The propagation properties of Si-based all-dielectric metamaterials (ADMs) structures were investigated systematically, taking into account the effects of structural parameters, operation frequencies, and graphene Fermi levels. The results manifested that ADMs indicated sharp resonant curves with large Q-factors of more than 60, and a figure of merit of approximately 20. Compared with that of thin metal metamaterial counterparts, the thickness of ADMs (in the range of tens of micrometers) required to excite obvious resonant curves was much larger. By introducing an asymmetrical structure, an obvious Fano-resonant peak was observed, which also became stronger with increasing asymmetrical degree. In addition, by unitizing a uniform graphene layer, the Fano-resonant curves can be flexibly modulated over a wide range, and the amplitude-modulation depth of the Fano peak was approximately 40% when the Fermi level varied in the range of 0.01–1.0 eV. These results are very useful for the design of high Q-factor dielectric devices in the future (e.g., biosensors, modulators, and filters).
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Recent years have witnessed a rapid development of terahertz (THz) technology in the areas of radiation sources and detectors [1–3], e.g. with practical applications in the fields of sensors, non-destructive testing, and high-speed wireless communication . However, the next stage of development requires a high demand for the functional waveguide devices with flexible control of THz waves. As a typical two-dimensional (2D) analogue of metamaterials (MMs), metasurfaces can be designed to interact with THz waves strongly and modify the amplitude, polarization, and phase of incident light [5–7], offering an efficient way to manipulate incident waves conveniently on a subwavelength scale. For present conventional metal-plasmonic MMs systems, however, it is very difficult to achieve high transmission and sharp resonant curves due to the inhibiting disadvantages of low efficiency, large dispersive refractive index, and low-quality factor (Q-factor, the value of which in plasmonic meta-surfaces is usually smaller than 10 in the THz regime). Although the Q-factor can be improved by incorporating gain media, this is usually accompanied by large optical-pump powers and serious noises and heats. Fortunately, in addition to metals, the materials comprising MMs devices also include semiconductors (SiC, InSb) and dielectrics [8–10]. The all-dielectric MMs (ADMs) structures exhibit strong resonances and attract increasing interest of researchers [11–13]. Compared with metal MMs counterparts, ADMs have the merits of high transmission, CMOS compatibility, and conversion efficiency [14–17]. Furthermore, the ADMs structures can support electric dipole, magnetic dipole, and higher-order multipolar resonances by replacing high-dissipation Ohmic currents with low-loss displacement currents [18–20].
With the merits of low dissipation and strong mode confinement, the ADMs structure serves as a platform to achieve resonant curves with a large Q-factor [21–24]. High permittivity semiconductors, such as Si, Ge, and ferroelectric materials, are the best candidates to build ADMs structures [25–27]. In recent years, much research has been devoted to obtaining high-performance ADMs structures. For instance, a hybrid ADMs structure based on rectangular bar and ring resonators was investigated that showed a large Q-factor of more than 500 in the near-infrared region because of the low absorption and coherent interaction between two kinds of resonators . Han et al. proposed a novel kind of all-dielectric Si structure, indicating that the Q-factor of resonant curves reached approximately 1160, and the group index approximately can reach 3000, resulting from the strong toroidal-dipolar resonance of the asymmetric E-shaped meta-molecular structure . The lossless Si-brick arrays have been experimentally demonstrated to act as half-wave plates (0.91 THz) and quarter-wave plates (0.79 THz), which achieved near-unity transmission with π-phase delay . With the composed double-layer structure of a half-wave plate and an antireflection layer, Zi et al. proposed a novel THz ADMs consisting of an elliptical pure Si unit cell to realize high-efficiency polarization conversion in which the cross-polarization transmission can reach 90% and the polarization conversion rate approximately 100% at 1.0 THz .
