设计制造，而且在构建多通道、多功能SSP器件方面也具有较大的优越性^[11-12]。2012年，Sun Sh L等人首先报道了工作在反射模式下的金属梯度超表面，将传输波（PW）转换为表面波（SW），其在微波区域的效率接近100%^[13]。PW和SW之间的动量失配由超表面的反射相位梯度来补偿，对于任意大于临界值的入射角，都可以发生近乎完美的PW-SW转换。到目前为止，大部分工作在反射模式下的超表面耦合器的工作频段都在微波范围，太赫兹SSP超表面耦合器的转换效率低于70%^[10]。此外，在这些耦合结构中金属结构单元的色散关系限制了工作频带宽度。另一方面，目前报道的工作在金属单元结构的耦合器具有结构复杂和微波范围工作频带窄等缺点^[14]。

太赫兹SSP传感器具有实时、无标记、超灵敏等特点，广泛应用在传感和无损检测等相关领域^[15]。Ng B等人利用棱镜或者散射方法，在周期性凹槽金属表面产生太赫兹SSP模式，进一步实现对不同流体样品的检测传感^[16-17]，用来检测不同的流体样品。Huang Y等人使用具有高折射率的高阻硅棱镜耦合器将入射太赫兹波转换为SSP模式，进一步进行了传感研究^[18]。他们通过结合可控等离子体共振和衰减全反射，实现了具有直接相位读出能力的超精密太赫兹传感器。反射的太赫兹相位对耦合间隙表现出两种完全不同的Q跳跃响应，其对应的相位谱Q因子在液体传感中的值为9.7~43.4。 Sathukarn A等人报道了一种基于金属涂层的表面等离子共振折射率传感器^[19]。设计了一种以聚二甲基硅氧烷（PDMS）为衬底的镀金光栅，对汽油-甲苯混合物进行了测量。通过改变光栅周期，使其表面等离子体共振频率与工作频率相匹配。目前报道的研究中多数利用棱镜作为耦合器激发SSP来实现传感，需要选择特定的材料并设计棱镜结构参数，且需要满足一定的角度关系来激发SSP模式。此外，棱镜耦合结构不易于集成在系统中^[20]。

近年来，在单个超表面结构上同时实现耦合以及SSP的激发也备受关注。通过在超表面上的部分区域设置相位梯度结构，从而在金属凹槽阵列上激发SSP模式。Yin L Z等人提出了一种用于SSP产生和波束偏转的太赫兹自旋解耦合双功能超表面耦合器^[21]。该超表面耦合器包括耦合超表面和传输超表面，前者可以将右旋圆偏振入射波异常反射，将左旋圆偏振入射波转换为SSP模式，而后者用于传播被激发的SSP模式。当频率为0.3 THz时，右旋和左旋圆偏振入射波的转换效率分别可达82%和70%。近期，本课题组报道了基于梯度介质超表面和二维介质超光栅结构的太赫兹SSP耦合结构，这两种结构可以将垂直入射的太赫兹波在衬底内偏折到特定的角度，使得-1级折射方向的功率显著增加，同时使其他反射和折射阶的功率减弱，从而实现对SSP波矢的补偿，进一步在底部金属沟槽阵列表面产生SSP模式^[11-12]。将这两种结构用于气体和液体等的检测，可以实现具有较高灵敏度的太赫兹传感性能。

本文提出使用单层光栅耦合超表面复合结构实现SPP模式激发以及获得高Q传感性能。基于光栅衍射原理，所提出的超表面结构可将特定角度衍射波的波矢作为实现太赫兹SSP的补偿波矢，从而产生表面等离子体共振，在透射谱中产生高Q谐振峰。相较于其他基于太赫兹SSP的传感器，本文所设计的结构有以下3个主要优点：（1）使用简单的单层光栅超表面复合结构作为耦合器，在激发SSP模式的同时，可以用作高Q传感；（2）所提出的光栅超表面结构工作在透射模式，克服了通过介质耦合器在实际应用时需要反射测量的缺点；（3）设计的超表面结构激发SSP后所产生谐振峰的Q值达到了1923，当超表面结构用于传感时，灵敏度为67 GHz/RIU。这项工作为太赫兹SSP在超薄和紧凑功能器件的多领域应用开辟了新的道路。

本文设计了一种类“E”字结构的金属超表面，实现了太赫兹波段的SSP模式激发。图1（a）给出了所提出光栅结构示意图，其由表面刻蚀的金属条结构和PDMS基底构成。太赫兹波垂直于金属微结构表面入射至器件，其电场与y方向平行，磁场与x方向平行。光栅耦合超表面的单元结构如图1（b）所示，P_x和P_y分别表示单元结构x方向和y方向的周期，凸出金属棒被平均分为两部分，长度均为w，由3个金属棒构成一个单元结构。3个金属棒组成的复合光栅结构与图2（a）所示光栅的衍射等效，而3个单独的金属棒形成了SSP结构。所选用的金属材料电导率为4.1×10⁷ s/m，PDMS的介电常数为2.34。利用有限元分析方法对所提出的光栅耦合超表面结构的透射特性进行研究，并且对单个金属棒结构以及光栅结构的色散特性进行分析研究。设置周期性边界条件，以有效减少仿真时间。

