Open Access
Add to BibSonomy
Abstract
For non-invasive detection, terahertz (THz) sensing shows more promising performance compared to visible and infrared regions. But so far, figure of merit (FOM) of THz sensor has been exceeding low due to weak radiation and absorption loss. Here, we propose an easily implemented THz sensor based on bulk Dirac semimetal (BDS). The presented structure not only achieves narrowband absorption and dynamic tunability at five perfect absorption bands, but also exhibits excellent sensing performance with a FOM of 813. These fascinating properties can be explained by the combination of the classical magnetic resonance induced by the anti-parallel current, the electric resonance of adjacent unit cells resulting from the air slots at both ends of the absorber, and Mie resonance supported by coating, respectively. Our work can provide a new avenue for the design of multi-band photodetectors and sensors in the future.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) technology are powerful tool for applications including disease diagnosis [1], quality control of food [2], high signal-to-noise ratio [3], etc [4–6]. THz sensing [7,8], label-free and non-invasive detection of refractive index change [9], is one of the most notable application of THz radiation. By contrast, infrared and visible optical sensing techniques are usually unsatisfactory. This is because the high photon energy and the inevitable loss in these regions can damage the molecular structure of the analyte [10]. Nowadays, THz sensor can be prepared experimentally with the proven nano-precision control [11]. Based on this support, various design for THz sensing have been demonstrated, such as microfluidic sensors [11,12], nanowires [13], photonic crystal sensors [14] and metamaterials [15,16]. In general, the key method is to improve the light-matter interaction between the THz wave and the analytes. For demonstrating sensing performance of a sensor, figure of merit (FOM), the ratio of the sensitivity to the full width at half maximum (FWHM) of the resonance is defined. The higher the value of FOM is, the better sensing performance will be. Regrettably, FOM is very small at the THz region due to the weak radiation effects and absorption loss [11,17].
Recently, for enhancing the THz sensing capability of the device, great efforts have been made on [18–22]. Wang et al. presented a metamaterial absorber based on gold that achieved a FOM of 24.6 [20]. Ng et al. presented linear arrays of subwavelength grooves with gold, achieving FOM of 49 [21]. Recently, Liang et al. demonstrated a THz sensor with a FOM as high as 692 based on silicon-grating slot waveguide [22]. Nevertheless, the above mentioned structures complicate the actual preparation because of their relatively complex design. Due to the gap sizes of their design a fabrication based on pure lithographic methods [11,22], for example, SU8 (Microchem) resist stripes, distance between two surfaces is determined by the thickness of the SU8 resist, leading to inevitable experimental error [22]. For a simple structure, it is possible to avoid sidewall damage creating steps as dry etching [22,23]. Another shortcoming is that to realize the adjustability of the resonant wavelength, the means of altering the geometrical parameter is implemented in most status. Fatally, this approach increases costs on account of the reconfiguration of the structure in actual application. In recent years, dynamically adjustable absorbers based on three dimensional (3D) bulk Dirac semimetal (BDS) exhibit promising sensing performance at THz region [24,25]. This lack of cost increases has been perfected by replacing traditional materials with BDS. 3D BDS, a state of quantum matter that can be identified as “3D graphene”, recently stimulating in-depth investigations due to its wonderful properties [26]. The BDS has a continuously tunable Fermi energy, which can be adjusted by chemical doping [27]. Owing to the symmetrical protection of the crystal preventing the gap formation [28–30], the mobility of BDS is much higher than that of graphene under the 5K, which is an appropriate temperature for graphene [31]. Lately, the excellent properties of BDS have been experimentally studied [32–37]. For instance, Borisenko et al [32] experimentally realized a 3D BDS in Cd3As2. Kharzeev et al [33] find a strong and narrow plasmon excitation in BDS relative to graphene. Liu et al [34] demonstrated the robustness of 3D Dirac fermions in 3D topological Dirac semimetals against in situ surface doping. Thanks to the excellent properties of BDS, it can be used as a promising candidate for use in THz sensor devices. However, there are currently very few reports on BDS-based THz sensors. Realization of advancing THz sensor based on BDS requires more effective methods.
In 2012, Gao et al. used a grating aperture array to experimentally achieve four-band absorption, and can effectively adjust the absorption rate and resonance position by changing the width of the gap [38]. In 2013, Piper et al. reported a photonic crystal slab model that can obtain the six-band absorption in the near-infrared and visible wavelength ranges. However, because of the relatively small size (period of 900 nm) and the limitations of the experimental conditions at the time, there is no in-depth exploration of this aspect [39]. Soon afterwards, Meng et al. proposed a four-band plasmonic perfect absorber based on graphene using the FDTD simulation [40]. Lately, Yan F et al. used numerical simulation to obtain a FOM of 12.5 based on six-band absorption in the THz band [41]. It should be mentioned that none of the above reports have stacked multiple similar structures to generate multiple resonances, but instead stimulated the resonance of higher-order modes through complex physical mechanisms, further simplifying the structure.
