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Abstract
An asymmetric metasurface capable of a dynamically controlled electromagnetically induced transparency (EIT) analogue is proposed by changing the polarization direction of the incident light. The metasurface composed of Z-L shape meta-atoms exhibits a narrowband transparency window at 1.858 THz for y-polarization incidence. This EIT window originates from the destructive interference between magnetic dipole (MD), toroidal dipole (TD) and electric quadrupole (EQ) resonances, where the coupling of MD and TD serves as bright mode and EQ acts as dark mode. By varying the polarization angle (φ) of the incident light, the transmission of the dip at 1.856/1.861 THz can be tuned from 0.90/0.95 to 0.08/0.03. Meanwhile, the Q-factor of 640.55 and the group delay of 117.21 ps are achieved at φ = 120°. This work will promote the development of novel multipolar supported EIT metasurfaces.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Electromagnetically induced transparency (EIT) is a quantum interference effect occurred in atomic system, which can lead to an originally opaque medium transparent in a narrowband spectrum [1]. Particularly, the steep phase dispersion accompanied with EIT window can greatly alter the group velocity of light. Slow light is of great scientific significance and strategic value for its ability to enhance the interaction between light and matter [2]. To date, many schemes are proposed to generate the slow light, such as photonic crystal waveguides [3], graded Bragg grating [4], stimulated Raman scattering [5], EIT [6] etc. Among these methods, EIT is one of the most common and promising methods to delay the speed of light. Based on the high dispersion of EIT, Hau et al. observed the group velocity of 17 m/s in an atomic system [6]. However, the strict requirements, such as gaseous medium and ultracold temperatures, limit the development of traditional quantum EIT. As an alternative, EIT analogues in metamaterials (metasurfaces) not only avoid the severe conditions in atomic system but provide a wider operating frequency range, from microwave to visible region [7–11]. In general, analog EIT effects in metasurfaces can be achieved by ‘'bright-bright'‘ coupling or ‘'bright-dark'‘ coupling or ‘'bright-quasi-dark'‘ coupling. And ‘'bright-dark'‘ coupling is the most conventional method. Concretely, the ‘'bright'‘ mode is directly excited by the incident light, whereas the ‘'dark'‘ mode is indirectly activated by the ‘'bright'‘ mode through the near-field coupling. When these two resonance modes are close in both frequency and spatial domains, the interference between them results in a transparency window, i.e. EIT effect supported by ‘'bright-dark'‘ coupling. So far, various metasurfaces, including plasmonic metasurfaces (often termed as PIT) and all-dielectric metasurfaces, are proposed to generate analog EIT phenomenon. For example, the twisted metallic strip [8], asymmetric split ring [12], reverse-symmetric spiral [13], E-shape structure [14] and so on. Among them, all-dielectric metasurfaces supporting Mie-type resonances show great advantages in realizing high-Q and high transparency EIT, because they evade the ohmic losses in metal counterparts. Utilizing high-index dielectric materials, researchers have proposed a large number of EIT metasurfaces and deeply investigated their mechanisms [12–19]. Some reports on EIT metasurfaces based on the coupling of two resonant modes like magnetic dipole-magnetic dipole [12], magnetic dipole-toroidal dipole [14,18], electric dipole-magnetic dipole [19,20] have been published. Nevertheless, there are only a few studies on analog EIT effects caused by the complex three-mode hybrid resonance [13], especially in THz region.
On the other hand, to meet the rapid development of contemporary photonic devices, it is highly desired to achieve the tunable group velocity of electromagnetic waves [21]. Driven by the practical applications, numerous metasurfaces are proposed by integrating various active components like graphene [18], semiconductor Si [21], MEMS [22], liquid crystal [23], PIN [24], and so on. The problem is these schemes usually need attachments to provide external stimuli such as optical pump and voltage bias, which may bring extra noises and instability to EIT spectra. Besides, complex components will increase the difficulty of preparation and are not conducive to photonic integration. Recently, polarization-controlled EIT analogue in metasurface attracts great attention from researchers due to its simple operation and good reliability. By breaking the spatial symmetry of structures, some polarization-dependent EIT metasurfaces are proposed [15,25]. Unfortunately, these metasurfaces are either limited by low Q-factor [25], or small group delay [15], or low transmission [25].
