 Nano Express
 Open Access
 Published:
HighQ Fano Resonance in Terahertz Frequency Based on an Asymmetric Metamaterial Resonator
Nanoscale Research Letters volume 13, Article number: 294 (2018)
Abstract
We propose a planar metamaterial formed by fourstrip metallic resonators, which can achieve highQ Fano resonance in terahertz regime. This terahertz planar metamaterial supports a sharp Fano resonance at 0.81 THz with 25% transmission. The resonance bandwidth of the dip is 0.014 THz with the Qfactor of 58. The interference between the bright mode and dark mode leads to the Fano line shape. This sharp Fano profile is explained by the electromagnetic theory of Fano resonance. Moreover, multiple Fano resonances can be realized by adding more strips into the original structure. As an example, two Fano dips with Qfactors of 61 and 65 can be achieved via a fivestrip structure.
Background
Metamaterial is a kind of artificial material exhibiting exotic properties, such as negative refractive index [1] and ultrahigh refractive index [2], which cannot be realized by natural materials in most situations. Such artificial material is composed of a large amount of periodic metallic units, and its characteristics (e.g., permittivity and permeability) can be easily controlled by changing the geometric parameters of the units [3]. As a result, the study of metamaterials has attracted wide attention in recent years. A great many novel applications have emerged in this domain, including perfect absorption [4, 5], metamaterial sensors [6,7,8,9], cloaking [10], Fano effects [11], etc.
The line shape of Fano resonance is quite different from symmetric Lorentzian profile. It is asymmetric and sharp with a relatively high Qfactor. Since Fano theoretically revealed the quantum mechanism of Fano resonance [12], it has become a hot topic. To illustrate the origin of Fano resonance, several theories have been set up, including Fano’s quantum mechanical analysis [12], classical oscillator model [13], coupledmode theory [14], and electromagnetic theory of Fano resonance [15, 16]. According to the electromagnetic theory of Fano resonance proposed by Gallinet and Martin [16], the distinctive Fano profile is attributed to the coupling between a nonradiative mode and a radiative mode which can also be seen as a continuum.
In terahertz regime, the sharp Fano resonance can be achieved by introducing a weak asymmetry in metamaterials [17,18,19,20], which may lead to the appearance of an underlying dark mode [21]. Besides, graphene materials can also be utilized to generate and even modulate the Fano resonance [22, 23]. Compared with a majority of EIT (electromagnetically induced transparency) [24, 25] and PIT (plasmoninduced transparency) [26, 27], Fano line shape is much sharper and narrower. The Qfactor of Fano [17, 28] profile is approximately ten times larger than that of Lorentzian line shape [29,30,31] in many situations. This property makes Fano resonance a promising choice to realize sensitive detecting [8]. However, the Qfactor of a lot of metamaterials is not high enough [17, 32, 33], which limits their applications in terms of sensing. In order to widely and efficiently apply Fano resonance into sensing, it is a necessary task to greatly improve the Qfactor of a metasurface.
Recently, some metamaterial structures have been designed to realize highQ Fano resonance. For instance, Ding et al. proposed a bilayer metamaterial which consists of two sets of asymmetric splitrings with different geometric parameters. It can support three Fano resonances whose Qfactors are respectively 33, 42, and 25 [19]. A symmetric dimer structure composed of identical spitring resonators on each layer was also presented to improve its Qfactor [34]. However, these stacked structures are suffering from technical challenges in manufacturing. HighQ resonance with simple structure design still remains to be a hot issue.
In this paper, we demonstrate a coplanar metamaterial structure consisted of four metallic strips. In each unit cell, three parallel strips are arranged perpendicular to the fourth one. This structure can support a highQ Fano resonance (Qvalue is about 58) at 0.81 THz with 25% transmission. This sharp line shape originates from the interaction between bright (radiative) mode and dark (nonradiative) mode. For further discussion, the electromagnetic theory of Fano resonance is employed [15, 16]. The properties of Fano resonance can be changed via controlling of geometric parameters. The sensing performance of the device is discussed. Moreover, by adding more strips into the originally designed structure, multiple Fano resonances can be realized.