In this letter, based on the excellent work before, we firstly propose a four-band perfect absorber with BDS realized by an easily implemented three layer structure. The resonance peak can be dynamically adjusted by altering the Fermi energy of the BDS. Numerical simulation results reveal the profound physical mechanism behind the simple system. The appearance of four narrow absorption bands are ascribed to the interaction of the classical magnetic resonance induced by the anti-parallel current and the electric resonance of adjacent unit cells resulting from the air slots at both ends of the absorber. Furthermore, our structure can achieve five-band perfect absorption by simply adding a layer of SiO2 coating on the BDS while the other four absorption peaks are nearly unaffected. This is because the addition of the SiO2 coating excites the Mie resonance [42]. Unexpectedly, the fifth absorption band shows excellent sensing performance with FOM of 813. These findings may provide a new guideline for the design of multi-band absorbers and sensors in the future.
2. Conductivity of BDS
5The complex conductivity of the BDS is obtained by using a random-phase approximation theory (RPA) [43]. The dynamic conductivity of the BDS can be written as follow:
where G(E) = n(-E) - n(E) with n(E) being the Fermi distribution function, Ω = ħω/EF + iħτ−1/EF, kF = EF / ħυF is the Fermi momentum, υF = 106 m/s is the Fermi velocity, ε = E / EF, εc = Ec / EF, g is the degeneracy factor and Ec is the cutoff energy beyond which the Dirac spectrum is no longer linear. Ec and EF satisfy the following relationship: Ec + EF = 0.6 eV [43]. The value of 0.6 eV is determined by Ref [32]. [see Fig. 2(a) therein]. BDS exhibits a metallic resonance in the THz band. However, unlike pure metal, its band structure exhibits three Dirac points at the Fermi level [28], which is why it is called 3D graphene. Owing to the outstanding nature, graphene as well as BDS, not only can change the Fermi level by chemical doping, but also the application of a gate voltage, achieving dynamic tunability of the resonance wavelength without redesigning the structure, which is confirmed by the first principle [44]. Employing the double-band model and taking into account the inter-band electronic transitions, the permittivity of the BDS can be written as [26]:where ε0 is the permittivity of vacuum and ε0 = 1 for g = 40 (AlCuFe quasicrystals [45]).3. Four-narrowband perfect absorption
Figure 1 shows the proposed four-narrowband absorber [see Fig. 1(a)] with a magnified cubic unit cell [Fig. 1(b)]. The proposed structure consists of a square-resonator array with BDS and a gold (Au) substrate separated by a silicon dioxide (SiO2) spacer with refractive index n = 2.1025, and the ambient medium is supposed to be air. The position of the three layers of materials can be precisely controlled experimentally by using photoresist technology [46] and dry etching [23]. The BDS sheet with Fermi energy EF = 0.14 eV has a width (w1) of 212 μm. The width (w2) of the SiO2 is 230 μm and the unit cell has a period constant (P) of 251μm. Thicknesses of the BDS-SiO2-Au layers from top to bottom are 20 μm (t1), 80 μm (t2) and 2 μm (t3), respectively. Our results are obtained by using finite-difference time-domain (FDTD) method. Since the value of t3 is much larger than the skin depth of the electromagnetic waves, the transmission channel is closed. Thus, the absorption (A) of the entire structure is obtained as A = 1 – R, where the R is reflection. In our simulation, the mesh size inside the BDS sheet is dx = 4 μm, dy = 4 μm, and dz = 0.5 μm. Perfectly matched layers (PML) are applied along the z direction. The simulated temperature remains unchanged at 300K. The background index in the FDTD simulation is set to 1 corresponding to the refraction index of the whole surrounding medium. Simulated time is set to 2000 ps and mesh type is auto non-uniform with 7 of mesh accuracy. The type of PML settings is selected as uniaxial anisotropic PML (legacy). Layers and kappa are set to 100 and 20, respectively. Other parameters remain default unless otherwise specified.
Fig. 1 (a) The structural schematic of the proposed material. (b) Magnified unit cell of the absorber (w1 = 212 μm, w2 = 230 μm, t1 = 20 μm, t2 = 80 μm, t3 = 2 μm, P = 251μm and Fermi energy EF = 0.14 eV).
Under the normally launching of the plane wave with wavelength λ, four-band perfect absorption is obtained, as shown in Fig. 2(a). Four different absorption peaks can maintain an average absorptivity 99.1% located at resonant wavelengths of 256.8 µm, 260.6 µm, 276.8 µm, and 318.2 µm (see Table 1), respectively. We note that there is an additional lower absorption peak, which will be discussed in the fourth section. Five modes are labeled as M1, M2, M3, M4 and M5, respectively [see Fig. 2(a)]. It is worth mentioning that all absorption bands at the THz range are extremely narrow. For a better description of the narrow band, the Q is defined as Q = λ0/Δλ, where λ0 is the resonant wavelength, Δλ is the full width at half maximums (FWHM). The higher value of Q, the narrower absorption and the better optical performance. Interestingly, the value of Q of M1, M2, M3 and M4 can reach about 396, 612, 651 and 637, respectively (see Table 1), showing potential sensing capability.
