Multi-Band Electromagnetically-Induced-Transparency Metamaterial Based on the Near-Field Coupling of Asymmetric Split-Ring and Cut-Wire Resonators in the GHz Regime

A metamaterial (MM), mimicking electromagnetically-induced transparency (EIT) in the GHz regime, was demonstrated numerically and experimentally by exploiting the near-field coupling of asymmetric split-ring and cut-wire resonators. By moving the resonators towards each other, the original resonance dip was transformed to a multi-band EIT. The phenomenon was explained clearly through the excitation of bright and dark modes. The dispersion characteristic of the proposed MM was also investigated, which showed a strongly-dispersive behavior, leading to a high group index and a time delay of the MM. Our work is expected to contribute a simple way to develop the potential devices based on the multi-band EIT effect.


Introduction
Electromagnetically-induced transparency (EIT) is a quantum phenomenon related to the destructive interference in atomic systems [1,2]. Thanks to this phenomenon, an absorptive medium can be transformed to a transparent one. Around the transparency region, the medium comes to be strongly dispersive and the transparency peak acquires a high Q-factor. Therefore, the EIT effect has many promising applications, such as energystorage devices [3], sensors [4] and filters [5]. However, the original quantum EIT requires rigorous and extreme conditions, including a high-intensity laser and cryogenic temperature, which limit the vast applications in reality. Recently, researchers showed that the EIT effect can be mimicked in classical systems, such as mechanical [6] and electromagnetic (EM) oscillators [7]. One of the research directions, which has obtained great interest, was to develop metamaterial (MM) mimicking the EIT effect (EIT-MM).
MM is an artificial material, which is composed of subwavelength electric and magnetic components, playing the role of an artificial meta-atom. The advantage of MM is that the flexibility in the design of the meta-atom makes the MM exhibit the desired properties unlimitedly. The birth of MM came from the idea by Veselago, who firstly proposed and studied the peculiar EM behavior of an unknown material at his time, which revealed negative permittivity and permeability simultaneously [8]. Nearly 30 years later, pioneer works by Pendry et al. [9,10] paved the way for structural models, which could provide the negative permittivity and permeability in the same microwave region. In 2000, based on these works, the first negative refractive-index.
MM was demonstrated by Smith et al. [11]. Since then, the development of MM has been performed quickly and different kinds of MM were proposed, leading to many potential applications, such as MM perfect absorber [12,13], MM perfect lens [14,15], chiral MM [16,17] and MM wireless power transfer [18,19]. Besides the aforementioned applications, the EIT-MM also attracted great interest due to its simplicity in comparison with the original quantum systems [20][21][22][23][24][25].
Basically, the EIT-MM can be categorized in two different types, which are brightbright and bright-dark couplings. In the bright-bright coupling, both resonances are excited directly by an external field, which is why these resonances are often called the bright mode. In the bright-dark coupling, one resonance can be excited directly by the external field while the other is excited only by the near-field of the previous resonance. Therefore, the directlyand indirectly-excited resonance are represented as the bright and dark mode, respectively. The destructive interference between two bright modes or bright and dark modes induces an analog of the EIT effect with a transparency in a narrow frequency region.