Nowadays, improvement of the interaction of THz waves with MMs structure and achieve resonant curves with high Q-factor is a burgeoning research topic, especially in the applications fields of narrow-band filtering, and absorbers . Currently, all-dielectric meta-surfaces in the THz regime were mainly reflection types [31,33,34], which acted as THz focusing lenses, polarization control, and reflection mirrors. However, from a practical viewpoint, transmission optical elements are preferable, and high efficiency is a key target, especially in the aspects of high sensitivity sensors, wave-plates, modulations, and metalens. For instance, in the fields of THz practical imaging and wireless communications, a full 2π phase modulation is demanded to manipulate the wave-fronts, the reflection MMs devices are not suitable, also with the disadvantages of low efficiency and weak coupling [35–38]. The common unit cells of ADMs structures include rods, cubes, disks, and rings. A bowtie antenna is also a typical kind of meta-molecular structure, consisting of two triangular plasmonic structures with their apexes facing each other and manifesting the merits of strong near-field enhancement and high Q-factors. Therefore, to achieve good mode confinement and large Q-factor resonant curves, the Si-ADMs structures have been explored in the THz regime, including the effects of structural parameters, operation frequencies, carrier concentration of the Si layer, and graphene-Fermi levels. The results indicate that the proposed Si-ADMs structure process sharp resonant curves with large Q-factors of more than 60, which is an order of magnitude larger than that of metal metamaterials. Additionally, with the help of a uniform graphene layer, the Fano-resonant peak can be modulated conveniently, and the amplitude modulation depth (MD) can reach approximately 40%.
2. Research methods
Figure 1 illustrates the geometric configurations of the Si-ADMs structures. The dielectric Si layer was deposited on the polymer substrate. The thickness of the polyimide-substrate layer was 2 μm. The periodic lengths along x and y directions were both 250 μm. The incident waves normally transmit through the dielectric metamaterials structure along the z direction.
The frequency-dependent dielectric constants of metals in the THz spectral ranges can be described using the Drude equation :
By utilizing a commercially silicon wafer, the proposed Si-ADMs can be fabricated by using electron-beam lithography or focused-ion-beam lithography . Including the effects of phonon scattering and electron transport as the doping density increases, the complex conductivity of doped Si can be described by using the generalized Drude equation ,Eq. (2) reduces to the Drude model, which assumes that the carrier-relaxation time τ is independent of energy. If α = 0 and 0≤β≤1, Eq. (2) is reduced to the Cole-Davidson (CD) model. If β = 1 and 0≤α<1, it is the Cole-Cole (CC) model. For our simulation, if the carrier concentrations are 1014 cm−3, 1015 cm−3, 1016 cm−3, the values of τCD were 0.341, 0.336, 0.264 ps, the values of α were 0.03, 0.02, and 0.02, the values of β are 0.84, 0.84, and 0.88, respectively.
Graphene is regarded as a 2D material and described by a surface conductivity σg, which depends on the operation frequency ω, chemical potential μc, the environmental temperature T, and the relaxation time τ. Under the random phase approximation, the graphene conductivity is described as :
The Q-factor value is defined as the ratio of resonant frequency to the full width at a half maximum (FWHM),
3. Results and discussion
The characteristics of the proposed bowtie Si-ADMs structures, such as Si-layer thickness, carrier concentrations, asymmetrical degree δ, and Fermi level of the graphene layer, have been systematically investigated by using the finite-integrated method, which was performed by using CST software. The boundary condition in the x-y plane was the unit cell, and along the z direction the Floquet ports were adopted. Then, the resonant curves were obtained from the S-parameters. To take into account the effects of Cu or doped Si layers, in the simulation we can create a new material (such as Si or Cu) by including the dielectric dispersion datum, obtained from Eqs. (1) and (2). The calculation was performed by using a Dell Precision Tower R7910 workstation with 32 cores with 128 G memory. From the obtained S-parameters, the transmission (T(ω)), reflection (R(ω)), and absorption (A(ω)) curves can be achieved by the formula, T(ω) = |S21|2, R(ω) = |S11|2, A(ω) = 1- T(ω)- R(ω). Figure 2(a) depicts the influences of Cu MMs thickness on the resonant curves. The thicknesses of the Cu layers were 0.2, 1, 2, 5, 8, and 10 μm, respectively. The top (TR) and bottom (BR) widths were 84 and 2 μm, respectively. The bottom (LB) and top (LT) lengths were both 84 μm. The period lengths along the x (px) and y (py) directions were both 180 μm. It can be found from Fig. 2(a) that even if the thickness of the metal layer was thin (e.g. less than 1 μm), the resonant strength was very strong, and an obvious resonant dip can be observed. As the thickness of the Cu layer increased, the resonant strength became stronger, and the resonant dip shifted to low frequencies. For example, if the thicknesses of the Cu layers were 0.2, 2, 5, and 10 μm, the respective values of the resonant dips were 3.708 × 10−5, 2.681 × 10−6, 1.004 × 10−6, and 7.373 × 10−7, and the according resonant frequencies were 1.329, 1.295, 1.276, and 1.254 THz, respectively. To measure the trade-off between Q-factor and resonant strength, we define the figure of merits, i.e. FOM = Q × Am, Am is the dip amplitude of resonant curve. The values of Q-factors and figure of merit (FOM) can be found in Fig. 2(b). As the metal layer thickness increased, their carrier concentration increased, the losses increased, and the resonant curve became broadened, leading to decreases in the Q-factor and FOM values.