基于光栅衍射原理，可以通过光栅耦合实现SSP模式的激发。当自由空间的太赫兹波垂直入射到周期性超表面结构上能够发生电磁波的衍射现象，光栅衍射角不同，则表示衍射阶次不同。因此，可以用某一特定角度衍射波的波矢补偿SSP模式的波矢，使得该衍射角对应的衍射电磁波波矢与SSP波矢相匹配，此时便能实现SSP共振。对外则表现出该衍射电磁波被吸收，在透射谱上能够产生对应的谐振峰。对比传统的棱镜耦合方式，这种结构减少了所使用的器件数目，可以进一步实现微型化。

本文所设计结构的具体参数如下：P_x=500 μm，P_y=400 μm，P=120 μm，L=3×P，w=0.5×P，a=40 μm，b=0.5×P，d=60 μm，其中P为单个金属棒小单元结构的周期，a为凸出金属棒第一节的宽度，b为凸出金属棒第二节的宽度，d为凸出金属棒与金属外框之间的距离。为了方便后续的器件制备，选择金属光栅的厚度t=50 μm，衬底层厚度h=400 μm。研究中首先通过改变金属棒第一节宽度a来对透射谱以及色散曲线进行分析，其中a的值分别设定为30、50、70、90 μm。透射特性随宽度a的变化趋势如图2（c）（彩图见期刊电子版）所示，从中可以看出，随着a的增加，谐振频率表现出显著的蓝移现象，且谐振峰的带宽极窄。

其次，分别对光栅结构以及单个金属棒结构进行色散分析，结果如图2（d）（彩图见期刊电子版）所示。图2（d）中黑色实线表示金属光栅结构的色散曲线。接下来，对周期性金属棒结构进行色散分析，如图2（d）中的点划线所示，该金属棒能够提供类似SSP模式的色散特性。分析两种色散曲线发现，光栅结构的色散和SSP色散存在交叉点，此时便能够通过光栅耦合结构实现对SSP模式的波矢补偿，数值意义上表示为通过光栅耦合结构产生的沿着金属表面的波矢k₀和SSP模式的波矢k_SSP相匹配。通过对比研究发现，图2（d）中4个交叉点的位置和图2（c）中透射谱上4个谐振峰的位置相对应，此结果表明通过光栅耦合超表面结构激发了太赫兹SSP模式。所激发的谐振展现了表面等离子体特性，形成了沿着金属表面传输的场分布，在金属表面大大增强了场限制能力，使得所设计的结构具有比较高的品质因子，该超表面结构可以用来作为超灵敏传感器。

进一步，研究了超表面结构的几何参数对太赫兹SSP模式激发的影响规律。采用控制变量法分别通过①改变凸出金属棒第一节的宽度a，②改变金属棒第二节宽度b，③令a=b时同时变化以及④改变金属棒和金属外框间距d进行研究，分别得出了其透射率变化曲线如图3（彩图见期刊电子版）所示。首先分析宽度a以步长为20 μm在30~90 μm范围内变化时的透射情况，固定其他参数不变。从图3（a）可以看出，随着宽度a增加，透射谱中的谐振频率表现出蓝移趋势。接着，改变b时，采用同样的变化区间以及步长来分析，从图3（b）可以看出，随着b的增加，透射谱中的谐振峰具有明显的红移趋势。当a=b时，同时改变a和b，从图3（c）中可以看出，透射谱中的谐振频率表现出轻微的蓝移。这是由于在改变a时谐振频率蓝移的程度大于改变b时出现红移的程度，所以两者同时改变时仅发生了轻微的蓝移。最后，研究了不同参数d对该超表面结构透射率的影响，如图3（d）所示。当改变d时透射谱中谐振位置未发生明显的变化，可以判断该结构产生的SSP对参数d不敏感。

上述研究中，分析了4个变量对透射特性的影响，为了进一步说明所设计的光栅耦合超表面结构对太赫兹SSP模式的激发效果，进一步研究了这4个结构参数对色散特性的影响，如图4（彩图见期刊电子版）所示。同样地，固定参数b以及参数d，当参数a以步长20 μm从30 μm增加到90 μm时，如图4（a）所示，其色散特性的渐近频率出现显著的蓝移趋势，这与图3（a）中改变a时对应的透射谱中谐振频率蓝移趋势一致，进一步证明该谐振峰为激发SSP模式后形成的谐振。接下来，固定其他参数不变而改变参数b，参数b以同样的步长从30 μm变化至90 μm，结果如图4（b）所示，其渐近频率发生了红移。然后以同样步长和变化区间对参数a=b进行分析，此时固定参数d不变，结果如图4（c）所示，可见，色散的渐近频率发生了轻微的蓝移。最后，固定参数a和b，分析参数d对色散特性的影响，如图4（d）所示，可见，其色散曲线的渐近频率未发生明显移动，这也与上述参数对透射率的影响分析相一致。通过上述分析可以确定透射谱上的谐振是由光栅耦合金属超表面激发SPP模式而形成的。