Fig. 2 (a) The absorption spectra of the proposed absorber [see Fig. 1(a)]. (c1)-(c5) Distributions of the y-component magnetic field (Hy), (d1)-(d5) x-component electric field (Ex) and (e1)-(e5) electric field (E) (in the plane of y = 0) for resonant positions of M1, M2, M3, M4 and M5, respectively. The monitored range along x direction is from −125.5 μm to 125.5 μm. The profile of the structure is indicated by the white line.
Table 1. Resonant wavelength, FWHM, factors of sensitivity (S), FOM and Q of M1, M2, M3, M4 and M5 modes of the proposed structure shown in Fig. 1
To reveal the physical mechanism of the proposed metamaterial absorber, y-component magnetic field (Hy), x-component electric field (Ex) and electric field (E) distributions at various resonant wavelengths (i.e. 318.173 μm, 276.751 μm, 260.550 μm and 256.782 μm, respectively) are simulated in the x-z plane and illustrated in Figs. 2(c1)-2(e5). Overall, it is seen from Fig. 2(c1) that, all of the magnetic field energy is concentrated in the SiO2 layer, indicating that, the classic magnetic resonance dominates in the M1 mode. In classical magnetic resonance, for a three- or multi-layer structure, magnetic energy distributes in the intermediate dielectric layer due to the anti-parallel currents of the upper and lower surfaces [47]. However, for the resonance peak of the M2 mode, not only the SiO2 layer, but also the air slots at both ends of the SiO2 layer and the BDS sheet store magnetic field energy [see Fig. 2(c2)], so that the magnetic field energy induced by the anti-parallel current is not simply concentrated in the SiO2 layer. A part of them is coupled to the incident light at the edge of each period. In the M3-M5 mode, even the air layer above the BDS is involved in the coupling [see Figs. 2(c3)-2(c5)]. This indicates that the presences of the air slots constitute a hybrid magnetic resonance mode and induce a stronger resonance, which facilitate the construction of narrowband absorption. For the M5 mode, we will be discussed in the sixth section. On the other hand, we can perform qualitative analysis by observing the Ex distribution. Figure 2(d1)shows that the electric field energy located in the air slots is less than counterpart in the SiO2 layer, implying that in the M1 mode, the magnetic resonance dominates. However, as the wavelength decreases, the Ex at the air slots become gradually stronger, and the Ex of the SiO2 layer begin to weaken, as shown in Fig. 2(d2). When the wavelength is equal to the resonance wavelength of the M3 mode, the Ex of the SiO2 layer is reduced to a negative value, and that of the air slots at both ends of the BDS sheet is positive [see Fig. 2(d3)]. One positive and one negative correspond to the mutual cancellation of the energy, that is, the destructive interference. As the phase changes periodically, when the wavelength is equal to 256.782 μm (M4 mode), the positive and negative phases of the two are once again interchanged, and the coupling at the air slots position is dominant [see Fig. 2(d4)]. We noticed that resonance positions of M3 and M4 modes, which are located very close together, can be combined into one absorption peak. In other words, the splitting of the absorption peak results in the appearance of absorption peaks of M3 and M4 due to the anti-phased mode. To give an intuitive evidence, the dependence of the absorption spectra on different sizes of air slots is shown in Fig. 2(b). As shown in Fig. 2(b), when w2 = P = w, the absorption peaks of M3 and M4 are gradually approached with the decreasing value of w, and finally merge into one absorption peak with blue shift due to the variation of the effective refractive index [25]. Accordingly, adjusting a suitable geometry parameter, especially the parameters of the air slots, allows the energy of incident light to be unimpededly coupled to the energy induced by the anti-parallel current. At the resonant wavelength, the interaction of the two parts cause the energy to no longer be only localized in the SiO2 layer, but is partially offset in the coupling [see Fig. 2(d3)-2(d4)], and the anti-phase mode induced by the coupling causes the absorption peak to occur splitting [see Fig. 2(b)]. The combined effect leads to narrower, more absorption peaks. Consequently, this method can achieve a multi-band perfect narrowband absorber and may provide direction for engineering multi-channel photodetectors. Compared to Ex, we can see that E distributions of resonant peaks of M1, M2, M3 and M4 are similar to those of Ex, respectively [see Figs. 2(e1)-2(e4)]. Next, we can perform quantitative analysis by observing the total electric field distributions. Compared to E of the resonance positions of the M1-M4 modes, respectively, we find that at 276.751 μm (M2 mode), the total electric field energy of the air grooves at both ends is broader and stronger, showing excellent sensing performance. We will discuss it in the fourth section.