In this paper, we propose an all-dielectric EIT metasurface with high Q-factor and large group delay, whose unit cell is composed of a Z-shape and a L-shape resonators. The EIT effect is induced by the destructive interference between the “bright mode'‘ supported by magnetic and toroidal hybrid resonance (MTHR) and the “dark mode'‘ supported by the electric quadrupole resonance (EQR). By controlling the polarization direction of the incident light, the transmission of the dip at the 1.856/1.861 THz can be tuned from 0.90/0.95 to 0.08/0.03. Under the excitation of y-polarized incidence, a narrowband EIT window at 1.858 THz with high transmission of 0.96, high Q-factor of 640.52 and large group delay of 102.95 ps is achieved. Based on these merits, the proposed metasurface shows great potentials in sensors and slow-light devices.
2. Structural design and simulation methods
In our previous work [26], we have demonstrated that the free-space coupling between the adjacent resonators could induce the circular displacement currents flowing opposite to those in the zigzag resonators by carefully optimizing the geometric parameters and the period of unit cells. Inspired by this, we attempt to excite the toroidal dipole resonance (TDR) in a Z-shape array by inducing the opposite circular displacement currents in the resonators and the interval between adjacent resonators. Besides, we expect the TDR to be accompanied by other resonance modes, such as magnetic dipole, by optimizing the geometric parameters of Z-shape resonator. Figure 1 shows the schematic of the proposed asymmetric EIT metasurface, whose unit cell consists of a Z-shape and an L-shape silicon resonators placed on a 45 µm thick SiO2 layer. To obtain the opposite circular displacement currents, geometric parameters and period of the Z-shape array are firstly optimized by CST Microwave Studio commercial software. In simulations, the unit cell boundary conditions in the x- and y-directions and open boundary conditions in ± z-directions are used. If no otherwise specified, normally y-polarized light in -z-direction is used to excited the metasurface. The permittivities of Si and SiO2 (Glass) are set as 11.68 and 3.84, respectively [27]. Remarkably, the optimized Z-shape structure can be coupled with the incident light directly as a bright resonator. In order to realize the EIT metasurface, an L-shape resonator is then introduced in the unit cell. The optimized parameters are set as: p = 100 µm, l1 = 39 µm, l2 = 36 µm, l3 = 23 µm, w = 7.5 µm, l4 = 21.5 µm, l5 = 35 µm, s = 10.25 µm.
Fig. 1. Schematic of the proposed EIT metasurface. Incident linearly polarized light propagates along -z direction. The blue regions are Si and the grey region is SiO2. Geometric parameters: p = 100 µm, l1 = 39 µm, l2 = 36 µm, l3 = 23 µm, l4 = 21.5 µm, l5 = 35 µm, w = 7.5 µm, s = 10.25 µm.
3. Results and discussion
We start the investigation from the optical responses of the Z-shape structure array and the L-shape structure array, as shown in Fig. 2(a). The transmission spectrum of the Z-shape array exhibits a transmission dip with a Q-factor of 97.98 at 1.893 THz due to the excitation of Mie-type resonance, where the Q-factor is calculated by fres/FWHM. Apparently, the resonance modes in the Z-structure serve as bright mode that can be directly excited by the incident light. However, there is no dip in the transmission spectrum of the L-shape structure array. Namely, the L-shape structures serve as dark resonators and cannot be directly coupled with the incident light. To analyze the optical response and identify the resonance modes, the scattered intensities of multipoles in the Z-shape structure array are calculated based on the general multipole scattering theory [28], as presented in Fig. 2(b). In the vicinity of the resonant frequency (1.893 THz), the scattered intensities of the toroidal and the magnetic dipole resonant modes are significantly higher than those of other multipole modes. Therefore, broad transmission dip marked by the red line is attributed to the excitation of MTHR. Figures 2(c)–2(d) provide the E-field distributions in the yz-plane and the H-field distributions in the xy-plane, where the black arrows represent the vector field directions. It is found that the vector E-fields in the Z-shape resonators circulate anticlockwise in the y-z plane, thus inducing a x-directed magnetic moment A. Meanwhile, the coupling between the adjacent resonators in the y-direction produces the clockwise circulating currents, as shown in Fig. 2(c). So, a magnetic moment oriented from the lower-right to the upper-left corner is observed, as marked by C in Fig. 2(d). Intriguingly, the diagonal resonators, such as I and IV, also interact with each other to generate the magnetic moment pointing from the upper-right to the lower-left corner (marked by B in Fig. 2(d)). These induced magnetic moments are arranged ‘'head-to-tail'‘ to form the clockwise magnetic currents within the unit cell (A→B→C, marked by the blue circle) and the anticlockwise magnetic currents between the neighboring unit cells (A→C→B, marked by the blue circle), respectively, as illustrated in Fig. 2(d). These features of the E-field and the H-field confirm the excitations of the toroidal dipoles.