通过对参数a和b的分析，可以判断该结构色散的渐近频率跟第一节金属棒宽度a成正比（a越小，渐近频率越低），跟第二节金属棒宽度b成反比（b越大，渐近频率越低）。当a=b时，此时同时改变金属棒宽度，参数a和参数b对色散渐近频率的影响处于相互抵消的状态，且参数a对频移造成的影响略大于参数b对频移造成的影响，导致渐近频率只是发生了轻微的蓝移。最后，改变金属棒和金属外框之间的距离d时发现色散特性没有发生明显改变。综上所述，可以通过改变参数a或者参数b实现对所激发的太赫兹SSP的调控。由于SSP具有较强的场限制能力，在谐振频率处具有很高的Q值，因此可以利用SSP共振进行高灵敏传感。

图5（彩图见期刊电子版）给出了谐振频率为0.22 THz时的电场分布。在x-z横截面的电场分布中，金属微结构表面存在着沿着金属表面传播的太赫兹SSP模式。结构表面产生的表面波对周围环境的变换十分敏感，利用这一现象将其用作传感时，可以将待测物放在结构表面来感知由于待测物变化而导致的表面电场分布的改变。由于折射率是样品物质的重要性质之一，不同的物质有其特定的折射率，因此便能够通过检测不同的折射率来区分识别不同的物质或者物质属性。因此，在传感研究中，假定使用不同的折射率来分析传感器的性能。

Q可以表征结构对电磁波的限制能力，Q值越高，对电磁波的限制能力也越强，周围环境的变化对结构场分布产生影响，通过检测该变化就可以实现传感。因此，具有较高Q值的结构，其传感性能也就越强。为了提高传感灵敏度，设计具有高Q值的结构是关键因素之一。通常情况下，若要利用SSP实现高灵敏传感，其结构需要具有较高的Q值。Q值的计算公式为Q=f₀/(|f₁−f₂|)，其中f₀为谐振中心频率，f₁和f₂分别为谐振峰幅度为最大值一半时所对应的频率。对图2所示透射谱谐振峰进行分析，其Q值达到了1923，表明该结构具有较强的场限制能力，有望用于诸多领域的实际应用。高Q值产生主要有以下几点原因：首先，由于谐振更接近渐近频率，谐振点附近的SSP模式更多地被限制在金属结构中，从图5（a）（彩图见期刊电子版）可以看出，局部场被有效增强，产生了非常尖锐的谐振峰^[22]；其次，周期性光栅结构激发共振并与SSP结构耦合，电磁波在3个金属棒组成结构中形成FP谐振，有利于产生高Q谐振；最后，如图5（b）（彩图见期刊电子版）所示，尖锐谐振峰在相邻的凹槽中具有反平行的电流分布，这保证了入射波的辐射损耗极低，且电流密度更大，形成了高阶模共振，产生高Q值。

接下来，通过改变金属表面周围环境的折射率来模拟不同物质，分析所设计结构的传感灵敏度。假定折射率的变化区间为1~1.5，步长为0.1。此时结构的尺寸为a=b=60 μm和d=60 μm。图6给出了光栅耦合超表面周围设定不同环境折射率时的透射率以及对应的传感灵敏度计算结果。从图6（a）可以看出，当待测物折射率逐渐增加时，透射谱中的谐振峰出现红移趋势。通过不同折射率所对应的透射谱中谐振峰位置的不同对物质进行区分，从而达到传感的目的。通过不同折射率时谐振位置的变化量来表征该结构的传感性能，如图6（b）所示。当折射率发生一定的变化时，谐振位置发生的偏移越大，表明该传感器对外界环境变化的感知表现的更为灵敏。在传感灵敏度分析中可以利用公式S=Δf/Δn表示待测物单位折射率变化引起的谐振峰频率偏移量，即灵敏度，其单位为RIU（Refractive Index Unit）。通过拟合计算得出所设计的结构的传感灵敏度为67 GHz/RIU。

本文设计了基于类“E”型光栅耦合超表面复合结构来实现太赫兹SSP激发和高Q传感。该超表面结构将特定角度的衍射波的波矢作为太赫兹SSP模式的补偿波矢，使其衍射角对应的衍射电磁波波矢与SSP模式的波矢相匹配，此时便能实现表面等离子体共振，在透射谱中产生高Q谐振峰，Q值达到1923。由于该结构工作在透射模式下，可通过改变超表面结构周围环境物质的折射率来表征其传感性能。结果表明，当超表面结构用于传感时，其灵敏度为67GHz/RIU。所提出的光栅耦合超表面结构在激发太赫兹SSP模式时不需要额外耦合器，其高Q谐振能够在诸多领域具有广阔的应用潜力。