Analog of multiple electromagnetically induced transparency using double-layered metasurfaces

We reported an analog of electromagnetically induced transparency (A-EIT) featured by double transparent peaks in the spectrum. The A-EIT is realized by double-layered metasurface which consists of spoof localized surface plasmons (S-LSP) and cut-wire (CW)-square rings (SR) hybrid. Electric and magnetic S-LSP are excited as bright and dark modes respectively then couple with resonant modes of CW and SR simultaneously to achieve multiple A-EIT. Two bright modes of the electric S-LSP and SR are excited by external electric field directly that produce a bright-bright mode A-EIT. Moreover, the magnetic S-LSP, which cannot be excited by external field directly, is excited through near field coupling from CW, inducing another bright-dark mode A-EIT. Theoretical analysis with corresponding experiment in microwave band are introduced for better insights into physical essence of the double-peaks A-EIT.


Bi-layered metamaterials structure design
The unit cell of our proposed bi-layered metamaterials structure is consisted of S-LSP (by the shape of clockwise 90° rotationally symmetric 4-arms spiral 24 ) pure copper strips on the front of substrate and CW-SR hybrid pure copper strips on the back, as show in Fig. 1. The thickness of metallic structures is 0.035 mm which attaching on the surface of F4B dielectric slab with a thickness of t = 1.575 mm and a permittivity of 2.2. The full-periods of arranged periodic metamaterials sample is manufactured with 10×10 units.
The schematic of the unit cell of bi-layered metamaterials is illustrated in Fig. 1. We have adopted the geometrical parameters definitions of bi-layered metamaterial unit cell are given as follows: w = 0.2 mm, s = 0.4 mm, L = 24 mm, M = 10.8 mm, l = 18.2 mm, a = 2.3 mm, R = 14.1 mm, R 0 = 17.6 mm, what is occurred in simulation under the periodic boundary conditions. The substrate's material is F4B, which is low dispersive and absorption while working below the terahertz frequencies. Numerical simulations are undertake using a finite element method. The simulation process of transmission curve is calculated in commercial software package CST Microwave Studio, with the plane electromagnetic wave incidence. theoretical analysis and experiment results. To comprehensively explain the coupling mechanism of the proposed double-peaks mode A-EIT, we should primarily observe the transmission curves of excited S-LSP, CW and SR working alone. According to ref. 24 , we set condition of external fields as the magnetic field vertical to the substrate plane and electric field parallel to the substrate plane, then removing the SR and CW from the substrate to get the transmission curve for S-LSP working alone be excited by external fields. In Fig. 2(a), there are two resonance dips at frequencies of 5.405 GHz and 6.445 GHz from the transmission curve for S-LSP alone. We know the S-LSP could be excited to produce simultaneously an electric dipole and a magnetic dipole by given condition of external fields (more pairs of electric dipole and magnetic dipole can be seen in enough wide frequency band) according to the electromagnetic feature of S-LSP. In order to distinguish which one is electric dipole and which one is magnetic dipole (frequency range of our investigation is limited to only one pair of electric and magnetic dipole be appeared), we investigate electric/magnetic field distributions at their corresponding frequencies of dipoles (5.405 GHz and 6.445 GHz), as shown in Fig. 2(a) insets. It can be observed that two pairs of equivalent electric currents flow along two curved routes on the metallic surface with opposite directions, resembling a electric dipole behavior. Furthermore, we can see the simulating E y field changes between negative and positive charges that making sure the electric dipole mode at 6.445 GHz, which is also similar to the molecular current that produces the electric dipole motions 33,35,36 . The H z distribution at 5.405 GHz presents the property of spirals and meanders. Similar to the above discussion for electric dipole, it is obvious this resonance at 5.405 GHz emerges by the magnetic S-LSP.
