Reciprocity quad-band electromagnetically induced transparency-like metamaterials

In this paper, a sandwich structure metamaterial was designed, in which the substrate is radio frequency (RF) F4B, and the metal pattern of copper is prepared by the substrate on both sides. Analyzed the transmission of the structure, and the quad-band and reciprocal electromag-netically induced transparency (EIT)-like phenomena of the structure were obtained. The physical mechanism of the EIT-like phenomenon was explained by the electric field distribution. Discussing the size of the structure, the influence of structure parameters on EIT-like phenomena was further illustrated. By comparing the measured results with the calculated results in a microwave anechoic chamber, the results are in good agreement. This structure has potential applications in multi-band filtering, sensing, and other fields. © 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0220287


I. INTRODUCTION
Electromagnetically induced transparency (EIT) was first discovered in atomic systems. 1 Later, researchers also found the phenomenon in experiments and further proved the existence of a slow light effect on the EIT effect in atomic systems. 2,3The slow light effect has potential application prospects in quantum information processing, small-scale atomic clocks, and optical information storage. 4However, the implementation of EIT in atomic systems requires extremely strict environments, such as extremely low temperature, high-intensity laser, and adaptive atomic-level systems. 5herefore, its application in practical devices will have many limitations, which also greatly limits the research and development of EIT in many fields. 6][9] As a kind of artificial materials, the arrangement and distribution of metamaterial units are similar to the natural materials which are composed of molecules and atoms. 10Therefore, a unit structure is similar to a molecule, so the metamaterials can be used to realize some classical phenomena in atomic systems, such as the EIT effect. 11EIT in metamaterials can not only overcome harsh conditions required in atomic systems conditions, but also operate in a wider frequency range.][14][15] The EIT phenomenon in metamaterals is formed by the interaction between two or more different structures which can be coupled by the incident electromagnetic (EM) waves or not, and this interaction refers to the destructive interference between different resonant elements under the excitation of the EM waves. 16In 2008, Zhang et al. investigated the two metal nanords perpendicular to the electric field direction and one parallel to the electric field to obtain the EIT phenomenon in metamaterials on the terahertz range. 82][23][24][25][26] The method of generating the multiband EIT effect can be extended from the multi-band absorber, that is, adding multiple resonant cells. 27,28ang et al. reported a simple design that adopts the classical two-layer structure of a terahertz metamaterial that can produce the triple-band EIT effect by using two "big-bright" mode coupling of two sub-resonators.The proposed triple-band EIT metamaterial having excellent properties, including thin size, good flexibility, simple and compact structure, and high sensing sensitivity, could provide guidance for the subsequent design and implementation of multifunctional multi-band EIT metamaterials. 29Chen et al. investigated the EIT effect with high-transmission and a large group delay triple-band was obtained in a metal-perovskite hybrid metasurface, which consists of a cross metal (CM), a pair of square metal frames (SMFs), and a pair of square split rings (SSRs).The multipole scattering theory shows that the first and third transparent windows are created by the coupling between the electric dipole and the toroidal dipole, and the second transparent window is created by the electric dipoles. 30Zhang et al. discussed the conversion of metamaterials with dual-band EIT into dual-band electromagnetically induced absorption (EIA), controlled by the characteristics of VO 2 .The rationality of the model is proved by a circuit model and four-level theory.The results can be widely used in multi-function devices. 17Ye et al. studied a structure based on the microstrip line (MSL) structure and calcium magnesium titanium (CMT) to realize the EIT phenomenon.The EIT phenomenon is analyzed by an equivalent circuit model.The wide band and dual-band EIT phenomena are verified by experiments. 31Multiband EIT-like metamaterials have potential applications in switchable devices, reconfigurable devices, and sensing, as well as in sensing applications and multi-band devices.Nourinovin et al. fabricated a terahertz EIT-like metasurface based on asymmetric resonators on an ultra-thin flexible dielectric substrate and experimentally verified the detection of skin cancer cells in the terahertz band. 32eng et al. studied a monolayer-patterned graphene structure to obtain a tunable double band plasmon-induced transparency (PIT).The proposed structure is composed of a middle graphene-strip and two π-shape graphene microstructures.The results show that the double band PIT effect originates from the destructive interference between two bright modes and one dark mode, and an equivalent CMT model is utilized to confirm the finite-difference-time-domain (FDTD). 33Mallick et al. proposed a multi-element metastructure unit cell consisting of a split ring and dipole resonators aiming to explore the intricate effects of the polarization dependency of these hybridized modes. 34Liu et al. proposed an analogy of polarization-independent multi-band and tunable EIT effect based on a 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. 35mong the numerous studies on multi-band EIT, few researchers have paid attention to the reciprocity which means that the incident EM wave propagates from the +z or −z axis, with the same result. 36EIT -like phenomena in metamaterial structures with reciprocal properties are not restricted in the direction of transmission and, thus, are more flexible in applications.
In this paper, a tri-layer metamaterial structure with a multiband EIT-like phenomenon is designed.The transmission of the structure is analyzed by the finite-integration time-domain (FITD) method.By analyzing the electric field distribution of the structure, the physical mechanism of the EIT-like effect is further studied.
The experimental results of the microwave anechoic chamber are in good agreement with the theoretical results.The results show that the proposed structure has potential applications in slow light devices, sensors, and filters.