4. Five-narrowband perfect absorption
In this section, the absorption and physical mechanism of the M5 mode is studied. In the structure shown in Fig. 1, the absorption of the M5 mode is very low under the illumination of plane waves. The stored energy at the entire structure is relatively low [see Figs. 2(c5), 2(d5) and 2(e5)], because the coupling strength between the air slots and the SiO2 layer is weak at 252.072 μm, and the energy is lost in the form of reflection. Moreover, we noticed that the air layer above the BDS has a considerable amount of energy. If the coupling at the upper air layer of the BDS can be strengthened, it is possible to achieve high absorption at this wavelength.
In order to enhance the coupling of the air slots at both ends of the absorber and the air layer above the BDS while reducing the impact on the other four modes, a method, coating a layer of SiO2 with thickness t4 = 21 nm on the BDS, is proposed [see Fig. 3(a)], which has been experimentally realized [46]. In this simulation, the mesh size inside the coating is dx = 212 μm, dy = 212 μm, and dz = 21 nm. Surprisingly, the absorptivity 98.9% of the M5 mode is obtained after improvement. Because the coating is extremely thin compared to the thickness of BDS, the effect on the M1-M4 modes can be ignored. For studying the physical mechanism of the M5 mode more deeply, the distributions of the Hy, Ex and E for resonant position of M5 mode are illustrated in Figs. 3(c), 3(d) and 3(e), respectively. Compared to the M5 mode of the previous structure [see Fig. 1], the coupling strength of H, Ex and E has been significantly enhanced, especially E, the range of coupling is wider than other modes, even up to the top of BDS, while the field distributions of absorption peaks of other modes has hardly changed (not shown here). In M5 mode, BDS is equivalent to a substrate to ensure transmission of zero and the addition of silica coating forms an additional Mie resonance [48]. The impedance of the proposed absorber match to free space [49]. Accordingly, the interaction between the incident light and the magnetic resonance through the air slots is the strongest. At the same time, the strength of magnetic resonance is the weakest, while the electric resonance of adjacent unit cells is completely dominant, even the coupling area is covered more, showing excellent sensing potential.
Fig. 3 (a) Schematic diagram of the proposed five-band perfect absorber. (b) Absorption spectra of the proposed five-band perfect absorber. (c) Distributions of the y-component magnetic field (Hy), (d) x-component electric field (Ex) and (e) electric field (E) (in the plane of y = 0) for resonant position of M5. The monitored range along x direction is from −125.5 μm to 125.5 μm. The profile of the structure is indicated by the white line.
The electric field distribution is a result of electromagnetic waves coupling with each other in the whole surrounding medium, and is affected by the shape of the irradiated structure, the wavelength of the incident light, and the refractive index of the whole surrounding medium. When light is incident on the sensor to produce resonance, each resonance position can be simplified to an interference model. When the optical path difference is equal to an even multiple of the half wavelength of the light (if there is a half-wave loss, it is an odd multiple), constructive interference occurs. Electric field strength is enhanced, and the corresponding wavelength is the resonant wavelength. A change of the refractive index of the whole surrounding medium causes a change in the optical path of each resonant position, which further leads to a change of the overall electric field strength because the overall electric field strength corresponds to the superposition of each electric field. Therefore, the smaller the range of resonance wavelengths (i.e., the narrower the resonance peak) and the stronger the corresponding electric field strength, the more sensitive they are to changes in the refractive index of the whole surrounding medium. For demonstrating sensing performance of the proposed absorber, the factors of sensitivity S and FOM [50–52] can be defined according to:
where ∆λ is the shift of resonant wavelength due to change of refractive index in the surrounding medium ∆n.According to Eqs. (4) and (5), we can evaluate the sensing performance of several modes of four-band (see Table 1) and five-band (see Table 2) absorbers. Resonant wavelengths for different whole surrounding medium refractive index n of M1, M2, M3, M4 and M5 modes are shown in Fig. 4. Here, the value of the background index in the FDTD simulation increases from 1 to 1.009 with an interval of 0.003. Under the change of refractive index, the average absorption rate of all modes can be maintained above 98%. Compared to the previous structure [see Fig. 1], the sensing ability of the M1-M4 modes has not changed notably. Remarkably, the M5 mode demonstrate excellent ability of sensing with the FOM 813 (see Table 2), which is much better than those in [17,20–22,53]. The larger value of the FOM is due to the wider area and stronger amplitude of the E distribution [see Fig. 3(e)] compared to those of absorption peaks of four other modes [see Figs. 2(e1)-2(e4)]. Therefore, the ultra-high FOM demonstrated by the M5 mode has a better application prospect in the sensing field and application. The proposed method increasing the value of FOM by inducing more surrounding medium around the sensor to participate in the coupling can provide idea for the design of sensor in the future.
