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Abstract
An analogy of polarization-independent, multi-band and tunable electromagnetically induced transparency (EIT) effect is proposed based on simple combination of circular ring resonators and vanadium dioxide film. The EIT-like effect is generated by bright-bright coupling resulting from adjacent ring resonators. High sensitivity up to 1.60 THz/RIU to the environmental refractive index is achieved utilizing the transparency peak. Accompanying with the EIT-like effect, the multi-band slow light phenomenon is obtained around the transparency windows. In addition, by inducing the insulator-metallic transition of the vanadium dioxide layer, the EIT-like curves can be actively manipulated while the multiple modulation is realized without refabricating the structure. Particularly, due to structural symmetry, the EIT-like windows keep unchanged and maintain noticeable with various polarization angles. The proposed structure has potential applications such as terahertz sensors, slow-light devices and modulators.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Electromagnetically induced transparency (EIT) is a kind of nonlinear optical phenomenon originally occurred in atomic system [1,2]. It refers to destructive interference which allows the incident light propagating through opaque medium within a narrow transparent window. The EIT effect exhibits potential applications in energy storage and quantum information processing due to the accompanying extreme dispersion characteristics [3,4]. Unfortunately, the realization of the quantum EIT effect requires relatively rigorous experiment conditions. To overcome the restrictions, the analogue of EIT effect based on metamaterials has been widely investigated in recent years [5–9]. Generally, the EIT-like spectra can be obtained via the coupling between the adjacent resonators in the metamaterials [10–13]. Metamaterial-based EIT-like phenomenon can be employed in a wide range of applications including terahertz filters, sensors, modulators and slow light devices [14–18].
The majority of previous studies focused on single or dual-band EIT-like metamaterials [19–24]. Motivated by multi-frequency applications, extensive efforts have been devoted to multi-band EIT-like effect. In order to generate multiple transparency peaks, various designs of complex unit cell structures were proposed and investigated [25–29]. By combining a multi-split ring and a split ring resonator inside a supercell configuration, Bagci et al. created multi-band transmission windows within a wide band [25]. Employing gate voltage to the liquid crystal layer and graphene strip layer, the dynamically controlled multi-band electromagnetically induced transparency-like metamaterials can be realized [26]. Xu et al. introduced a terahertz metamaterial with triple-band electromagnetically induced transparent window which is composed of two sets of arc-ring-type resonators. The EIT-like effect can be transformed from triple-band to dual-band or single-band by exciting the photosensitive silicon substrate [27]. Shen et al. presented multi-band electromagnetically induced transparency-like metamaterials with different shapes and sizes of split-ring resonators, achieving high values of group delay at three transparency peaks [28]. However, these multiple EIT-like phenomena were usually realized based on the asymmetric structures, exhibiting sensitive to the polarization direction of the incident wave which may hinders the practical application range. To overcome the restriction, developing multi-band EIT-like metamaterials with both polarization-insensitive and controllable characteristics attracts growing interests.
In this work, an analogy of the multi-band, polarization-independent and actively controlled EIT-like effect with high sensing performance is realized based on terahertz metamaterial. The structure is rather simple compared with the configuration presented in Ref. [29] and the unit cell is composed of centric ring resonators with different radius. The transmission spectra are investigated by numerical simulations. And the surface current and electric field distributions are calculated to study the near coupling between the circular rings which consequently leads to the multi-band EIT-like effect. High sensitivity of 1.60 THz/RIU to the environmental refractive index is realized based on the transparency window. By inducing the phase change of the vanadium dioxide (VO2) film, the EIT-like phenomenon are dynamically switched then the multi-band modulations can be fulfilled. The slow light performance of the EIT-like metamaterial is further exploited. Particularly, due to the symmetry of the designed unit cell, the multi-band EIT-like transmission spectra are insensitive to the polarization direction and remain unchanged with various polarization angles.
2. Design and simulation model
The schematic design and the unit cell of the proposed EIT-like metamaterial are depicted as shown in Fig. 1(a) and (b). As can be seen, the structure is composed of three layers: metal circular ring arrays, polyimide substrate and the vanadium dioxide film on the bottom. The unit cell is arranged as an array with period of Px = Py = 130µm in the x and y direction respectively. The first layer of the unit cell consists of three concentric circular rings with different radius of R1= 35µm, R2= 28µm. R3= 21µm. The width of the circular rings is 2 µm. The metal layer is gold and considered as ultrathin film in simulations. The middle layer is polyimide with permittivity of ɛr = 3.5 in 2µm thickness and the dielectric loss tangent is 0.002. The thickness of the VO2 layer is 200 nm.