Traditionally, in order to create a single-band EIT-MM, the requirement is an MM structure consisting of, at least, two different types of resonators [26,27]. So far, to our knowledge, most of the multi-band EIT-MMs have exploited more than three different types of resonators in the structure [28][29][30]. Increase of the number of resonators leads to a complicated geometrical structure, which might not be easy for the fabrication, especially at high frequencies such as the optical region. In this work, we propose a simple multi-band EIT-MM based on only two types of resonators, asymmetric split-ring (ASR) and cutwire (CW) resonators. The advantage of the proposed EIT-MM is that both bright-bright and bright-dark couplings can be excited by simply changing the distance between the resonators, resulting in a multi-band EIT effect in the GHz region. The EIT-MM sample was fabricated and measured to confirm the suggestions. In addition, the field distribution was also simulated to clarify the nature of the EIT effect. Finally, the typical characteristics of EIT-MM, including the group index and the time delay, are also investigated. Figure 1 illustrates the unit cell of designed EIT-MM and the polarization of the incoming EM wave. The EIT-MM was composed of two layers: a continuous dielectric layer at the bottom and a patterned metallic layer on the top. Copper and FR-4 were chosen as the metal and dielectric, respectively. The conductivity of copper was 5.96 × 10 7 S/m, while the dielectric constant of FR-4 was 4.3 and the loss tangent was 0.025. The patterned copper layer consisted of four rotated ASRs and identical CW resonators. The ASR resonators had a side length r 1 = 15 mm, an arm width r 2 = 1 mm and a gap between the arms of rings g = 1.5 mm. The CW resonator was made with a width w = 1 mm and a length l = 15 mm. The separation between the CW and ASR was fixed to be s = 0.5 mm, while the distance between ASRs d was varied. The thicknesses of the copper and FR-4 layers were t m = 0.035 and t d = 1 mm, respectively. The EIT-MM was composed of repeated unit cells in two dimensions on a plane with a periodicity of p = 40 mm. and studied the peculiar EM behavior of an unknown material at his time, which revealed negative permittivity and permeability simultaneously [8]. Nearly 30 years later, pioneer works by Pendry et al. [9,10] paved the way for structural models, which could provide the negative permittivity and permeability in the same microwave region. In 2000, based on these works, the first negative refractive-index. MM was demonstrated by Smith et al. [11]. Since then, the development of MM has been performed quickly and different kinds of MM were proposed, leading to many potential applications, such as MM perfect absorber [12,13], MM perfect lens [14,15], chiral MM [16,17] and MM wireless power transfer [18,19]. Besides the aforementioned applications, the EIT-MM also attracted great interest due to its simplicity in comparison with the original quantum systems [20][21][22][23][24][25].

Materials and Methods
Basically, the EIT-MM can be categorized in two different types, which are brightbright and bright-dark couplings. In the bright-bright coupling, both resonances are excited directly by an external field, which is why these resonances are often called the bright mode. In the bright-dark coupling, one resonance can be excited directly by the external field while the other is excited only by the near-field of the previous resonance. Therefore, the directly-and indirectly-excited resonance are represented as the bright and dark mode, respectively. The destructive interference between two bright modes or bright and dark modes induces an analog of the EIT effect with a transparency in a narrow frequency region. The EM properties of the EIT-MM were investigated using three-dimensional EM simulation based on a finite-integration package (CST Microwave Studio) [31]. The unit-cell structure was repeated on a plane by applying the unit-cell boundary conditions. The incident EM wave propagated normally to the EIT-MM plane with electric (E) and magnetic (H) fields polarized perpendicularly to each other and parallel to the side lengths of the ASR resonators.
The EIT-MM sample was fabricated using FR4 coated with copper and the lithography technique. Figure 2 shows the fabricated sample with a magnified unit cell. After the fabrication process, the sample was measured with vector network analyzer R&S ZNB20, which was connected to two horn antennas. In the transmission-measurement configuration, the EIT-MM was put in the middle between the two antennas and normal to the wave propagation direction. The calibration was done by measuring the transmission in free space without the sample as the reference signal.
cially at high frequencies such as the optical region. In this work, we propose a simple multi-band EIT-MM based on only two types of resonators, asymmetric split-ring (ASR) and cut-wire (CW) resonators. The advantage of the proposed EIT-MM is that both brightbright and bright-dark couplings can be excited by simply changing the distance between the resonators, resulting in a multi-band EIT effect in the GHz region. The EIT-MM sample was fabricated and measured to confirm the suggestions. In addition, the field distribution was also simulated to clarify the nature of the EIT effect. Finally, the typical characteristics of EIT-MM, including the group index and the time delay, are also investigated.  Figure 1 illustrates the unit cell of designed EIT-MM and the polarization of the incoming EM wave. The EIT-MM was composed of two layers: a continuous dielectric layer at the bottom and a patterned metallic layer on the top. Copper and FR-4 were chosen as the metal and dielectric, respectively. The conductivity of copper was 5.96 × 10 7 S/m, while the dielectric constant of FR-4 was 4.3 and the loss tangent was 0.025. The patterned copper layer consisted of four rotated ASRs and identical CW resonators. The ASR resonators had a side length r1 = 15 mm, an arm width r2 = 1 mm and a gap between the arms of rings g = 1.5 mm. The CW resonator was made with a width w = 1 mm and a length l = 15 mm. The separation between the CW and ASR was fixed to be s = 0.5 mm, while the distance between ASRs d was varied. The thicknesses of the copper and FR-4 layers were tm = 0.035 and td = 1 mm, respectively. The EIT-MM was composed of repeated unit cells in two dimensions on a plane with a periodicity of p = 40 mm.