In addition, Fig. 2(c) depicts the effects of Si ADMs thickness on the transmission curves. The thicknesses of the Si layer were 0.2, 1, 2, 5, 8, and 10 μm, respectively. The doping concentration of the Si layer was 1.0 × 1015 cm−3. If the Si thickness was 0.2 μm (a typical value for metal MMs structures), the resonant dip almost disappeared. As the Si layer increased, the resonant strength became stronger, and resonant dip shifted low frequency. For example, if the thicknesses of the Si layer were 0.2, 2, 5, and 10 μm, the values of the resonant dips were 0.7252, 0.4238, 0.0939, 0.0368, and 0.02391, and the corresponding resonant frequencies were 1.526, 1.487, 1.391, and 1.283 THz, respectively. Correspondingly, the amplitude and frequency modulation depths of resonant dips were 96.7% and 18.6%, respectively. As the Si layer thickness increased, the carrier concentrations increased, the loss enhanced, and the resonant curve became broadened, leading to decreased Q-factor values, as shown in Fig. 2(d). However, simultaneously, the displacement current increased, resulting in enhancement of the resonant strength; that is, the resonant strength became stronger. Consequently, the FOM showed a peak. The Q-factor and FOM values of Si-ADMs layers could reach higher than 60 and 20, respectively.
Next, we compared metal MMs and ADMs structures. The resonant curves of metal MMs structures were not sensitive to layer thickness. Even if the thickness was very small, about 0.2 μm, the resonant curves could be strongly excited. However, the effects of thicknesses on the ADMs structures were obvious and significant. At small thickness, the resonant curve was very weak. As the Si-layer thickness increased, the resonant curve became stronger (i.e. on condition that the thickness is larger than 5 μm) and the resonant dip was very distinct. These differences between metal and dielectric Si layers are explained below. The metal MMs manifested good plasmonic properties in the THz regime because of their large carrier concentration, and the resonant curves were associated with the conduction currents. For the Si-ADMs structures, however, the carrier concentration was significantly lower compared with that of the metal layer, so its resonant curve mainly depended on displacement current. Furthermore, the Si-ADMs structures manifested very sharp curves with large Q-factors of more than 60, much larger than that of metal MMs structures. For metal MMs structure, the carrier concentrations and permittivity were very large, which lead to large losses with broad resonant curves with low Q-factor, less than 3 as given in Fig. 2(b), while the carrier concentration and permittivity of the Si layer was relatively smaller, resulting in smaller loss and larger Q-factors. For instance, at a frequency of 1.25 THz, the permittivity of the Cu and Si layers were −5.005 × 105 + 8.787 × 105i and 11.56 + 0.06909i, respectively. Therefore, the dissipations of dielectric Si-MMs structures are small, and their resonant curves are sharper with larger Q-factors.