The VO2 layer undergoes insulator-metallic transition under the external stimuli such as thermal, optical or electrical excitation [30–32]. Accompanying with the phase change, the conductivity of VO2 increases prominently by up to 4-5 orders in magnitude, which may cause noticeable changes to the EIT-like phenomenon induced by metamaterials [33]. The phase change properties of VO2 can be illustrated by the Drude model, which manifests almost frequency-independent conductivity in low THz region. Generally, the different conductivity of the VO2 film can alternatively describe the phase transition characteristics for simplicity [34]. In our work, the conductivities of the VO2 layer in insulator and metallic state are set as 20 S/m and 20000 S/m respectively [35,36]
The multi-band EIT-like responses of the proposed metamaterials are numerically calculated using frequency domain finite element method via commercial electromagnetic solver CST Microwave Studio. The Floquet mode is utilized as the excitation source in z direction and the unit cell boundary is set in x and y direction. The terahertz wave illuminates normally the metamaterial with the electric field polarized in y direction initially. The investigated frequency range is from 0.6 to 3.2 THz.
3. Results and discussions
Figure 2 shows the transmission spectra of the y-polarized terahertz wave propagating normally through the proposed metamaterial. It is evident that triple-band transparency windows can be obtained in the investigated frequency region. Three transmission peaks appear at 1.15THz (marked B), 1.66THz (marked D) and 2.22 THz (marked F) between four dips located at 1.03 THz (marked A), 1.42THz (marked C), 1.99THz (marked E) and 2.55 THz (marked G). Apparently, the dipole resonances associated with the circular ring resonators are evoked by the incident waves which result in the transmission dips. And the destructive interference between the adjacent resonators results in the multi-band transmission peaks. It is interesting to point out that there is only three circular ring resonators but four transmission dips and three transparency peaks are observed. Generally, three dips are expected in the transmission spectra due to three circular rings [37]. The reason for the appearance of four dips is that in our work certain transmission dip is not only attributed to electric dipole of single circular ring but also the coupling effect in the investigated range.
Fig. 2. The transmission spectra of the y-polarized terahertz wave propagating through the proposed metamaterial with the transmission dips and peaks marked A, B, C, D, E, F and G respectively.
To explain the mechanism of the multi-band EIT-like effect, the surface current distributions on the unit cell of metamaterial at transmission peaks and dips are depicted in Fig. 3(a) to (g) respectively. The amplitude scale of surface currents is fixed in different figures for accurate comparison. As observed in Fig. 3(a), the noticeable currents distribute on the outer ring and the middle ring. The electric dipole resulting from the outer ring resonator leads to the first transmission dip. The anti-phase currents on the middle ring weaken the effective resonance, causing the dip more shallow and its amplitude is up to 0.6. Similar circumstance is also found for the second transmission dip from Fig. 3(c). The surface currents on the outer and middle rings contribute to the electric dipole while the currents on the inner rings are anti-phase. Besides, for other transmission dips, surface currents are observed mainly on the inner ring resonator as shown in Fig. 3(e) and (g). By comparison, relatively less surface currents are observed distributing on the circular rings at the transparency peaks as presented in Fig. 3(b), (d) and (f). The near coupling between the adjacent rings results in the weakening of the surface currents. Particularly, there is almost no current flowing on the ring resonators at the third peak, which coincides with the nearly total transmission (marked F) shown in the Fig. 2.