Materials and Methods
The EM properties of the EIT-MM were investigated using three-dimensional EM simulation based on a finite-integration package (CST Microwave Studio) [31]. The unitcell structure was repeated on a plane by applying the unit-cell boundary conditions. The

Results and Discussion
In our structure, d was reduced from 3.5 to 0.5 mm to induce the EIT effect. The simulated transmission spectra of the proposed EIT-MM, according to d, are presented in Figure 3a. It is shown that, at the initial position (3.5 mm) of the ASRs, only one resonance is excited, which is presented by a transmission dip at 13.82 GHz in the transmission spectrum. When the rings are closer to each other, the near-field coupling between the ASRs and between the ASR and the CW are induced. Firstly, when d = 2.5 mm, a transmission peak arises at 14.4 GHz, which lies between a broad transmission dip around 13.8 GHz and another one at 14.6 GHz. Then, for d = 1.5 mm, it is observed clearly that three transmission dips at 13.5, 14.0 and 14.8 GHz are interleaved with two transmission peaks at 13.8 and 14.6 GHz. Finally, when d = 0.5 mm, the separations between dips and peaks are farther owing to the stronger coupling, and a multi-band EIT effect is achieved with high transmission peaks of 60% at 13.73 GHz and 80% at 14.69 GHz. Figure 3b shows the dependence of the transmission phase spectrum on d. It is presented that, when the distance between rings is closer, the transmission phase is more dispersive. Furthermore, the dispersion curve exhibits more turning points, where the uptrend or the downtrend of the phase is reversed. The observed phenomena suggest that a strong multi-band EIT effect is induced in the investigated frequency region. The EIT-MM sample was fabricated using FR4 coated with copper and the lithography technique. Figure 2 shows the fabricated sample with a magnified unit cell. After the fabrication process, the sample was measured with vector network analyzer R&S ZNB20, which was connected to two horn antennas. In the transmission-measurement configuration, the EIT-MM was put in the middle between the two antennas and normal to the wave propagation direction. The calibration was done by measuring the transmission in free space without the sample as the reference signal.

Results and Discussion
In our structure, d was reduced from 3.5 to 0.5 mm to induce the EIT effect. The simulated transmission spectra of the proposed EIT-MM, according to d, are presented in Figure 3a. It is shown that, at the initial position (3.5 mm) of the ASRs, only one resonance is excited, which is presented by a transmission dip at 13.82 GHz in the transmission spectrum. When the rings are closer to each other, the near-field coupling between the ASRs and between the ASR and the CW are induced. Firstly, when d = 2.5 mm, a transmission peak arises at 14.4 GHz, which lies between a broad transmission dip around 13.8 GHz and another one at 14.6 GHz. Then, for d = 1.5 mm, it is observed clearly that three transmission dips at 13.5, 14.0 and 14.8 GHz are interleaved with two transmission peaks at 13.8 and 14.6 GHz. Finally, when d = 0.5 mm, the separations between dips and peaks are farther owing to the stronger coupling, and a multi-band EIT effect is achieved with high transmission peaks of 60% at 13.73 GHz and 80% at 14.69 GHz. Figure 3b shows the dependence of the transmission phase spectrum on d. It is presented that, when the distance between rings is closer, the transmission phase is more dispersive. Furthermore, the dispersion curve exhibits more turning points, where the uptrend or the downtrend of the phase is reversed. The observed phenomena suggest that a strong multi-band EIT effect is induced in the investigated frequency region. To verify the simulated results, the EIT-MM sample with d = 0.5 mm was fabricated and the transmission spectrum was measured. The comparison of simulated and meas-  To verify the simulated results, the EIT-MM sample with d = 0.5 mm was fabricated and the transmission spectrum was measured. The comparison of simulated and measured transmission spectrum is demonstrated in Figure 4a. The measurement and simulation results are in good agreement. In the experiment, the two transmission peaks occur at 13.7 and 14.7 GHz while the transmission dips are at 13.3, 14 and 15 GHz. The measured transmission magnitudes of the first and the second peak are 60% and 80%, respectively, which are in accordance with the simulated ones anyhow. The simulated and experimental transmission phase spectra