Methods/Experimental
A large amount of researches indicate that breaching the symmetry of a structure may induce an asymmetric Fano line shape [17, 18, 35,36,37]. Based on this concept, we design this fourstrip metamaterial displayed in Fig. 1, where strip 2 is set to realize a symmetry breaking. Figure 1a shows the threedimensional diagram of the proposed metamaterial. Figure 1b, c respectively shows the side view and top view of the structure unit. The metallic fourstrip resonators are placed on the top of an ideal dielectric substrate whose real part of refractive index is 1.5 and imaginary part is 0. In reality, this dielectric material is corresponding to silica. That is to say, the substrate is lossless in terahertz region. We choose Au with conductivity σ = 4.09 × 10^{7} S/m to form the metallic planar resonator whose thickness is 0.2 μm. The repeat period is P_{x} = P_{y} = 180 μm. Three parallel strips (1, 2, and 3) have the same size. Their length is l_{x} = 120 μm and width is w = 20 μm. Strip 4 is perpendicular to the other strips (1, 2, and 3). Its length is l_{y} = 150 μm and width is w = 20 μm. The distance between the axis of strip 2 and the central point of the structure is d = 30 μm. Finitedifference timedomain method is used to simulate this planar metamaterial. In order to save simulation time and computing memory, we choose the mesh sizes of Δx = Δy = 1 μm and Δz = 0.02 μm. We find the simulation results are quite accurate in this case. Even if smaller mesh sizes are applied, the simulation results are nearly unchanged. The simulating boundary conditions along xaxis and yaxis are set as periodic, and the condition along zaxis is set as perfectly matched layers. Figure 1a shows that the whole structure is illuminated by a beam of normally incident THz wave. As seen in Fig. 1b, c, the electric vector E and magnetic vector H of the incident THz beam are yaxis polarized and xaxis polarized, respectively.
Results and Discussion
The transmission spectrum of the proposed metasurface is shown in Fig. 2a. There are two transmission dips at the frequencies of 0.430 THz and 0.809 THz with the transmission rates of 0.10% and 26.45%, respectively. In order to make the following explanation more concise, we use R_{s}R_{s} and R_{d} to mark these two resonant modes, R_{s} for the mode resonant at 0.430 THz and R_{d} for the resonant mode at a higher frequency. The optical transmission rate of R_{s} shows a symmetric Lorentz profile with a relatively wide bandwidth of 0.256 THz. By comparison, R_{d} exhibits an asymmetric Fano line shape which is much sharper with a bandwidth of 0.014 THz. Qfactor is an important criterion to judge the line shape. It can be obtained through dividing the central frequency by bandwidth. In fact, the Qfactor of R_{d} can reach 58, 30 times more than the Qvalue of R_{s}, which contributes to underlying applications in many fields. The existence of the asymmetric Fano profile roots in the interaction between a dark mode and a bright mode, i.e., the interaction between a nonradiative state and a continuum, generates from a radiative state [16, 38, 39]. In the rest of the paper, detailed mechanism of the Fano line shape will be discussed and theoretical transmission spectra will be analyzed. Although the transmission at 0.809 THz is 26.45% in the proposed metasurface, it can be reduced further. According to [40, 41], the utilization of lossy dielectric materials may reduce transmission. In our simulations, the substrate material we choose is an ideal material with a real refractive index of 1.5 that has no loss in terahertz region. A feasible method to reduce transmission is using a lossy material with a complex refractive index to form the substrate rather than this ideal lossless material.