Fig. 3. The surface current distributions on the metamaterial at the frequencies of transmission dips and peaks: (a) 1.03 THz (b) 1.15THz (c) 1.42THz (d) 1.66THz (e) 1.99THz (f) 2.22 THz (g) 2.55THz
To further explore the generation of the multi-band EIT-like windows, the z-component electric field distributions at the peak and dip frequencies are depicted in Fig. 4(a) to (g). The results derived from the field distributions are right consistent with analysis above and reveal more details on the resonances. The different field distributions can be found from Fig. 4(a), (c), (e) and (g), which all indicates electric dipole resonances corresponding to the transmission dips. The in-phase field distributions are observed on different circular rings in Fig. 4(e) and (g) whereas anti-phase fields are found in Fig. 4(a) and (c). Therefore, the transmission dips at 1.99 THz and 2.55 THz are much deeper than the dips at 1.03 THz and 1.42 THz because of the opposite effect between constructive interference and destructive interference. Especially, almost no evident electric fields can be found on inner ring resonator at first transmission dip but all ring resonators are evoked at other transmission dips. As for the transparency peaks, the anti-phase field with similar intensity can be found on different ring resonators from Fig. 4(b), (d) and (f). In Fig. 4(b), the fields on the inner and outer rings are in-phase, which are both anti-phase compared with the fields on the middle ring. In Fig. 4(d), the fields on the middle and outer rings are both anti-phase compared with the fields on the inner ring. The radiative electromagnetic fields are fully cancelled out via the destructive interference as the intensities of the anti-phase fields are similar, which consequently leads to the transparency peaks.
Fig. 4. The z-component electric field distributions on the metamaterial at the frequencies of transmission dips and peaks: (a) 1.03 THz (b) 1.15THz (c) 1.42THz (d) 1.66THz (e) 1.99THz (f) 2.22 THz (g) 2.55THz.
The influence of the ring radius on the transmission spectra is investigated. Figure 5 shows the calculated transmission spectra with varying radius of one certain ring in unit cell while the geometric parameters of other two rings remain unchanged. From Fig. 5(a) we can find that as the radius of the outer ring R1 increases from 33 to 39 µm, only the first transmission dip deepens drastically and exhibits slight frequency shift. This indicates that the outer ring is mainly related to the low-frequency resonance and has much less effect on transmission in other frequency region. Meanwhile, as can be seen from Fig. 5(b), with the radius of the middle ring R2 varying from 26µm to 32 um, the first, second transmission dips and the first transmission peak are influenced while noticeable variation cannot be find in other resonances. The second transmission dip deepens while the first dip weakens gradually. Therefore, the first transparency peak turns more unnoticeable and finally disappears as R2 = 32 µm. As for the inner ring, it is observed from Fig. 5(c) that the second, third and fourth transmission dips and the second transparency peak exhibit red shift as R3 rises from 19µm to 25µm. The second transmission dip weakens whereas the third dip deepens gradually. The first transmission dip shows insensitive to the varying R3. Interestingly, the position of the third transparency peak remains invariable though the adjacent transmission dips are changed. The various resonances are closely related to the circular ring with certain radius and the transmission spectra may be intentionally designed by adjusting the geometric size. It is worthy to mention that when the radius of the circular ring varies, the distances between the adjacent rings are also changed. Then, the coupling between these ring resonators is inevitably influenced, which also contribute to the variations in transmission spectra.
Fig. 5. The transmission spectra with varying radius (a) R1 (b) R2 (c) R3 of the different circular ring resonators.
We investigate the sensitivity of our proposed metamaterial to the refractive index n of surrounding media. Figure 6(a) shows the transmission spectra of the designed structure immersed in medium with different refractive index. It is observed that the EIT-like curves are sensitive to the environmental refractive index varying from 1.10 to 1.14. Remarkably, the transparency peaks move towards the lower frequency region showing red-shift with increasing refractive index. To evaluate the sensing performance, the frequency variations of the transmission peaks as a function of refractive index are plotted in Fig. 6(b). As can be observed, the frequency shifts manifest nearly linear relation with the increasing refractive index. It is noted that different transparency peaks show distinctive sensitivity to the environmental refractive index. Particularly, the frequency shifts of the third transmission peak are larger than those of other peaks. We define the sensitivity S as frequency shift of the transmission peak per refractive index (RIU) and the equation can be described: S = Δf/Δn. Hence, the sensitivities of the EIT-like metamaterial to environmental refractive index can be calculated, which are 0.52 THz/RIU, 0.88 THz/RIU and 1.60 THz/RIU for the first, second and third peaks respectively. For comparison, the results of the relevant published studies in the similar investigated frequency region are listed in Table 1 [14–40]. It is clear that the sensing performance of the transparency peaks especially the third peak is relatively higher than that in most previous works. These results indicate that the proposed metamaterial may provide high-resolution sensing of refractive index, which is attractive in detecting the surrounding media [41].
Fig. 6. (a) The transmission spectra of the metamaterial in surrounding environment with the refractive index varying from 1.10 to 1.14. (b) The frequency shift of the transparency peaks as the refractive index changes from 1.10 to 1.16.