Fig. 2. (a) Simulated transmission spectra of the individual Z-shape structure array and L-shape structure array. (b) Scattered intensities of the electric dipole (IP), magnetic dipole (IM), toroidal dipole (IT), electric quadrupole ($I_Q^e$), and magnetic quadrupole ($I_Q^m$) resonances in the Z-shape structure array. Distributions of the (c) electric field in yz-plane (x = −7.75 µm, position of white dotted line in (d)) and the (d) magnetic field in xy-plane (z = 0 µm) at the resonant frequency (f = 1.893 THz) of the Z-shape structure array.
Next, we explore the EIT analog response of the metasurface (shown in Fig. 1) composed of Z- and L-shape resonators. In Fig. 3(a), the EIT window characterized by a peak located between two dips is observed at 1.858 THz. Specifically, the transmission peak reaches 0.96 and the corresponding Q-factor is 640.52. High transmission of EIT window arises from the destructive interference between the bright-dark resonance modes. Figure 3(b) shows the results of the multipole decomposition. One can observe that the magnetic dipole and electric quadrupole dominate the scattered intensity at dip I, while the toroidal dipole shows the highest scattered intensity at dip III. Around the EIT peak II, the scattered intensities of the dominating magnetic dipole, toroidal dipole and electric quadrupole are approximate equality. Therefore, the EIT peak II results from the destructive interference between MTHR and EQR. Figure 3(c) shows the H-field distributions in the xy-plane of the proposed EIT metasurface excited by y-polarized light at different frequencies (dip I, peak II, dip III). At the resonant dip I, the H-fields are mainly localized around the Z- and L-structure and at the bottom of Z-structure. Meanwhile, a series of locally parallel H-field vectors marked by the bold black arrows demonstrate the dominant resonance mode is magnetic dipole resonance. The H-field vectors (at peak II) localized at the top of Z-structure and the gap between Z- and L-structure resembles the magnetic moments marked by bold black arrows. Particularly, there are two opposite ring magnetic fields located on the vertical arm of the Z structure and on the horizontal arm of the L structure. At the resonant dip III, the H-fields in the Z-structures are strongly coupled with those in L-structure. To be specific, the induced H-fields in the Z-structure flow from bottom-left to top-right, while the induced H-fields in the L-structure flow from top-right to bottom-left. Meanwhile, the coupling of these two opposite magnetic moments forms the toroidal dipole moment along −z-direction, which is in agreement with the multipole decomposition in Fig. 3(b). From the perspective of a three-level EIT system, as shown in Fig. 3(d), the MTHR-allowed transition from the ground state ($|0 \rangle $) to the excitation state ($|1 \rangle $) is analogy to the excitation of the bright mode in the Z-shape metasurface. Correspondingly, the ‘'bright mode'‘ is featured with a resonant frequency ω1 and a damping factor γ1. Meanwhile, the direct transition from $|0 \rangle $ to $|2 \rangle $ (metastable state) is forbidden, which is analogy to the ‘'dark'‘ resonance mode (EQR) that cannot be directly excited by the incident light. And the ‘'dark mode'‘ is characterized by a resonant frequency ω2 and a damping factor γ2. However, the near-field coupling between the ‘'bright'‘ and the ‘'dark'‘ modes, related to a coupling coefficient κ, can lead to the transition between $|1 \rangle $ and $|2 \rangle $. In short, there are two feasible pathways, i.e. $|0 \rangle \to |1 \rangle $ and $|0 \rangle \to |1 \rangle \to |2 \rangle \to |1 \rangle $, to realize the transition from $|0 \rangle $ to $|1 \rangle $, and both of which can result in a transmission dip. The destructive interference between such two pathways leads to a narrow transparent window. By defining the incident light as ${E_0}{e^{iwt}}$, the bright mode as ${A_1}(\omega ){e^{iwt}}$ and the dark mode as ${A_2}(\omega ){e^{iwt}}$, one can write the coupling equations as [10]:
Fig. 3. (a) Transmission spectra of the proposed EIT metasurface. (b) Scattered intensities of electric dipole (IP), magnetic dipole (IM), toroidal dipole (IT), electric quadrupole ($I_Q^e$), and magnetic quadrupole ($I_Q^m$) resonances in EIT metasurface. (c) Distributions of magnetic field in xy-plane (z = 0 µm) at the dip I, peak II, and dip III of the Z-shape structure array. (d) Schematic of the light excitation pathways in the proposed EIT metasurface.