II. DESIGN AND SIMULATION
In this paper, a three-layer structure was designed, in which the substrate is F4B, as shown in Fig. 1, and the 10 × 10 element arrays were fabricated, as shown in Fig. 1(a).The dielectric constant of substrate F4B is 3, the loss tangent is 0.001, the thickness is h 1 , and the surface material is copper.The conductivity of metal copper is 5.8 × 10 7 S/m and its thickness is h 2 .Figure 1(a) shows the front view of the structure, which is an H-shaped structure, and its unit cell is shown in Fig. 1(c).The back side of the structure is shown in Fig. 1(b) as a double E-shaped structure, and its unit cell is shown in Fig. 1(d).The size parameters are shown in Table I.The structure is located in the xy-plane, and the EM wave incident direction is the z axis, as shown in Fig. 1(e), which is a 3D-view structure.The FITD method was used, the boundary conditions of the x and y axes were periodic boundaries, and the boundary conditions of the z axis were open space.The incident angle of the EM wave defined as θ = 0°, the incident EM wave travels along the z axis, and the response of the transverse (TE) wave to the incident EM wave is studied.
Figure 2 shows the TE wave response of the transmission spectrum of the structure in the range of 1-16 GHz.It can be seen that the electromagnetic wave is transmitted from the +z and the −z directions, and the transmission is almost the same from the +z and −z axes, indicating that the structure has reciprocity.In addition, it can be seen that the structure can generate quad-band EIT-like phenomena.