The dielectric particle with high permittivity can be seen as a resonator with a magnetic wall, which induces and reflects the electromagnetic waves between the interfaces of the dielectrics and free space to form a standing wave. More energy can be concentrated around dielectric resonators at larger resonator permittivity. Silicon is chosen for ADMs structure due to its high refractive index and low loss. In many published articles, the refractive index of Si is adopted as 3.4, and its loss is omitted [12,20,29]. Practically, however, the refractive index of Si changes, strictly speaking, with frequency. The dissipations of the Si layer significantly affect the resonant curves, especially if its thickness layer is large. For the doped Si layer, if the carrier concentration is low (e.g. smaller than 1.0 × 1016 cm−3), phonon scattering plays an important role. If the carrier concentration increases, the electron-electron scattering should also be taken into account. The dielectric constant of Si has been calculated from the generalized Drude Eq. (2), and it agrees well with experimental results. The carrier concentration plays an important role in the dielectric properties of the Si layer and resonant curves. Figure 3 shows the resonant curves at different doping-carrier concentrations. The doping concentrations of the Si layer were 0, 1.0 × 1014, 5.0 × 1014, 1.0 × 1015, 5.0 × 1015, 1.0 × 1016, 2.0 × 1016, and 3.0 × 1016 cm−3, respectively. As shown in Fig. 3(a), if the carrier concentration was not very large (e.g. smaller than 1.0 × 1015 cm−3), the effects of doping on the resonant curves were not very obvious. As the carrier concentration increased further, the dissipation improved significantly, the resonant strength became weaker, and the transmission curves broadened. For example, if the carrier concentrations were 0, 1.0 × 1015, 1.0 × 1016, and 3.0 × 1016 cm−3, the values of the resonant dips were 0.01614, 0.02249, 0.09524, and 0.2927, respectively, and the corresponding resonant frequencies were 1.271, 1.278, 1.295, 1.316 THz, respectively. Figures 3(b) and 3(c) show the reflection and absorption curves of Si ADMs structures, respectively. With increasing carrier concentration, the value of absorption increased and the reflection decreased. At low-carrier concentration, the reflection dominated (1.0 × 1015 cm−3), and at larger values of carrier concentration (1.0 × 1016 cm−3) the absorption played an important role. The effects of carrier concentrations on Q-factor and FOM can be found in Fig. 3(d). If the carrier concentration was low (i.e. smaller than 1.0 × 1015 cm−3), the Q-factor value was approximately 10, and the effects of carrier concentrations were not very obvious. However, if the carrier concentration increased further (i.e. reached higher than 1.0 × 1016 cm−3), the Q-factor and FOM values decreased significantly. For example, on condition that the carrier concentrations were 1.0 × 1015, 1.0 × 1016, and 3.0 × 1016 cm−3, the Q-factor values were 10.56, 9.608, and 7.049, respectively, and the corresponding FOM values were 9.618, 7.980, and 4.394, respectively.
A 2D field plot is a good means with which to learn the propagation properties of Si ADMs structures. The effects of doping concentrations on surface-current density and magnetic fields values are shown in Fig. 4. The corresponding resonant frequencies were 1.278, 1.295, and 1.316 THz, respectively. The top and bottom widths were 120 and 2 μm, respectively. The bottom and top lengths of the bowtie sections were both 120 μm. The period lengths along x and y directions were both 250 μm. The polarization was along the y direction. It can be found from Fig. 4 that the surface currents were mainly focused along the Si bowtie MMs structures. As the carrier concentration increased, the losses increased, resulting in decreasing Hz values, as shown in Fig. 4. For example, if the carrier concentrations were 1.0 × 1015, 1.0 × 1016, an 3.0 × 1016 cm−3, the Hz values were 1112, 915, and 620 A/m, respectively.