Table 1. Comparison with similar published works.
It is widely acknowledged that the EIT-like phenomenon occurs with strong dispersion which results in the slow light effect around the transparency window frequency range. Generally, the group delay defined as τg = -dφ/dω is employed to evaluate the slow light performance of the metamaterials, where φ is the transmission phase shift and ω denotes the circular frequency of the incident waves [42]. The transmitted phase shift and group delay spectra as the incident waves propagate through the proposed metamaterial are depicted in Fig. 7. The steep phase slope can be found in the vicinity of the transparency windows. The positive and negative values of group delay can be observed corresponding to slow and fast light. It is noticed that three maximal values up to 0.72ps, 0.9ps and 1.3ps can be obtained at 1.08THz, 1.91THz and 2.05THz in the group delay spectra. These results correspond to 216µm, 270µm and 390µm distance delays in free space which are several hundred times larger than the thickness of the proposed EIT-like metamaterial. This manifests unambiguous decline in the group velocity of the incident wave. Therefore, the multi-band slow light effect can be accomplished in the investigated frequency range.
Fig. 7. The phase shift and the corresponding group delay spectra when the incident wave propagates normally through the metamaterial.
Unlike the multi-band EIT-like phenomenon realized in metal metamaterials, the transparency windows of the proposed metamaterials can be manipulated significantly by controlling the state of the VO2 film via optical, electrical, or thermal excitation. Figure 8 shows the transmission spectra of the designed structure with VO2 film in insulator state and metallic state under normal incidence. It can be observed from the simulated results that three transparency windows disappear completely as VO2 undergoes insulator-metallic transition. The increasing conductivity of the VO2 film occurring in the phase-change process devastates the dipole resonances evoked by the circular ring resonators as well as their coupling effect. Therefore, the corresponding amplitude of the transmission peaks is modulated drastically when the multi-band EIT-like effect is switched off. Here, we define the amplitude modulation depth as ${T_{MD}} = |{T_{max}} - {T_{min}}|\textrm{ }/\textrm{ }{\textrm{T}_{max}}$. Then, modulation depth of 48%, 51% and 54% can be achieved in three peaks located at 1.15THz, 1.66THz and 2.22THz respectively. Thus, by inducing the insulator-metallic phase transition of the bottom VO2 film, the active control of transparency windows can be realized without adjusting the geometric parameters, which may be applied in the multi-band terahertz modulation.
Fig. 8. The dynamically controlled multi-band EIT-like response when the bottom VO2 film is in the insulator phase and the metallic phase.
Particularly, the dependence of the polarization angle of incident waves on the EIT-like response under perpendicular incidence is investigated. Figure 9 shows the simulated transmission spectra with different polarization angle ϕ of the incident wave. As can be seen, very slight variation can be observed with ϕ varying from 0° to 90° and the multi-band EIT-like curves maintain almost unchanged. The design of the unit cell structure is highly rotationally symmetrical. Therefore, the multi-band EIT-like effect based on the designed metamaterial shows polarization-insensitive characteristics. This feature is essential in potential practical applications such as modulating, detecting and slow light devices.
Fig. 9. The transmission of the designed metamaterial as a function of polarization angle and frequency under perpendicular incidence of the terahertz waves.
4. Conclusions
In summary, a metamaterial analogy of polarization-independent, multi-band and controllable electromagnetically induced transparency metamaterial is proposed and numerically investigated. By generating dipole resonance and the near coupling function based on the simple combination of circular rings with different radius, multi-band transparency windows are obtained in the transmission spectra. The influence of the radius of different ring resonators on the EIT-like curve is studied. High sensing performance with sensitivity up to 1.60 THz/RIU to the refractive index of the surrounding medium is realized by the proposed structure. Additionally, the multi-band EIT-like effect can be dynamically controlled by inducing the insulator-metallic transition of the vanadium dioxide layer. The modulation depth in three transmission peaks can reach up to 48%, 51% and 54%. The distinguishing multi-band slow light effect is also observed around the three transparency windows. Furthermore, due to the symmetric unit cell, the multi-band EIT-like responses maintain invariable with different polarization angles. The proposed multi-band EIT-like metamaterial is simply designed with both polarization-independent and controllable characteristics, which is highly desirable for practical applications in filtering, switching, modulating light buffering and sensing.
Funding
National Natural Science Foundation of China (62101565).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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