In order to figure out the origin of the transmittance curve, the distribution of electric field ∣E∣ and the z component of magnetic field (H_{Z}) at the central frequency of two resonant dips are given in Fig. 3. We can find great differences between the field distributions of R_{s} and R_{d}. Figure 3a indicates that the electric field of resonant mode R_{s} is mainly concentrated on strip 1 and strip 3, especially the ends of these two strips. However, there is very little electric field distribution on other portions of the structure, including strip 2 and strip 4. Such electric field distribution is owing to the electromagnetic field of the normally incident light whose electric vector E is along yaxis. Therefore, R_{s} can be regarded as fundamental resonance (i.e., localized electromagnetic EM (electromagnetic) response) [42]. Besides, the distribution of the z component of magnetic field (H_{Z}) for mode R_{s} is shown in Fig. 3b from which we can get surface current distribution. It has been demonstrated that analysis of surface current can serve as a vital method to reveal how the coupling of modes generates Fano resonance [28]. As shown in Fig. 3b, surface current flows from the bottom to the upper part of the structure, contributing to the collection of opposite charges on both sides of strip 1 and strip 3. In contrast, the field distribution at the central frequency of R_{d} is rather different. Intense electric field is found around strip 1 and strip 2 (Fig. 3c), which is approximately four times larger than that of the mode R_{s}. According to the distribution of H_{Z} field shown in Fig. 3d, it is clear that the surface current flows upwards between strip 1 and strip 2 while the current between strip 2 and strip 3 flows oppositely. At the macro level, such field distribution can be seen as some kind of charge induction between the horizontal strips. From the perspective of mode coupling, this phenomenon is due to the interaction between the bright mode and dark mode.
Aiming to deepen and quantify our explanation, the spectra of bright mode and dark mode are simulated and the electromagnetic theory of Fano resonance [15, 16] is used in the proposed structure. Figure 2b shows the transmission spectrum of a structure whose periodic unit consists of strips 1, 3, and 4. The resonant mode supported by such a structure can be excited directly by plane wave; therefore, it is “bright mode.” In contrast, a dark mode cannot be excited by a beam of plane wave; it can be excited through a rapidly varying field, for instance, the near field of a dipole [15, 43]. Figure 2c displays the field intensity of the fourstrip metamaterial illuminated by a dipole source [44]. Maxwell’s equations form a solid basis of the electromagnetic theory of Fano resonance in nanostructures. According to Maxwell’s equations, electric vector E obeys the wave equation below:
where ω is the frequency of incident beam and ∈(r, ω) is the complex dielectric constant of the lossy material. The electric field E and the permittivity ∈ are both related to the frequency ω as well as the position vector r. Two orthogonal projection operators P and Q can be used to separate wave function ∣E> into a bright mode P ∣ E> and a dark mode Q ∣ E>, i.e., a radiative mode and a nonradiative mode [15, 38]. Through complicated derivation, the ratio of the total field’s strength to the intense of the bright mode can be given as
where W_{a} and ω_{a} are the bandwidth and central frequency of the asymmetric resonance, respectively. The asymmetric parameter q and the modulation damping parameter b are both indispensible to describe I_{a}(ω) [15, 16]. The Eq. (2) suggests that I_{a}(ω) exhibits an asymmetric profile, which finally results in the asymmetric Fano line shape in the transmittance curve.
The intensity of the bright mode R_{s} follows a smooth Lorentzian profile. It depends on the frequency ω and obeys the following equation:
of which W_{s} and ω_{s} are respectively the bandwidth and central frequency of the spectrum displayed in Fig. 2b, and a is the maximum value of the resonance’s amplitude. The total strength I(ω) of the resonance can be calculated by the product of I_{a} and I_{s}, from which we can finally get the transmittance T(ω).
In order to meet the requirement of energy conservation, a should not be greater than 1. W_{a} and ω_{a} can be calculated from the central frequency and bandwidth [15, 16]. The asymmetric parameter q as well as the modulation damping parameter b can be obtained through the method given by [16]. In this way, we can get the theoretical transmission spectrum of this asymmetric structure. In Fig. 2f, the black curve represents the transmission spectrum given by FDTD method and the red curve gives the results of our calculation based on electromagnetic theory of Fano resonance. The consistent trend of black and red curve indicates that it is reasonable to attribute the resonator’s transmission characteristics to the coupling of the bright mode and dark mode. This conclusion also coincides with the distribution of field in Fig. 3.