Table 2. Resonant wavelength, FWHM, S, FOM and Q of M1, M2, M3, M4 and M5 modes of the improved structure shown in Fig. 5(a)
Fig. 4 (a) Absorption spectra and (b) resonant wavelength (M2 mode) of the five-band perfect absorber with varying refractive index of surrounding environment, respectively.
5. Tunability of the five-band absorber
Most absorbers need to achieve adjustable of resonant wavelength for application requirements. Next, we will study the tunability of the resonant wavelength of the proposed structure. Figures 5(a) and 5(b) show the absorption spectra of the proposed structure with different lengths of the SiO2, EF of the BDS, respectively. Other parameters are kept unchanged unless otherwise specified. It is clearly shown that the resonant peak with same order mode shifts to a longer wavelength by increasing the value of the w2 [see Fig. 5(a)]. It is mainly because the effective refractive index increases as w2 is increased [25]. Nevertheless, like traditional metal-based devices, this method of adjusting the resonant wavelength can only be achieved by re-preparing the device. On the other hand, the resonant wavelength exhibit a blue shift as EF of the BDS increases [see Fig. 5(b)]. As mentioned above, the adjustment of the Fermi level can be achieved by chemical doping and application of a gate voltage, which saves cost and increases work efficiency. We use perturbation theory to explain this phenomenon. According to perturbation theory:
where ∆ε and ∆μ are the change in permittivity and permeability of the BDS, respectively; ∆ω and ω are change of electromagnetic energy caused by the perturbation of BDS and total energy undisturbed, respectively; E and E0 are the perturbed electric fields and unperturbed, respectively. H and H0 are the perturbed magnetic fields and unperturbed, respectively. Then, evolution of the real and imaginary parts of permittivity of BDS on the Fermi energy EF are plotted in Figs. 5(c) and 5(d), respectively. As shown, the real (imaginary) part of permittivity of BDS decreases (increases) with the increasing of EF at a fixed wavelength. For qualitative analysis, we only need to consider the real part, i.e. ∆ε is less than zero. Therefore, ∆ω is greater than 0 through Eq. (6). As a result, the resonance peak exhibits a blue shift with the increasing of EF on account of inverse proportional relationship between wavelength and frequency.Fig. 5 Absorption spectra for (a) different length w2, (b) different EF of the BDS. (c) The real and (d) imaginary parts of the permittivity of BDS.
Table 3 lists some of the information of existing THz sensors. All FOMs of the demonstrated sensors have the same definition. The proposed sensor offers clear advantages over existing designs, especially in FOM and preparation. First, the FOM of the proposed sensor is the largest compared to those of other sensors. Second, from the preparation point of view, the sensor demonstrated is composed of only four layers with uniform air slots. Compared with other structures such as nanohole and perforated rectangular, the structure shown is easier and more convenient to prepare. On the other hand, it should be mentioned here that the value of FOM in other regions can be several times larger than that of THz, but the sensing capability of the THz region has more powerful and useful functions.
Table 3. Comparison of reported THZ sensor designs (s-simulation, e-experiment)
In the end, the experimental implementability for fabricating demonstrated THz sensor is also worth considering. As previously mentioned, BDS has been fabricated by experiment [32], in agreement with a theoretical study by the first principles calculations [35,56]. The structural design shown can be prepared experimentally using photoresist technology [46] and dry etching [23]. In Table 3, three published work have used both theoretical and experimental methods to obtain FOM. In [21], [54] and [55], numerical simulations and experimental results are highly consistent. Especially in [55], the simulated and experimental data can be fitted to a same curve since the difference between the simulated data and the experimental data is too small, resulting in the FOM obtained from the simulation and experiment being equal. Unfortunately, in [22], because the pattern of the device is somewhat complicated and the lithography method used by this experimental group has a large error in the preparation of the sample, it has not been successfully matched with the simulated data. However, the author has proposed a more efficient preparation method, dry etching. This method has not been adopted due to the limitations in their experiments. In general, the success of the THz sensor experiment requires simple structure, advanced experimental instruments and method support. On this basis, the simulated and experimentally calculated FOM differs by less than 5% due to the reasonable experimental error.
6. Conclusion
In summary, we demonstrate a four-band perfect absorption and dynamically tunable structure using a three layer structure with uniform air slots. The underlying physical mechanism lies in the combination of the classical magnetic resonance induced by the anti-parallel current and the electric resonance of adjacent unit cells resulting from the air slots at both ends of the absorber. Based on this, the quintuple narrowband perfect absorption can be realized by simply adding a layer of SiO2 coating on the BDS while the other four absorption peaks are nearly unaffected, which is supported by the interaction of the electric resonance of periodic edge and Mie resonance excited by coating. Compared to four-band absorption achieved by the construction of the three layer structure, the improved structure has more outstanding sensing performance with FOM of 813. The shown structural design can be prepared experimentally using photoresist technology [46] and dry etching [23]. Moreover, the relatively simple structure is easier to prepare. The proposed designs and developed approaches can advance practical applications of multi-band photoelectric detection and THz sensing.