The necessary conditions for obtaining A-EIT are that the frequency difference between the two modes is small and the difference of their Q-value is large 37,38 . In order to achieve A-EIT phenomenon, we also need to utilize two extra coupling modes to acquire a pair of resonances that respective coupling to magnetic S-LSP (magnetic dipole) and electric S-LSP (electric dipole) from the excited S-LSP. Moreover, the different coupling ways to induce A-EIT (excite by external fields or near field coupling) unable to alter the type of dipoles and their resonance frequencies. We adopt a CW and SR structure adding on the back of the substrate meanwhile keeping the polarization direction of electric field to pointing the CW's radial direction and polarization direction of magnetic field parallel to the substrate plane. By this direction of external field, the magnetic S-LSP is regards as dark mode which cannot be excited directly by external magnetic field but can be induced by electric resonance of CW. The CW's electric resonance near field couples to the S-LSP will transform a magnetic resonance on the S-LSP. Therefore, After using CW and SR structure on the back of substrate, two electric dipoles from CW and SR are coupled separately to electric S-LSP and magnetic S-LSP as resonant modes. The frequencies of two electric dipole from CW and SR is f CW = 6.51 GHz and f SR = 5.585 GHz as shown in Fig. 2(b,c), and their Q-value are much lower than the electric dipole and magnetic dipole's from S-LSP, respectively. According to the Fig. 2(b,c), two frequencies of electric dipoles from CW and SR are very close to the frequencies of S-LSP's magnetic dipole and electric dipole, satisfy the necessary condition of generating A-EIT. Now, we consider the transmission properties for the whole unit cell structure of bi-layered metamaterials which consisting of CW-SR hybrid and S-LSP. Under the effect of external fields according to upper right corner of Fig. 1, three electric resonances from the CW, SR and electric S-LSP are excited directly by the electric field. One bright-dark mode A-EIT occurs between in electric resonance caused by CW and magnetic S-LSP resonance from the CW near field couple to the S-LSP. Moreover, an A-EIT cannot occur between in two same type dipoles in general, such as in two electric resonances or two magnetic resonances. From the Fig. 2(a,c), the magnetic field on left and right side of SR are opposite but it is different interval for the electric S-LSP's magnetic field, led to the amplitude of magnetic field of SR on left is larger than right's, which is reason for the A-EIT occurring between in two same type dipoles for this structure. The differences of electric S-LSP and SR, magnetic S-LSP and CW's resonance frequencies are △f 1 = 0.18 GHz and △f 2 = 0.065 GHz respectively which are far less than coherent frequencies of resonances themselves. The destructive interferences are between in bright-bright mode (SR and electric S-LSP) and bright-dark (CW and magnetic LSP) mode what having close frequencies will lead to two sharp A-EIT transmission peaks at frequencies of f L = 5.255 GHz and f R = 6.425 GHz, as shown in Fig. 3(a). So double-peaks mode A-EIT is successfully realized by introducing CW-SR hybrid and S-LSP bi-layered metamaterials structure and schematic of energy coupling path for each mode as shown in Fig. 4. Moreover, it can be clearly seen that an extra transmission peak at frequency of f M = 5.805 GHz among the two A-EIT peaks at f L and f R . To confirm whether this extra peak is an A-EIT transparency window, we have examined the phase curve without wrap of corresponding frequencies for the three transmission peaks, as shown in Fig. 3(b). At f M , the phase drastic change is too weak that unable to satisfy characteristic of A-EIT phenomenon. However, comparing to the other two peaks for f L and f R 's exist strength phase drastic change because both frequencies of CW and SR approach corresponding frequencies of magnetic S-LSP and electric S-LSP adequately. On the other hand, the resonance frequencies of CW and SR are not close. We should unfortunately deduce this resonance at f M producing among f L and f R not an A-EIT peak. The inference effectives in the EIT phenomenon can be similar to the interactions of mass-spring system. Based on this, we can equivalent the metamaterials structure to the oscillator equations for analyzing them in detail. Referring to oscillator-coupled system from the instructive works of predecessors 23,26,41 , the oscillator equations for coupling modes of proposed A-EIT what are based on the coupled Lorentz oscillator model being shown as follows:    In above equations, S i , q i , m i , γ i , к i (i is CW, SR, electric S-LSP or magnetic S-LSP) are the effective displacement, effective charge, effective mass, loss factor and coupling strength. χ eff is linearly polarization and T is transmission coefficient. They are only dictated by the shape, geometric parameters and materials of structure that independent of the external fields. The incident wave for frequency domain can be expressed by  www.nature.com/scientificreports www.nature.com/scientificreports/ including the electric field component. In Eq. (3), the magnetic S-LSP cannot be excited by external field that only be near field coupled by the CW, so the equation right only including the coupling component from the CW. Finally, the electric S-LSP and SR can also be excited directly by electric field and partial energy exchanges between electric-SLSP and SR, it is reason for the Eq. (4) right inducing the electric field and SR components. According to the theory of higher order differential equations, we have solved the expression of χ eff and T by Eqs. (5) and (6).