The plasmonic-induced transparency (PIT) phenomenon can be obtained by breaking the structural symmetry or subwavelength-scale coupling. For most of the studies of Fano resonances employing metallic split-ring resonators, a transmission window results from the conduction-current oscillation. Alternatively, the accompanying displacement currents of ADMs structures provide another promising means of achieving Fano resonances. Figure 5 illustrates the influences of asymmetrical degree on the resonant curves of ADMs structures. The asymmetrical degree has been defined as the difference between the length of top triangular and that of bottom triangular, i.e. δ = LB-LT. The thickness of the Si bowtie MMs structure was 10 μm with a doping concentration of 1.0 × 1015 cm−3. The values of asymmetrical degree were 0, 10, 20, 30, 40, 50, and 60 μm. It can be found from Fig. 5(a) that there was only one resonant dip near 1.211 THz for the symmetrical structure, coming from the excitation of displacement currents. For the asymmetric Si-ADMs structure, the length of upper section was smaller than that of the bottom part, and an obvious peak was observed. With increasing asymmetric degree δ, the Fano-resonance strength became stronger, and the resonant peak shifted to a larger frequency (i.e. a blue shift). For example, if the values of δ were 10, 20, 30, and 60 μm, the resonant frequencies were 1.076, 1.106, 1.129, and 1.178 THz, respectively, and the values of the Fano resonant peaks were 0.7196, 0.7930, 0.8421, and 0.9149, respectively. Accordingly, the frequency- and amplitude-modulation depths of Fano resonances were 8.66% and 21.89%. Figure 5(b) shows that a novel peak appeared in the reflection curves because of the Fano resonance, which also increased with asymmetrical degree. At the same time, the reflection at larger frequency decreased with asymmetrical degree. The effects of asymmetrical degree on the absorption curves are also shown in Fig. 5(c), which indicates a novel resonant peak near the Fano resonance. Figure 5(d) depicts the Q-factor and FOM values. As the asymmetric degree increased, the resonant strength became stronger, the dissipation was enhanced, and the Fano-resonance curve broadened, resulting in a decreasing Q-factor. Simultaneously, Fano-resonant strength and amplitude became stronger; therefore, the FOM showed a peak. It can be found from Fig. 5(d) that if the asymmetrical degree was approximately 30 μm, the FOM value showed a peak, which means that Q-factor and FOM are roughly satisfactory at this optimum asymmetrical-degree value.
The influences of asymmetric degree on surface-current density and Hz values can be found in Fig. 6. The corresponding resonant frequencies were 1.076, 1.106, and 1.172 THz. The polarization direction of incident light was along the y direction. The asymmetric degrees of the Si layers were 10, 20, and 50 μm, respectively. For the asymmetric bowtie ADMs structure, Fig. 6 shows that the surface current densities of the upper and bottom sections were opposed, resulting in a net dipole moment. Thus, a quadrupolar-like mode was excited with a reduction of radiation loss, whose anti-phase currents interacted strongly with the original electric dipolar resonance and lead to a Fano-resonant peak, in which both the upper and bottom sections of the Si ADMs had been excited. Furthermore, as the asymmetric degree increased, the interaction between the upper and bottom sections of the bowtie structure increased, a larger loss was incurred, and dissipation arose, which resulted in decreasing values of the surface current density and Hz. For example, if the asymmetrical degrees were 10, 20, and 50 μm, the Hz values of Hz were 918, 771, and 403 A/m, respectively.