Funding
National Natural Science Foundation of China (61505052, 61775055, and 11847230), China Postdoctoral Science Foundation (2018M642967).
References
1. R. M. Woodward, V. P. Wallace, R. J. Pye, B. E. Cole, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging of ex vivo basal cell carcinoma,” J. Invest. Dermatol. 120(1), 72–78 (2003). [CrossRef] [PubMed]
2. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007). [CrossRef]
3. M. Naftaly and R. Dudley, “Methodologies for determining the dynamic ranges and signal-to-noise ratios of terahertz time-domain spectrometers,” Opt. Lett. 34(8), 1213–1215 (2009). [CrossRef] [PubMed]
4. R. Asadi, Z. Ouyang, and M. M. Mohammd, “A compact, all-optical, THz wave generator based on self-modulation in a slab photonic crystal waveguide with a single sub-nanometer graphene layer,” Nanoscale 7(26), 11379–11385 (2015). [CrossRef] [PubMed]
5. J. M. Bae, W.-J. Lee, S. Jung, J. W. Ma, K.-S. Jeong, S. H. Oh, S. M. Kim, D. Suh, W. Song, S. Kim, J. Park, and M. H. Cho, “Ultrafast photocarrier dynamics related to defect states of Si1-xGex nanowires measured by optical pump-THz probe spectroscopy,” Nanoscale 9(23), 8015–8023 (2017). [CrossRef] [PubMed]
6. X. Zhao, C. Yuan, L. Zhu, and J. Yao, “Graphene-based tunable terahertz plasmon-induced transparency metamaterial,” Nanoscale 8(33), 15273–15280 (2016). [CrossRef] [PubMed]
7. W. Xu, L. Xie, and Y. Ying, “Mechanisms and applications of terahertz metamaterial sensing: a review,” Nanoscale 9(37), 13864–13878 (2017). [CrossRef] [PubMed]
8. S. D. Liu, X. Qi, W. C. Zhai, Z. H. Chen, W. J. Wang, and J. B. Han, “Polarization state-based refractive index sensing with plasmonic nanostructures,” Nanoscale 7(47), 20171–20179 (2015). [CrossRef] [PubMed]
9. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). [CrossRef] [PubMed]
10. P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52(10), 2438–2447 (2004). [CrossRef]
11. X. Hu, G. Q. Xu, L. Wen, H. C. Wang, Y. C. Zhao, Y. X. Zhang, D. R. S. Cumming, and Q. Chen, “Metamaterial absorber integrated microfluidic terahertz sensors,” Laser Photonics Rev. 10(6), 962–969 (2016). [CrossRef]
12. Y. Shi, S. Xiong, L. K. Chin, J. Zhang, W. Ser, J. Wu, T. Chen, Z. Yang, Y. Hao, B. Liedberg, P. H. Yap, D. P. Tsai, C. W. Qiu, and A. Q. Liu, “Nanometer-precision linear sorting with synchronized optofluidic dual barriers,” Sci. Adv. 4(1), o0773 (2018). [CrossRef] [PubMed]
13. M. Khorasaninejad, N. Abedzadeh, J. Walia, S. Patchett, and S. S. Saini, “Color matrix refractive index sensors using coupled vertical silicon nanowire arrays,” Nano Lett. 12(8), 4228–4234 (2012). [CrossRef] [PubMed]
14. H. Kurt, M. N. Erim, and N. Erim, “Various photonic crystal bio-sensor configurations based on optical surface modes,” Sens. Actuators B Chem. 165(1), 68–75 (2012). [CrossRef]
15. H. Tao, L. R. Chieffo, M. A. Brenckle, S. M. Siebert, M. Liu, A. C. Strikwerda, K. Fan, D. L. Kaplan, X. Zhang, R. D. Averitt, and F. G. Omenetto, “Metamaterials on paper as a sensing platform,” Adv. Mater. 23(28), 3197–3201 (2011). [CrossRef] [PubMed]
16. R. Singh, W. Cao, I. Al-Naib, L. Q. Cong, W. Withayachumnankul, and W. L. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014). [CrossRef]
17. G. Liu, M. He, Z. Tian, J. Li, and J. Liu, “Terahertz surface plasmon sensor for distinguishing gasolines,” Appl. Opt. 52(23), 5695–5700 (2013). [CrossRef] [PubMed]
18. Q. Li, L. Cong, R. Singh, N. Xu, W. Cao, X. Zhang, Z. Tian, L. Du, J. Han, and W. Zhang, “Monolayer graphene sensing enabled by the strong Fano-resonant metasurface,” Nanoscale 8(39), 17278–17284 (2016). [CrossRef] [PubMed]
19. W. Tang, L. Wang, X. Chen, C. Liu, A. Yu, and W. Lu, “Dynamic metamaterial based on the graphene split ring high-Q Fano-resonnator for sensing applications,” Nanoscale 8(33), 15196–15204 (2016). [CrossRef] [PubMed]