The geometric parameter d describes the distance between the axis of strip 2 and the central point of the whole structure (Fig. 1c). It can greatly affect the central frequency of transmission dips as well as their transmission coefficients. Corresponding transmission spectra with different d are shown in Fig. 2d, e. The black curve and red curve represent the transmission spectrum based on simulation and theoretical calculation, respectively. With d changing from 10 to 30 μm, it is clear that a sharp Fano dip deepens, resulting from the increasing coupling strength between the bright mode and dark mode. Furthermore, the central frequency of the mode R_{d} exists a distinct blue shift when strip 2 is placed closer to strip 1. Based on LC circuit model, the resonance frequency of R_{d} is given by [45].
where l is the equivalent length of the corresponding resonator. Equation (6) indicates that the central frequency ω_{d} is in inverse proportion to l. In our structure, equivalent length l is indicated by the length of dotdash line in Fig. 1c. This is because the field distributions of R_{d} are mainly restricted to the strip 1 and 2. The length of strip 1 (and 2) and the distance between the two strips together decide l. When d increases, the distance between the two strips declines. Hence, as shown in Fig. 1c, the equivalent length decreases when d changes from 10 to 30 μm. This leads to the increase of R_{d}’s resonant frequency.
According to the theory of Fano resonance suggested by Fano in 1961 [12], the process of autoionization is studied and the asymmetric line shape of the resonance is attributed to the interference between a continuum and a discrete state. This is also the origin of those asymmetric characteristics of the metamaterial resonator presented in this paper. As shown in Fig. 4, a threelevel system can be utilized to clarify the transition mechanism of the structure. R_{0} serves as the ground state of the whole system. Bright mode R_{1} is a radiative mode that can be directly excited by the normally incident beam. In this system, the nonradiative state R_{2} can be regarded as a “dark mode” [21] as discussed before. R_{2} can be excited through the symmetry breaking. Introducing an asymmetry offers a channel to allow the bright mode to couple with the dark mode, and therefore, leads to the Fano resonance [46].
The strong interaction between incident electromagnetic wave and the analyte layer makes highQ Fano resonance, a promising method to realize ultrasensitive detecting of refractive index n [8]. The device proposed in Fig. 5a can function as an effective sensor to detect the refractive index n of the analyte layer on the top whose thickness is 4 μm. The central frequency of the Fano dip will change with the change of n. Therefore, we can get the refractive index by analyzing the resonant frequency of R_{d}. Figure 5b shows the shift of Fano dip’s resonant frequency in the device. A distinct red shift appears when n is increased from 1 to 1.6. The sensing sensitivity S is equal to \( \frac{\varDelta f}{\varDelta n} \). Here, S of the sensor is calculated to be 0.105 THz/RIU (refractive index unit). It is well known that FOM (Figure of merit) is a vital criterion for the performance of a sensor [47]. It can be calculated by FOM = \( \frac{S}{\mathrm{linewidth}} \). In this presented structure, the FOM value can reach 7.501, which is on an ideal level [47, 48]. The sensing capability is also usually discussed by FOM* = \( \frac{S^{\ast }}{I} \) and S* = \( \frac{\varDelta I}{\varDelta n} \), which is related to the detected intensity. The calculation result of S* in this structure is 2.6/RIU. And the FOM* in our structure is calculated to be 10. We also did some work to figure out the variation of the response with the thickness of the analyte layer. Please refer to the Additional file 1.