For dielectric MMs structures, because the near fields exist mostly inside the dielectric resonators, they are insensitive to the refractive index of the environment. Furthermore, this volumetric mode property hampers the dynamical modulation of resonant curves, which is different from the case of metal plasmonic MMs components with strong field confinement. With the merits of high mobility, good confinement, and flexible tenability, a graphene layer is utilized to achieve the manipulation of resonant curves. The effects of a graphene Fermi levels on the Fano-resonant curves of asymmetric dielectric Si bowtie structures are given in Fig. 7. The thicknesses of the uniform graphene layer, SiO2 and doped Si layers at the back gate were 1 nm, 30 nm, 2 μm, respectively. For the structural parameters of Si MMs, its thickness was 10 μm, the top and bottom widths of Si bowtie structure were 120 and 2 μm, respectively. Bottom and top lengths were both 120 μm. Period lengths along x and y directions were both 250 μm. The Fermi levels were 0, 0.01, 0.05, 0.1, 0.2, 0.3, 0.5, and 1.0 eV. The inset of Fig. 7(a) is a sketch of a uniform graphene-layer-supported dielectric Si bowtie structure. Compared with the patterned MMs structures, the uniform graphene layer has the merits of simple structure and is much more easily achieved from the experimental viewpoint. Figure 7 shows that, if the Fermi level was small, its effect on the resonant curve was weak. However, on the condition that the Fermi level of graphene layer was large (i.e. >0.3 eV), the Fermi level significantly affected the Fano resonances. As the Fermi level increased, the Fano-resonant peak indicated a blue shift and the peak value decreased. The reasons are given as follows. With the increase of the Fermi level of the graphene layer, the carrier concentration increases and much larger dissipation arises, leading to a decreasing value of the Fano peak. In addition, the Fano peak can be tuned in a wide range by altering the graphene Fermi level. If the Fermi level changed in the range 0.01–1.0 eV, the Fano-resonant peaks varied in the range 0.8895–0.5372 and the resonant frequencies modulated in the range 1.187–1.655 THz. Correspondingly, the amplitude- and frequency-modulation depths were 39.62 and 28.28%, respectively. The influences of the graphene layer on the reflection curves are shown in Fig. 7(b). If the graphene Fermi level was small (i.e. <0.3 eV) the reflection curves decreased with Fermi level, resulting from the larger absorption at the larger graphene Fermi level. However, if the graphene Fermi level was large enough (i.e. > 0.5 eV), the reflection peak near the Fano resonance was not very obvious. If the graphene layer was about 1.0 eV, the reflection curve increased significantly. As graphene Fermi-level increased, the absorption increased, as shown in Fig. 7(c). For the results of Q-factor and FOM, as Fermi level increased, the interaction between graphene layer and Si-ADMs structure increased, resulting into the values of Q-factor increasing. But if graphene layer Ef was large enough (i.e. >0.5 eV), the Q-factor value decreased because the graphene layer manifested a larger carrier concentration and dissipation loss. Additionally, the amplitude of Fano resonances decreased with Fermi level, leading to a decreasing FOM, as shown in Fig. 7(d).
Figure 8 shows the effects of the graphene layer on the surface current density and Hz of Si ADMs structures. The graphene Fermi levels were 0.01, 0.2, and 0.5 eV. It can be found from Fig. 8 that if the graphene Fermi level was small, the surface-current density and Hz values were low. However, as the graphene Fermi level increased, the surface-current density and Hz value increased, which resulted from the fact that the graphene layer shows much better plasmonic properties. Another noteworthy point is that the Fano resonances became weaker at larger Fermi levels. As shown in Figs. 8(a) and 8(d), compared with the results at low Fermi level, the surface-current density and Hz values were both excited at the bottom and upper sections, and the surface current density and Hz values were excited mainly at the upper bowtie section if the Fermi level was larger.
Based on the Si bowtie unit-cell structures, the resonant properties of AMDs were systematically investigated in the THz regime, including the effects of structural parameters, Si-layer doping concentration, operation frequencies, and the Fermi level of uniform graphene. To excite obvious resonant curves, the thickness of the dielectric MMs layer (in the range of tens of micrometer) was much larger than that of its thin metal counterparts (usually approximately 0.2 μm). The results showed that all-dielectric MMs structures manifested sharp resonant curves with a large Q-factor greater than 60 and a FOM value of greater than 20. As the carrier concentration of the Si layer increased, the resonant strength became weaker and the absorption increased, leading to decreasing Q-factor. With the asymmetrical meta-molecular structure, an obvious Fano-resonant peak appeared and was enhanced with increasing asymmetrical degree. In addition, by changing the Fermi level of the uniform graphene layer the Fano-resonant curves can be conveniently modulated in a wide range, e.g. the amplitude MD of the Fano peak was 39.62% if the Fermi level varied in the range 0.01–1.0 eV. The results are very helpful in understanding the resonant mechanisms of dielectric MMs and in the design of novel high Q-factor devices in the future, e.g. sensors, modulators, and filters.
National Natural Science Foundation of China (Grant Nos. 61674106 and U1531109); Funding of Shanghai Pujiang Program (Grant Nos. 15PJ1406500); Funding of Natural Science Foundation of Shanghai (Grant No. 16ZR1424300).