20. B. X. Wang, X. Zhai, G. Z. Wang, W. Q. Huang, and L. L. Wang, “A novel dual-band terahertz metamaterial absorber for a sensor application,” J. Appl. Phys. 117(1), 014504 (2015). [CrossRef]
21. B. H. Ng, J. F. Wu, S. M. Hanham, A. I. Fernandez-Dominguez, N. Klein, Y. F. Liew, M. B. H. Breese, M. H. Hong, and S. A. Maier, “Spoof Plasmon Surfaces: A Novel Platform for THz Sensing,” Adv. Opt. Mater. 1(8), 543–548 (2013). [CrossRef]
22. L. Liang, X. Hu, L. Wen, Y. H. Zhu, X. G. Yang, J. Zhou, Y. X. Zhang, I. E. Carranza, J. Grant, C. P. Jiang, D. R. S. Cumming, B. J. Li, and Q. Chen, “Unity Integration of Grating Slot Waveguide and Microfluid for Terahertz Sensing,” Laser Photonics Rev. 12(11), 1800078 (2018). [CrossRef]
23. W. Nickel, M. Oschatz, S. Rico-Francés, S. Klosz, T. Biemelt, G. Mondin, A. Eychmüller, J. Silvestre-Albero, and S. Kaskel, “Synthesis of Ordered Mesoporous Carbon Materials by Dry Etching,” Chemistry 21(42), 14753–14757 (2015). [CrossRef] [PubMed]
24. J. Luo, Y. Su, X. Zhai, Q. Lin, and L. L. Wang, “Tunable terahertz perfect absorbers with Dirac semimetal,” J. Optics21 (2019).
25. G. D. Liu, X. Zhai, H. Y. Meng, Q. Lin, Y. Huang, C. J. Zhao, and L. L. Wang, “Dirac semimetals based tunable narrowband absorber at terahertz frequencies,” Opt. Express 26(9), 11471–11480 (2018). [CrossRef] [PubMed]
26. H. Chen, H. Y. Zhang, M. D. Liu, Y. K. Zhao, X. H. Guo, and Y. P. Zhang, “Realization of tunable plasmon-induced transparency by bright-bright mode coupling in Dirac semimetals,” Opt. Mater. Express 7(9), 3397–3407 (2017). [CrossRef]
27. K. Ueda, J. Fujioka, Y. Takahashi, T. Suzuki, S. Ishiwata, Y. Taguchi, and Y. Tokura, “Variation of charge dynamics in the course of metal-insulator transition for pyrochlore-type Nd2Ir2O7,” Phys. Rev. Lett. 109(13), 136402 (2012). [CrossRef] [PubMed]
28. S. M. Young, S. Zaheer, J. C. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, “Dirac semimetal in three dimensions,” Phys. Rev. Lett. 108(14), 140405 (2012). [CrossRef] [PubMed]
29. C. Fang, M. J. Gilbert, X. Dai, and B. A. Bernevig, “Multi-Weyl topological semimetals stabilized by point group symmetry,” Phys. Rev. Lett. 108(26), 266802 (2012). [CrossRef] [PubMed]
30. X. G. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, “Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates,” Phys. Rev. B Condens. Matter Mater. Phys. 83(20), 205101 (2011). [CrossRef]
31. T. Liang, Q. Gibson, M. N. Ali, M. Liu, R. J. Cava, and N. P. Ong, “Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2,” Nat. Mater. 14(3), 280–284 (2015). [CrossRef] [PubMed]
32. S. Borisenko, Q. Gibson, D. Evtushinsky, V. Zabolotnyy, B. Büchner, and R. J. Cava, “Experimental realization of a three-dimensional Dirac semimetal,” Phys. Rev. Lett. 113(2), 027603 (2014). [CrossRef] [PubMed]
33. D. E. Kharzeev, R. D. Pisarski, and H. U. Yee, “Universality of Plasmon Excitations in Dirac Semimetals,” Phys. Rev. Lett. 115(23), 236402 (2015). [CrossRef] [PubMed]
34. Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S. K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, “Discovery of a three-dimensional topological Dirac semimetal, Na3Bi,” Science 343(6173), 864–867 (2014). [CrossRef] [PubMed]
35. G. Manzoni, L. Gragnaniello, G. Autès, T. Kuhn, A. Sterzi, F. Cilento, M. Zacchigna, V. Enenkel, I. Vobornik, L. Barba, F. Bisti, P. Bugnon, A. Magrez, V. N. Strocov, H. Berger, O. V. Yazyev, M. Fonin, F. Parmigiani, and A. Crepaldi, “Evidence for a Strong Topological Insulator Phase in ZrTe_5,” Phys. Rev. Lett. 117(23), 237601 (2016). [CrossRef] [PubMed]
36. A. A. Burkov, “Mirror Anomaly in Dirac Semimetals,” Phys. Rev. Lett. 120(1), 016603 (2018). [CrossRef] [PubMed]
37. Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S. K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, “A stable three-dimensional topological Dirac semimetal Cd3As2,” Nat. Mater. 13(7), 677–681 (2014). [CrossRef] [PubMed]
38. W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012). [CrossRef] [PubMed]
39. J. R. Piper and S. J. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1(4), 347–353 (2014). [CrossRef]
40. H. Y. Meng, X. X. Xue, Q. Lin, G. D. Liu, X. Zhai, and L. L. Wang, “Tunable and multi-channel perfect absorber based on graphene at mid-infrared region,” Appl. Phys. Express 11(5), 052002 (2018). [CrossRef]
41. F. Yan, L. Li, R. X. Wang, H. Tian, J. L. Liu, J. Q. Liu, F. J. Tian, and J. Z. Zhang, “Ultrasensitive Tunable Terahertz Sensor With Graphene Plasmonic Grating,” J. Lightwave Technol. 37(4), 1103–1112 (2019). [CrossRef]
42. S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002). [CrossRef]
43. O. V. Kotov and Y. E. Lozovik, “Dielectric response and novel electromagnetic modes in three-dimensional Dirac semimetal films,” Phys. Rev. B 93(23), 235417 (2016). [CrossRef]
44. L. Xu, W. Q. Huang, W. Y. Hu, K. Yang, B. X. Zhou, A. L. Pan, and G. F. Huang, “Two-Dimensional MoS2-Graphene-Based Multilayer van der Waals Heterostructures: Enhanced Charge Transfer and Optical Absorption, and Electric-Field Tunable Dirac Point and Band Gap,” Chem. Mater. 29(13), 5504–5512 (2017). [CrossRef]
45. T. Timusk, J. P. Carbotte, C. C. Homes, D. N. Basov, and S. G. Sharapov, “Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity,” Phys. Rev. B Condens. Matter Mater. Phys. 87(23), 235121 (2013). [CrossRef]
46. Z. Tang, L. Chen, C. Zhang, S. Zhang, C. Lei, D. Li, S. Wang, S. Tang, and Y. Du, “Enhancing the figure of merit of refractive index sensors by magnetoplasmons in nanogratings,” Opt. Lett. 43(20), 5090–5093 (2018). [CrossRef] [PubMed]
47. Y. Q. Ye, Y. Jin, and S. L. He, “Omnidirectional, polarization-insensitive and broadband thin absorber in the terahertz regime,” J. Opt. Soc. Am. B 27(3), 498–504 (2010). [CrossRef]
48. Q. Zhao, J. Zhou, F. L. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009). [CrossRef]
49. X. M. Liu, Q. Zhao, C. W. Lan, and J. Zhou, “Isotropic Mie resonance-based metamaterial perfect absorber,” Appl. Phys. Lett. 103(3), 031910 (2013). [CrossRef]
50. N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10(7), 2342–2348 (2010). [CrossRef] [PubMed]
51. A. E. Cetin and H. Altug, “Fano resonant ring/disk plasmonic nanocavities on conducting substrates for advanced biosensing,” ACS Nano 6(11), 9989–9995 (2012). [CrossRef] [PubMed]
52. R. Ameling, L. Langguth, M. Hentschel, M. Mesch, P. V. Braun, and H. Giessen, “Cavity-enhanced localized plasmon resonance sensing,” Appl. Phys. Lett. 97(25), 253116 (2010). [CrossRef]
53. Q. Xie, G. Dong, B. X. Wang, and W. Q. Huang, “Design of Quad-Band Terahertz Metamaterial Absorber Using a Perforated Rectangular Resonator for Sensing Applications,” Nanoscale Res. Lett. 13(1), 137 (2018). [CrossRef] [PubMed]
54. V. Astley, K. S. Reichel, J. Jones, R. Mendis, and D. M. Mittleman, “Terahertz multichannel microfluidic sensor based on parallel-plate waveguide resonant cavities,” Appl. Phys. Lett. 100(23), 231108 (2012). [CrossRef]
55. L. Q. Cong, S. Y. Tan, R. Yahiaoui, F. P. Yan, W. L. Zhang, and R. Singh, “Experimental demonstration of ultrasensitive sensing with terahertz metamaterial absorbers: A comparison with the metasurfaces,” Appl. Phys. Lett. 106(3), 031107 (2015). [CrossRef]
56. H. Weng, X. Dai, and Z. Fang, “Transition-metal pentatelluride ZrTe 5 and HfTe 5: A paradigm for large-gap quantum spin Hall insulators,” Phys. Rev. X 4(1), 011002 (2014). [CrossRef]