Multiple Fano resonances could have applications in many situations. However, most of the plasmonic Fano metamaterials are designed to support single Fano resonance [11, 17]. Therefore, it is not easy for them to realize multiple Fano resonances through the adjustment of structure. In this paper, we realize multiple Fano resonances by adding more horizontal strips into the original design of the metamaterial. We present a fivestrip structure as a representative example. The schematic diagram of the fivestrip resonator is shown in Fig. 6a. Strips 1, 2, 3, and 4 are in the same size and parallel to each other. Their length is l_{x} = 120 μm and width is w = 20 μm. Strip 3 is located in the middle, and the distance d between the axes of strip 2 and strip 3 is 32 μm. Strip 5 is perpendicular to the other four strips. Its length is l_{y} = 150 μm and width is w = 20 μm. The boundary conditions and mesh size are kept the same as the simulation of fourstrip resonator. The simulation result is shown in Fig. 6b, in which we can clearly find two sharp Fano dips at 0.75 THz and 0.91 THz. The Q values of these two dips are respectively 61 and 65. More Fano dips should be generated if more horizontal strips are added into the structure.
Conclusion
In conclusion, we design a fourstrip planar resonator which can support sharp Fano resonance with a high Qvalue. The bandwidth of the Fano dip is 0.014 THz and its Qfactor is 58. The interaction between bright mode and dark mode results in the appearance of the asymmetric Fano profile. The theoretical transmission spectrum is calculated in this paper. Furthermore, multiple highQ Fano resonances can be realized by adding more horizontal strips to the structure. This structure can be applied in sensing and other fields.
Abbreviations
 EIT:

Electromagnetically induced transparency
 EM:

Electromagnetic
 FOM:

Figure of merit
 PIT:

Plasmoninduced transparency
 Q :

Quality factor
 RIU:

Refractive index unit
References
 1.
Smith DR, Padilla WJ, Vier DC, NematNasser SC, Schultz S (2000) Composite medium with simultaneously negative permeability and permittivity. Phys Rev Lett 84:4184
 2.
Choi M, Lee SH, Kim Y, Kang SB, Shin J, Kwak MH, Kang KY, Lee YH, Park N, Min B (2011) A terahertz metamaterial with unnaturally high refractive index. Nature 470:369–373
 3.
Pendry JB, MartínMoreno L, GarciaVidal FJ (2004) Mimicking surface plasmons with structured surfaces. Science 305:847–848
 4.
Landy NI, Sajuyigbe S, Mock JJ, Smith DR, Padilla WJ (2008) Perfect metamaterial absorber. Phys Rev Lett 100:207402
 5.
Liu N, Mesch M, Weiss T, Hentschel M, Giessen H (2010) Infrared perfect absorber and its application as plasmonic sensor. Nano Lett 10:2342–2348
 6.
Singh R, Cao W, AlNaib I, Cong L, Withayachumnankul W, Zhang WL (2014) Ultrasensitive terahertz sensing with highQ Fano resonances in metasurfaces. Appl Phys Lett 105:171101
 7.
Xu WD, Xie LJ, Ying YB (2017) Mechanisms and applications of terahertz metamaterial sensing: a review. Nanoscale 9:13864–13878
 8.
Jaksic Z, Vukovic S, Matovic J, Tanaskovic D (2010) Negative refractive index metasurfaces for enhanced biosensing. Materials. 4:1–36
 9.
Yu P, Wu J, Ashalley E, Govorov AO, Wang ZM (2016) Dualband absorber for multispectral plasmonenhanced infrared photodetection. J Phys D Appl Phys 49:365101
 10.
Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF, Smith DR (2006) Metamaterial electromagnetic cloak at microwave frequencies. Science 314:977–980
 11.
AlNaib I (2018) Thinfilm sensing via Fano resonance excitation in symmetric terahertz metamaterials. J Infrared Millim Terahertz Waves 39:1–5
 12.
Fano U (1961) Effects of configuration interaction on intensities and phase shifts. Phys Rev Lett 124:1866
 13.
Joe YS, Satanin AM, Kim CS (2006) Classical analogy of Fano resonances. Phys Scr 74:259
 14.
Ruan Z, Fan S (2010) Temporal coupledmode theory for Fano resonance in light scattering by a single obstacle. J Phys Chem C 114:7324–7329
 15.