1. H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013). [CrossRef]
2. C. G. Wade, N. Sibalic, N. R. de Melo, J. M. Kondo, C. S. Adams, and K. J. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11(1), 40–43 (2017). [CrossRef]
3. Z. Zhou, T. Zhou, S. Zhang, Z. Shi, Y. Chen, W. Wan, X. Li, X. Chen, S. N. Gilbert Corder, Z. Fu, L. Chen, Y. Mao, J. Cao, F. G. Omenetto, M. Liu, H. Li, and T. H. Tao, “Multicolor T-Ray imaging using multispectral metamaterials,” Adv. Sci. (Weinh.) 5(7), 1700982 (2018). [CrossRef] [PubMed]
4. S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013). [CrossRef]
5. N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014). [CrossRef]
7. C. Shi, X. Y. He, J. Peng, G. N. Xiao, F. Liu, F. T. Lin, and H. Zhang, “Tunable terahertz hybrid graphene-metal patterns metamaterials,” Opt. Laser Technol. 114(1), 9931–9944 (2019).
9. M. Qin, S. Xia, X. Zhai, Y. Huang, L. Wang, and L. Liao, “Surface enhanced perfect absorption in metamaterials with periodic dielectric nanostrips on silver film,” Opt. Express 26(23), 30873–30881 (2018). [CrossRef] [PubMed]
10. Y. Yang, W. Wang, A. Boulesbaa, I. I. Kravchenko, D. P. Briggs, A. Puretzky, D. Geohegan, and J. Valentine, “Nonlinear Fano-resonant dielectric metasurfaces,” Nano Lett. 15(11), 7388–7393 (2015). [CrossRef] [PubMed]
11. P. Moitra, B. A. Slovick, W. Li, I. I. Kravchencko, D. P. Briggs, S. Krishnamurthy, and J. Valentine, “Large-scale all-dielectric metamaterial perfect reflectors,” ACS Photonics 2(6), 692–698 (2015). [CrossRef]
13. C. S. Sui, B. X. Han, T. T. Lang, X. J. Li, X. F. Jing, and Z. Hong, “Electromagnetically induced transparency in an all-dielectric metamaterial-waveguide with large group index,” IEEE Photonics J. 9(5), 1 (2017). [CrossRef]
14. C. H. Chu, M. L. Tseng, J. Chen, P. C. Wu, Y. H. Chen, H. C. Wang, T. Y. Chen, W. T. Hsieh, H. J. Wu, G. Sun, and D. P. Tsai, “Active dielectric metasurface based on phase-change medium,” Laser Photonics Rev. 10(6), 986–994 (2016). [CrossRef]
15. Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009). [CrossRef]
16. A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat. Photonics 11(2), 130–136 (2017). [CrossRef]
18. C. Wu, N. Arju, G. Kelp, J. A. Fan, J. Dominguez, E. Gonzales, E. Tutuc, I. Brener, and G. Shvets, “Spectrally selective chiral silicon metasurfaces based on infrared Fano resonances,” Nat. Commun. 5(1), 3892 (2014). [CrossRef] [PubMed]
19. M. V. Rybin, K. L. Koshelev, Z. F. Sadrieva, K. B. Samusev, A. A. Bogdanov, M. F. Limonov, and Y. S. Kivshar, “High-Q supercavity modes in subwavelength dielectric resonators,” Phys. Rev. Lett. 119(24), 243901 (2017). [CrossRef] [PubMed]
20. M. Rahmani, L. Xu, A. E. Miroshnichenko, A. Komar, R. Camacho-Morales, H. Chen, Y. Zarate, S. Kruk, G. Zhang, D. N. Neshev, and Y. S. Kivshar, “Reversible thermal tuning of all-dielectric metasurfaces,” Adv. Funct. Mater. 27(31), 1700580 (2017). [CrossRef]
21. A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015). [CrossRef] [PubMed]
24. X. Y. He, G. N. Xiao, F. Liu, F. T. Lin, and W. Z. Shi, “Flexible properties of THz graphene bowtie metamaterials structures,” Opt. Mater. Express 9(1), 44–55 (2019). [CrossRef]