The theoretically fitted curve based on Eq. (2) is shown in Fig. 3(a), where the fitting parameters are γ1 = 0.0038, γ2=∼0.0002, κ=0.0023. Obviously, the fitting result is in good agreement with the simulation curve. In particular, the value of γ2 is one order of magnitude smaller than γ1 owing to the significant difference of the coupling extent between the incident light and the two resonators.
Subsequently, we explore the polarization-controlled EIT effect by increasing the polarization angle from 0° to 180° in a step of 30°, as shown in Fig. 4(a). As φ increase, the ‘'bright'‘ resonance mode in the Z-shape structures can be effectively excited, and the most distinct EIT-like spectrum is observed at 120°, with a transparent peak of ∼0.97. However, with the further increase of φ, the EIT spectral contrast ratio declines with the increase of transmission of the resonance dips. The modulation depth, defined as $\frac{{{T_{\max }} - {T_{\min }}}}{{{T_{\max }} + {T_{\min }}}} \times 100\%$, of dip I and dip III reaches 82.71% and 93.56% respectively. Large modulation depth at the resonance dips may find potential application in information encoding. It is worth noting that the transmission and the frequency of peak II remain relatively stable with the increase of φ, which implies the robust destructive interference between the ‘'bright'‘ and ‘'dark'‘ resonance modes at EIT window. To visually illustrated the coupling behavior between the ‘'bright'‘ and ‘'dark'‘ resonators, the H-field distributions at peak II with four different polarization angles are calculated, as shown in Fig. 4(b). As φ increases from 60° to 120°, the H-field intensity between the Z-shape and the L-shape resonators is gradually strengthened. Further increase φ to 150°, the Z-shape resonators are ineffectively excited, and the H-field intensity between the Z-shape and the L-shape resonators is weakened obviously. To quantitatively analyze the change of coupling strength, the dependence of the fitting parameters on the polarization angle φ is shown in Fig. 4(c). It is found that the geometric parameter g firstly increases and then decreases with the increase of φ. In other words, the coupling strength of the bright mode with the incident light reaches the peak when φ is 90°. Differently, the magnitude of coupling coefficient κ almost keeps a constant with the increase of φ, which indicates the change of coupling strength between the bright and dark resonators is relatively flat. In addition, the damping factor of the bright mode γ1 is always larger than that of the dark mode γ2, indicating the radiative loss of the ‘'bright'‘ resonator is greater than the ‘'dark'‘ resonator.
Fig. 4. (a) Transmission spectra of the proposed EIT metasurface with different polarization angles, where red solid lines represent the simulation results and blue dash lines represent the fitting results. (b) Magnetic field distributions at EIT peak II under the incident light with 60°, 90°, 120° and 150° polarization angles. (c) The extracted fitting parameters with different incident polarization angles.
Generally, the transmission, Q-factor and the group delay are three important parameters to estimate the performance of EIT metasurfaces. Table 1 shows the comparisons of the EIT performance between the proposed metasurface and some published metasurfaces in THz region. Among these studies, some metasurfaces relying on magnetic dipole [12] resonance or LC-LSP resonance [31] have realized the relatively high Q-factors, but the EIT responses are uncontrollable. The metasurfaces in Refs. [9,29,30] exhibit the dynamically controllable EIT, however, these metasurfaces suffer from either low transmission [29] or small group delay [9,29,30]. In addition, the graphene-based metasurface in Ref. [32] shows a tunable EIT with high transmission peak. Nevertheless, this metasurface requires attachment such as voltage bias to provide the external stimuli to graphene, which increases the complexity of the system. Differently, the proposed dynamically controllable metasurface based on the destructive interference between MTHR and EQR shows the transmission of 0.97, Q-factor of 640.55 and group delay of 117.21 ps.