Gallinet B, Martin OJF (2011) Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials. Phys Rev B 83:235827
 16.
Gallinet B, Martin OJF (2011) Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances. ACS Nano 5:8999–9008
 17.
Singh R, AlNaib I, Koch M, Zhang WL (2011) Sharp Fano resonances in THz metamaterials. Opt Express 19:6312–6319
 18.
Cao W, Singh R, AiNaib I, He M, Taylor AJ, Zhang WL (2012) Lowloss ultrahighQ dark mode plasmonic Fano metamaterials. Opt Lett 37:3366–3368
 19.
Ding CF, W L, Xu DG, Yao JQ, Sun XH (2016) Tripleband high Q factor Fano resonances in bilayer THz metamaterials. Opt Commun 370:116–121
 20.
Xiao X, Wu JB, Miyamaru F, Zhang MY, Li SB, Takeda MW, Wen WJ, Sheng P (2011) Fano effect of metamaterial resonance in terahertz extraordinary transmission. Appl Phys Lett 98:011911
 21.
Fedotov VA, Rose M, Prosvirnin SL, Papasimakis N, Zheludev NI (2007) Sharp darkmode resonances in planar metamaterials with broken structural symmetry. Phys Rev Lett 99:12243–12254
 22.
He XY, Lin FT, Liu F, Shi WZ (2016) Terahertz tunable graphene Fano resonance. Nanotechnology 27:485202
 23.
Xiao SY, Wang T, Jiang XY, Yan XC, Cheng L, Wang BY, Xu C (2017) Strong interaction between graphene layer and Fano resonance in terahertz metamaterials. J Phys D 50:195101
 24.
Lu XQ, Shi JH, Liu R, Guan CY (2012) Highlydispersive electromagnetic induced transparency in planar symmetric metamaterials. Opt Express 20:17581–17590
 25.
Liao Z, Liu S, Ma HF, Li C, Jin BB, Cui TJ (2016) Electromagnetically induced transparency metamaterial based on spoof localized surface plasmons at terahertz frequencies. Sci Rep 6:27596
 26.
Xu Q, Su XQ, Ouyang CM, Xu NN, Cao W, Zhang YP, Li Q, Hu C, Gu JQ, Tian Z, Azad AK, Han JG, Zhang WL (2016) Frequencyagile electromagnetically induced transparency analogue in terahertz metamaterials. Opt Lett 41:4562–4565
 27.
Zhang XQ, Li Q, Cao W, Gu JQ, Singh R, Tian Z, Han JG, Zhang WL (2013) Polarizationindependent plasmoninduced transparency in a fourfold symmetric terahertz metamaterial. IEEE J Sel Top Quantum Electron 19:8400707
 28.
Chen Y, Chu JR, Xu XF (2016) Plasmonic multibowtie aperture antenna with Fano resonance for nanoscale spectral sorting. ACS Photonics 3:1689–1697
 29.
Chowdhury DR, Singh R, Reiten M, Chen HT, Taylor AJ, O’Hara JF, Azad AK (2011) A broadband planar terahertz metamaterial with nested structure. Opt Express 19:15817–15823
 30.
Dong GX, Xie Q, Zhang Q, Wang BX, Huang WQ (2018) Plasmoninduced transparency based on triple arcrings. Materials 11:964
 31.
Park SJ, Yoon SAN, Ahn YH (2016) Dielectric constant measurements of thin films and liquids using terahertz metamaterials. RSC Adv 6:73
 32.
Singh R, AlNaib I, Cao W, Rockstuhl C, Koch M, Zhang WL (2013) The Fano resonance in symmetry broken terahertz metamaterials. IEEE Trans Terahertz Sci Technol 3:820–826
 33.
Li Q, Cong LQ, Singh R, Xu NN, Cao W, Zhang XQ, Tian Z, Du LL, Han JG, Zhang WL (2016) The monolayer graphene sensing enabled by the strong Fano resonant metasurface. Nanoscale 8:17278–17284
 34.