25. A. Howes, W. Wang, I. Kravchenko, and J. Valentine, “Dynamic transmission control based on all-dielectric Huygens metasurfaces,” Optica 5(7), 787–792 (2018). [CrossRef]
26. J. Tian, Y. Yang, M. Qiu, F. Laurell, V. Pasiskevicius, and H. Jang, “All-dielectric KTiOPO4 metasurfaces based on multipolar resonances in the terahertz region,” Opt. Express 25(20), 24068–24080 (2017). [CrossRef] [PubMed]
27. F. Zhang, Q. Zhao, J. Zhou, and S. Wang, “Polarization and incidence insensitive dielectric electromagnetically induced transparency metamaterial,” Opt. Express 21(17), 19675–19680 (2013). [CrossRef] [PubMed]
29. B. Han, X. Li, C. Sui, J. Diao, X. Jing, and Z. Hong, “Analog of electromagnetically induced transparency in an E-shaped all-dielectric metasurface based on toroidal dipolar response,” Opt. Mater. Express 8(8), 2197–2207 (2018). [CrossRef]
30. D. C. Wang, S. Sun, Z. Feng, W. Tan, and C. W. Qiu, “Multipolar-interference-assisted terahertz waveplates via all-dielectric metamaterials,” Appl. Phys. Lett. 113(20), 201103 (2018). [CrossRef]
31. J. C. Zi, Q. Xu, Q. Wang, C. X. Tian, Y. F. Li, X. X. Zhang, J. H. Han, and W. L. Zhang, “Antireflection-assisted all-dielectric terahertz metamaterials polarization converter,” Appl. Phys. Lett. 113(10), 101104 (2018). [CrossRef]
33. P. Moitra, B. A. Slovick, W. Li, I. I. Kravchencko, D. P. Briggs, S. Krishnamurthy, and J. Valentine, “Large-scale all-dielectric metamaterial perfect reflectors,” ACS Photonics 2(6), 692–698 (2015). [CrossRef]
34. Z. Ma, S. M. Hanham, P. Albella, B. H. Ng, H. T. Lu, Y. D. Gong, S. A. Maier, and M. H. Hong, “Terahertz all-dielectric magnetic mirror metasurfaces,” ACS Photonics 3(6), 1010–1018 (2016). [CrossRef]
35. D. Jia, Y. Tian, W. Ma, X. Gong, J. Yu, G. Zhao, and X. Yu, “Transmissive terahertz metalens with full phase control based on a dielectric metasurface,” Opt. Lett. 42(21), 4494–4497 (2017). [CrossRef] [PubMed]
36. C. Liewald, S. Mastel, J. Hesler, A. J. Huber, R. Hillenbrand, and F. Keilmann, “All-electronic terahertz nanoscopy,” Optica 5(2), 159–163 (2018). [CrossRef]
37. Z. L. Fu, L. L. Gu, X. G. Guo, Z. Y. Tan, W. J. Wan, T. Zhou, D. X. Shao, R. Zhang, and J. C. Cao, “Frequency up-conversion photon-type terahertz imager,” Sci. Rep. 6(1), 25383 (2016). [CrossRef] [PubMed]
38. H. Chen, Z. Wu, Z. Li, Z. Luo, X. Jiang, Z. Wen, L. Zhu, X. Zhou, H. Li, Z. Shang, Z. Zhang, K. Zhang, G. Liang, S. Jiang, L. Du, and G. Chen, “Sub-wavelength tight-focusing of terahertz waves by polarization-independent high-numerical-aperture dielectric metalens,” Opt. Express 26(23), 29817–29825 (2018). [CrossRef] [PubMed]
39. M. A. Ordal, R. J. Bell, R. W. Alexander Jr., L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24(24), 4493–4499 (1985). [CrossRef] [PubMed]
41. K. J. Willis, S. C. Hagness, and I. Knezevic, “A generalized Drude model for doped silicon at terahertz frequencies derived from microscopic transport simulation,” Appl. Phys. Lett. 102(12), 122113 (2013). [CrossRef]
42. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007). [CrossRef]