To further understand the behavior of double-peaks mode A-EIT, we have investigated the surface current distributions for the frequencies of three transmission peaks of A-EIT as shown in Fig. 5(a-c) respectively. At the three frequencies of transmission peaks, it can be found that most of the electromagnetic energy concentrating on S-LSP that indicates the S-LSP near field coupling from the CW and SR, then the CW and SR do not play a very important role. It indicates that the destructive interference existing between in electric and magnetic dipole that can be explained by the anti-bonding modes 40,42,43 , indicating the reason of the disappearing dipole moment excited from the SR. The orders to the amplitude for surface current density on each transmission peaks are f R > f SR > f M , which consistent with the orders of their Q-value and extent of phase changes. The distributions of surface currents for S-LSP, CW and SR also like electric dipoles and magnetic dipoles' moments, and the direction of magnetic dipoles from the S-LSP are opposite for the SR's. So that surface current distributions sufficiently prove the transmission curve is from the double-peaks mode A-EIT exciting.
We numerically calculate the effect of the transparency window for the different permittivity. It can be observed a clear red-shift of the transmission curve when increasing the permittivity of the substrate from 2.0 to 2.6 as shown in Fig. 6. Owing to the feature of A-EIT transmission spectra changes linearly with the dielectric,  www.nature.com/scientificreports www.nature.com/scientificreports/ this structure also can be regarded as a permittivity sensor at free space. We can foreseeable that the frequencies of transmission peaks depend on the dielectric properties that has potential application on permittivity sensor.
At last, we have manufactured the bi-layered metamaterials sample for the experiment. The front side is consist of 10 × 10 CW-SR hybrids, then the back is consist of 10×10 S-LSPs as shown in Fig. 7(a,b). The sample is measured by a pair of X-band horn antennas and vector network analyzer in anechoic chamber. From the Fig. 8, it can be clearly observed three transmission peaks from the experimental results which is good agreement with the simulation transmission curve, but slight drifts in Q-value of three transmission peaks and some frequencies deviation existing. We assume the reason for the errors is due to the uncertainty of dielectric and limited manufacture level of the sample. So experimental evidence of the existence for double-peak A-EIT in the microwave regime have been described.

conclusion
In conclusion, we had designed a A-EIT with double transparent peaks in the spectrum based on plane double-layered metasurface structure composing of S-LSP and CW-SR hybrid. The proposed structure simultaneously utilizes electric and magnetic dipole originating from the S-LSP which be used as the coupling modes to achieve double-peaks mode A-EIT. Furthermore, we analyzed the surface current distributions at the frequencies of three transmission peaks and their equivalent Lorentz model had been established. The experiment results matched well to the simulations. The double-peaks mode A-EIT provides a kind of ways to design the optical computing and communications in highly integrated optical circuits frequency selective, slow light and width band fitters in the microwave regime.