are presented in Figure 4b. The results show that the phase is changed rapidly and significantly in the frequency region corresponding to the two transmission windows. The magnitude of phase variation is around 80 degrees, which is approximately from 40 to −40 degrees. The discrepancy between simulation and experiment is small around the EIT transparency window, while it is slightly increased outside the resonance region. The possible explanation might be due to the influence of unwanted scattering from the outside environment during the free-space measurement, which is a limitation of our measurement system. changed rapidly and significantly in the frequency region corresponding to the two transmission windows. The magnitude of phase variation is around 80 degrees, which is approximately from 40 to −40 degrees. The discrepancy between simulation and experiment is small around the EIT transparency window, while it is slightly increased outside the resonance region. The possible explanation might be due to the influence of unwanted scattering from the outside environment during the free-space measurement, which is a limitation of our measurement system. Figure 5 presents the simulated surface currents on the patterned copper layer at the resonance frequencies in the non-activated (d = 3.5 mm) and the activated (d = 0.5 mm) EIT states. When d = 3.5 mm, the ASRs are far from each other, making them isolated. In addition, the relative position between the ASR and CW is symmetric in this structural configuration. Hence, the near-field coupling of the ASR and CW cannot be excited. As a consequence, only the surface current of dipole is induced on the ASRs, leading to a transmission dip at 13.82 GHz as shown in Figure 3a. When d = 0.5 mm, the ASRs are closer to each other, giving the bright-bright coupling of ASRs, which is similar to previous works [13,32]. Furthermore, the relative position between the ASR and CW also becomes asymmetric, activating the bright-dark coupling of the ASRs and CWs. The activation of the dark mode on the CW, which was perpendicular to the incident E field, was reported to be based on the asymmetry of the structure [33].    Figure 5 presents the simulated surface currents on the patterned copper layer at the resonance frequencies in the non-activated (d = 3.5 mm) and the activated (d = 0.5 mm) EIT states. When d = 3.5 mm, the ASRs are far from each other, making them isolated. In addition, the relative position between the ASR and CW is symmetric in this structural configuration. Hence, the near-field coupling of the ASR and CW cannot be excited. As a consequence, only the surface current of dipole is induced on the ASRs, leading to a transmission dip at 13.82 GHz as shown in Figure 3a. When d = 0.5 mm, the ASRs are closer to each other, giving the bright-bright coupling of ASRs, which is similar to previous works [13,32]. Furthermore, the relative position between the ASR and CW also becomes asymmetric, activating the bright-dark coupling of the ASRs and CWs. The activation of the dark mode on the CW, which was perpendicular to the incident E field, was reported to be based on the asymmetry of the structure [33].   Therefore, the multi-band EIT appears due to these couplings. In the EIT region, the surface currents are induced on both the ASR and CW. For the first transparency peak (13.73 GHz), the surface currents on the ASRs still behave like the traditional dipoles. On the other hand, the dipoles on the left and the right CWs are anti-parallel, furthermore, the currents on the top and the bottom CWs are also anti-parallel. These reversed currents confirm the dark-mode nature of CWs. For the second transparency peak (14.69 GHz), the field on the CW seems to be more dominant than that on the ASR. Interestingly, the current directions on the CWs are reversed in comparison with those for the first transparency peak. For the first transparency dip (13.36 GHz), the field is mostly excited on the ASRs since this frequency lies in the region of bright-bright coupling. For the second transparency dip (14.03 GHz), the ASRs and CWs contribute equally to the induced surface currents on EIT-MM, which indicates the influences of both bright-bright and bright-dark couplings at this frequency. Similarly, for the third transparency dip (15.09 GHz), the surface currents are induced on both the ASRs and CWs. However, the current directions on the CWs at the third dip are reversed to those at the second dip, which confirms the significance of dark mode at this frequency.