Du LH, Li J, Liu Q, Zhao JH, Zhu LG (2017) HighQ Fanolike resonance based on asymmetric dimer structure and its terahertz sensing application. Opt Mater Express 7:1335–1342
 35.
Cong LQ, Manjappa M, Xu NN, AlNaib I, Zhang WL, Singh R (2015) Fano resonances in terahertz metasurfaces: a figure of merit optimization. Adv Opt Mater 3:1537–1543
 36.
Nguyen TK, Le TD, Dang PT, Le KQ (2017) Asymmetrically engineered metallic nanodisk clusters for plasmonic Fano resonance generation. J Opt Soc Am B 34:668–672
 37.
Li XF, Bian XY, Milne WI, Chu DP (2016) Fano resonance engineering in mirrorsymmetrybroken THz metamaterials. Appl Phys B 122:95
 38.
Feshbach H (1958) A unified theory of nuclear reactions. Ann Phys 5:357–390
 39.
Zhang W, Govorov AO, Bryant GW (2006) Semiconductormetal nanoparticle molecules: hybrid excitons and the nonlinear Fano effect. Phys Rev Lett 97:146804
 40.
Yu P, Besteiro LV, Wu J, Huang YJ, Wang YQ, Govorov AO, Wang ZM (2018) Opt Express 26:20471–20480
 41.
Xie Q, Dong GX, Wang BX, Huang WQ (2018) Design of quadband terahertz metamaterial absorber using a perforated rectangular resonator for sensing applications. Nanoscale Res Lett 13:137
 42.
Wang BX, Xie Q, Dong GX, Zhu HX (2017) Broadband terahertz metamaterial absorber based on coplanar multistrip resonators. J Mater Sci 28:17215–17220
 43.
Zhang WL, Gallinet B, Martiin OJF (2010) Symmetry and selection rules for localized surface plasmon resonances in nanostructures. Phys Rev B 81:233407
 44.
Martin OJF, Girard C (1999) Generalized field propagator for arbitrary finitesize photonic band gap structures. Phys Rev Lett 82:315–318
 45.
Wang BX, Wang LL, Wang GZ, Huang WQ, Li XF, Zhai X (2013) A simple design of ultrabroadband and polarization insensitive terahertz metamaterial absorber. Appl Phys A 115:1187–1192
 46.
Han S, Singh R, Cong LQ, Yang HL (2014) Engineering the Fano resonance and electromagnetically induced transparency in nearfield coupled bright and dark metamaterial. J Phys D 48:035104
 47.
Zhang YP, Li TT, Zeng BB, Zhang HY, Lv HH, Huang XY, Zhang WL, Azad AK (2015) A graphene based tunable terahertz sensor with double Fano resonances. Nanoscale 7:12682–12688
 48.
Ye J, Dorpe PV (2011) Improvement of figure of merit for gold nanobar array plasmonic sensors. Plasmonics 6:665–671
Funding
This work was supported by the National Natural Science Foundation of China (Grant No. 11647143), Natural Science Foundation of Jiangsu (Grant No. BK20160189), and the Fundamental Research Funds for the Central Universities (Grant No. JUSRP115A13).
Availability of Data and Materials
All data are fully available without restriction.
Author information
Affiliations
Contributions
BXW conceived the research and supervised the whole work. QX and GXD conducted the simulations and analyses and wrote the manuscript. WQH assisted in processing the data and figures. All authors read and approved the final manuscript.
Corresponding author
Correspondence to BenXin Wang.
Ethics declarations
Competing Interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Additional File
Additional file 1:
The variation of the response with the thickness of the analyte layer. (DOCX 297 kb)
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Xie, Q., Dong, G., Wang, B. et al. HighQ Fano Resonance in Terahertz Frequency Based on an Asymmetric Metamaterial Resonator. Nanoscale Res Lett 13, 294 (2018). https://doi.org/10.1186/s1167101826770
Received:
Accepted:
Published:
Keywords
 Metamaterial
 Fano
 Terahertz
 Sensing