III. ANALYSIS AND DISCUSSION
To investigate the quad-band EIT-like phenomenon generated by the structure, Fig. 3 shows the electric field distribution at the transmission peak and the transmission valley frequencies; the left is the electric field distribution in the front view and the right is the back view.It can be seen from Fig. 3(a) that the energy at the low frequency resonant of 5.029 GHz is mainly concentrated on the double E shaped structure, indicating that the resonance at the frequency is to the double E shaped structure.It is demonstrated that in Fig. 3(b), on the 6.44 GHz, the electric field on the double E shaped structure weakened, and the electric field on the H shape on the other side is slightly enhanced, but not obvious.However, the electric field on the H-shape is enhanced on 9.211 GHz in Fig. 3(c), the electric field is concentrated on the horizontal bar of the E-shape structure, and an alternating change is observed.Compared with Fig. 3(a), the resonant frequency on 9.211 GHz is the high-order harmonic on 5.029 GHz.In this EIT window, the energy is coupled from the double E-shaped structure to the H-shaped structure.Therefore, it can be considered that the double E-shaped structure acts as the bright mode and the coupling acts as the H-shaped structure of the dark mode.As can be seen in Figs.3(c)-3(e), the energy is coupled from the double E-shaped structure to the H-shaped structure, where the higher harmonics of the double E-shaped structure acts as the bright mode and the coupling acts as the dark mode of the H-shaped structure.It can be seen from Figs. 3(e)-3(g) that the energy is coupled back from the H-shaped structure to the double E-shaped structure.Compared with Fig. 3(e), the direction of the electric field on the H-shaped structure in Fig. 3(g) has changed.It can be seen from Figs. 3(g)-3(i) that the electric field at 12.169 and 13.818 GHz is weak, while the electric field is the strongest at 13.036 GHz.
To further investigate that the structure produces EIT-like effects, Fig. 4 shows the response characteristics of a part of the structure to the incident electromagnetic waves.It demonstrates only one vertical bar, the response of the structure to the electromagnetic wave is strong on the TE mode, and the vertical bar is equivalent to an electric dipole coupling the incident electromagnetic wave in Fig. 4(a).Figure 4(b) represents that there are only horizontal bars and the response of the structure to electromagnetic waves is weak on the TE mode.When the double E-shaped structure couples the electromagnetic wave, the low frequency resonance and the high frequency harmonics are generated in Fig. 4(c).In the case of two vertical bars under the action of electromagnetic waves, the structure generates two resonant frequencies for electromagnetic waves as shown in Fig. 4(d).When the H-shaped structure is used, the dual-band EIT is generated as in Fig. 4(e).When the complete structure is under the action of electromagnetic waves, the EIT-like effect of the multi-band can be generated.The H-shaped structure as a bright mode coupled a double E-shaped structure as the dark mode.Because of the existence of multiple bright-modes and high-order harmonics, the EIT-like phenomenon of the multi-band can be obtained.
To further study the influence of the geometric size of the structure on the multibandeit-like phenomenon, Fig. 5 shows the change of the transmission spectrum caused by the decrease in l 1 .It is described that the reduction of l 1 has almost no effect on the resonant frequency in Fig. 5, which is because the horizontal bar acts as a dark mode; so changing the length of the horizontal bar has almost no effect on the transmission spectrum.
Figure 6 shows the impact of changing l 5 on transmission.The horizontal bars on the double E-shaped structure generate the high-order harmonics in Fig. 4(c).Therefore, the increase of l 5 has a great influence on the middle frequency band, but has little influence on the low-frequency and high-frequency bands as shown in Fig. 6.
Figure 7 shows the influence of the change of the two vertical bars of the H-type structure on the transmission spectrum.It is represented that the change of l 3 has little influence on the high frequency and the low frequency bands as shown in Fig. 7(a), and has a great influence only in the middle frequency band, which is because the resonant frequency generated by the H-type structure is important in the middle frequency band whose result is consistent with Fig. 4(d), so it has a great influence on the middle frequency band.Comparing Fig. 7(a) with 7(b), in addition to the large change in the middle frequency band, the high frequency band also has a large change: it is because l 2 is the length of the short horizontal bar and its change in value has a greater impact on the high frequency band.Therefore, the high frequency band also changes with it.
To discuss the sensing of the structure, Fig. 8 shows the variation of the transmission spectrum of the structure when changing the environmental permittivity ε b .It can be clearly observed that when ε b varies between 1 and 2, the transmission spectrum undergoes a significant blue shift, indicating that the structure is sensitive to ε b of the environment and, therefore, can be used as a refractive index sensor.Moreover, due to the reciprocity of the structure, it has a wider range of application scenarios.
Figure 9(a) shows the test site in a microwave anechoic chamber.Figure 9(b) shows the schematic diagram of the test link, where the frequency band of the horn antenna is 1-18 GHz, and the vector network analyzer is E5063A.Figure 9(c) shows the sample of the 10 × 10 unit cells to be tested.Figure 10 shows the comparison of the test results with the simulation results.In the +z and −z directions, for the transmission spectrum of the TE mode, the resonant frequencies of the test results are basically consistent with the simulation results, but the amplitude is smaller than the simulation results.The possible reason is that the receiver antenna does not add an amplification module, resulting in a small gain of the receiver antenna.

IV. CONCLUSION
In this paper, a sandwich metamaterial structure of RF dielectric F4B material is designed, which is composed of a substrate and metal copper, where the front side is the H-shaped structure and the reverse side is the double E-shaped structure.The multi-band EIT-like effect is obtained by analyzing the transmission of the structure, and the mechanism of the multi-band EIT-like effect is analyzed by the electric field distribution.It is concluded that the principle of generating the multi-band EIT-like effect in the structure is realized by the bright mode coupling of the dark mode and the high order harmonic coupling of the bright mode.By discussing the structure parameters and analyzing the influence of the structure on the transmission window, it is found that the size variation of the metal copper structure has a great influence on the transparent window.Moreover, the results show that the structure has reciprocity.By comparing the experimental results with the simulation results, it is found that the experimental results of the structure are in good agreement with the simulation results.The results show that the structure has potential applications in the fields of filter devices, refractive index sensing, and so on.

FIG. 1 .
FIG. 1.The schematic illustration of the proposed EIT-like structure.(a) Front view (10 × 10 unit cell), (b) back view (10 × 10 unit cell), (c) unit cell of the front view, (d) unit cell of the back view, and (e) 3D-view of the structure.

FIG. 7 .
FIG. 7. The effect of varying (a) l 3 and (b) l 2 on the transmission spectrum.

FIG. 9 .
FIG. 9. Schematic diagram of the test site and test link.