It is well-known that the material undergoes a strong dispersion around the transparency peak in the EIT effect. During the steep change of the phase in the transmission window, the refractive index of the material varies rapidly, leading to a great reduction of the group velocity when the wave is travelling inside the material. Consequently, the wave is spatially compressed inside it and the transmitted time through it is delayed in comparison to that through the air. The capability of slowing the wave is useful and interesting for components and devices relevant to signal modulation. Therefore, we also investigated the potential of the proposed EIT-MM to be used in the slow-light application by assessing the two typical quantities, which are the time delay and the group index. The time delay of the material can be defined as [34]  where ϕ is the transmission phase. Then, the corresponding group index, which is also a characteristic quantity related directly to the wave velocity, is calculated to be [34] where c is the wave velocity in free space, v g and τ g are the group velocity and the time delay of the EIT-MM, respectively, and t is the thickness of the EIT-MM. Figure   Therefore, the multi-band EIT appears due to these couplings. In the EIT region, the surface currents are induced on both the ASR and CW. For the first transparency peak (13.73 GHz), the surface currents on the ASRs still behave like the traditional dipoles. On the other hand, the dipoles on the left and the right CWs are anti-parallel, furthermore, the currents on the top and the bottom CWs are also anti-parallel. These reversed currents confirm the dark-mode nature of CWs. For the second transparency peak (14.69 GHz), the field on the CW seems to be more dominant than that on the ASR. Interestingly, the current directions on the CWs are reversed in comparison with those for the first transparency peak. For the first transparency dip (13.36 GHz), the field is mostly excited on the ASRs since this frequency lies in the region of bright-bright coupling. For the second transparency dip (14.03 GHz), the ASRs and CWs contribute equally to the induced surface currents on EIT-MM, which indicates the influences of both bright-bright and bright-dark couplings at this frequency. Similarly, for the third transparency dip (15.09 GHz), the surface currents are induced on both the ASRs and CWs. However, the current directions on the CWs at the third dip are reversed to those at the second dip, which confirms the significance of dark mode at this frequency.
It is well-known that the material undergoes a strong dispersion around the transparency peak in the EIT effect. During the steep change of the phase in the transmission window, the refractive index of the material varies rapidly, leading to a great reduction of the group velocity when the wave is travelling inside the material. Consequently, the wave is spatially compressed inside it and the transmitted time through it is delayed in comparison to that through the air. The capability of slowing the wave is useful and interesting for components and devices relevant to signal modulation. Therefore, we also investigated the potential of the proposed EIT-MM to be used in the slow-light application by assessing the two typical quantities, which are the time delay and the group index. The time delay of the material can be defined as [34] (1)

Conclusions
We investigated numerically and experimentally a GHz multi-band EIT-MM by employing the near-field coupling of ASR and CW resonators, in which the ASR and the CW gave rise to the bright and the dark mode, respectively. At an initial position, d = 3.5 mm, there was no coupling and only one resonance dip corresponding to the bright mode. When the distance between the ASRs was reduced, the two types of coupling occurred, which were the bright-bright and the bright-dark one, leading to the appearance of transparency regions. At d = 0.5 mm, a multi-band EIT was clearly observed in the 12-16 GHz region with a transmission magnitude of 60% and 80% for the first and the second transmission peak, respectively. The nature of EIT was clarified by the surface-current distribution, which explained the origin of two couplings. The close distance between the ASRs yielded the bright-bright coupling, while the relative asymmetric position between the ASR and CW led to the excitation of the dark mode on the CW and the bright-dark coupling. Consequently, the multi-band EIT was activated by these two near-field couplings. Furthermore, the intense dispersion of the EIT-MM makes it possible for slow-light applications. The time delays were maximized to be 1.1 and 0.7 ns, and the corresponding group index reached the highest values of 750 and 500 for the first and the second transmission windows, respectively. Our proposed EIT-MM is simple and might contribute to applications such as energy-storage devices, sensors and multi-channel filters.