Table 1. Comparison of the recently reported EIT metasurfaces in THz region.
4. Applications
4.1 Large group delay for slow-light effect
A remarkable characteristic of EIT effect is the large phase dispersion around the transparency window, which can result in the slow light effect. In general, the slow light capability is quantitative evaluated by the group delay [15]:
where ϕ and ω represent the transmission phase and the angular frequency, respectively. In Fig. 5(a), the metasurface exhibits strong phase dispersion around EIT window and the dispersion strength is polarization-dependent. Furthermore, polarization-controlled group delay in the range of 0 ∼ 117.21 ps is observed around the EIT window, as shown in Fig. 5(b). Notably, the maximum group delay is up to 117.21 ps at 1.856 THz when the polarization angle is 120°. This delay time corresponds to a ∼35139 µm propagating distance of light in free space, about 404 times as the proposed structural thickness. Benefiting from the high transmission and the polarization-dependent delay group, the proposed metasurface shows tremendous practical implications in low-loss slow light applications.Fig. 5. (a) Transmission phase and (b) group delay of the proposed EIT metasurface with different polarization angles. Here, the transmission phases are extracted from the co-polarized coefficients. Inset shows the extracted maximum group delay around EIT window with different polarization angles.
4.2 High Q-factor EIT peak for gas sensing
The EIT-like effect in our metasurface is promising to be applied in THz gas sensing due to its narrow linewidth and high transmission. It is widely known that the refractive index of gas can be varied by changing the concentration or pressure [33]. To measure the frequency shift with the gas concentration, we calculated the transmission spectra with the background refractive index (n) increases from 1.00 to 1.01, as shown in Fig. 6(a). The EIT peak of the metasurface moves toward low frequency as n increases, and even slight change of Δn = 0.0002 can bring a significant frequency shift. Typically, Q-factor, sensitivity (S), and figure of merit (FOM) are three important metrics to evaluate the performance of refractive sensor, where the latter two parameters are expressed as follows:
Fig. 6. (a) Transmission spectra and corresponding (b) EIT peak positions of the proposed metasurface with different background refractive indexes. The function f = −0.4314 n+2.289 of linear fitting in (b) determine the sensitivity as ∼0.43 THz/RIU. (c) FWHM and (d) FOM and Q-factor as the functions of background refractive indexes.
By fitting the spectrum of EIT peak positions with linear function of f =−0.4314 n+2.289, we determine the sensitivity of the proposed sensor is ∼0.43 THz/RIU (see Fig. 6(b)), which is much greater than previously published works [12,34,35]. Figure 6(c) shows the FWHM as a function of n. It is found that the FWHM varies on the order of 10−3 as n increases, implying that the linewidth of EIT window is maintained well. In Fig. 6(d), the Q-factor and FOM are larger than 463 and 107 in the detect range, respectively. To intuitively evaluate the performance of our metasurface in refractive index sensing, we compared the sensitivity and FOM of our metasurface with the reported devices in Table 2. Obviously, the proposed metasurface shows superior metrics in terms of sensitivity and FOM compared with these reported sensors. Therefore, the proposed EIT metasurface with high sensitivity, large figure of merit and quality factor shows attractive potential applications in refractive-index sensing.
Table 2. Sensitivity, FOM comparison with the reported works in THz
5. Conclusion
We proposed a polarization-controlled EIT metasurface consisting of Z-shape and L-shape resonators for THz gas sensing and slow light. Based on the general multipole scattering theory and the coupled Lorentz oscillator model, the formation mechanism of EIT window could be interpreted by the destructive interference between MTHR (bright mode) and EQR (dark mode). The optimized metasurface exhibits a high transmission of 0.96, a large group delay of 102.95 ps and a high Q-factor of 640.52 under the excitation of y-polarized light. Particularly, the group delay around EIT window is controllable in the range of 0∼117.21 ps by modulating the polarization direction of the incident light. In addition, the position of EIT peak strongly depend on the background index. Numerical results show that the sensitivity and the maximum FOM of EIT peak excited by y-polarized light reach ∼0.43 THz and 148.76, respectively. This work paves a new way for designing novel multipole response-based EIT metasurfaces.
Funding
Natural Science Foundation of Shandong Province (ZR2020MF129); National Natural Science Foundation of China (62075048).
Disclosures
The authors declare no conflicts of interest.
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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