Conversion and Active Control between Electromagnetic Induced Transparency and Absorber in Terahertz Metasurface

Abstract

In this study, we use a phase-changing material vanadium dioxide (VO₂) to design a multilayer metasurface structure to achieve the transition from an electromagnetically induced transparency(EIT) device to an absorber. The structure consists of a gold layer, a polyimide spacer layer, a VO₂ layer, and a sapphire substrate. The top layer consists of one cut wire and two split-ring resonators with the same parameters. When the VO₂ layer is in its insulating phase at room temperature, the peak of the EIT device will appear near 1.138 THz. When the VO₂ layer is in the metallic state, two absorption peaks above 99.5% appear separately at 1.19 and 1.378 THz, respectively. To the best of our knowledge, this is the first time that a coupled mode equation is used to perform theoretical calculations for EIT devices and perfect absorbers simultaneously, and this is also the first time that coupled mode equations are used for the theoretical calculations of two absorption peaks in an absorber. The proposed metasurface combines the advantages of terahertz absorption, EIT and active device control, which will provide more ideas for the design of future terahertz devices and is also significant for the design and development of radomes for future stealth aircraft.

1. Introduction

The terahertz band lies between the infrared and microwave frequency systems, characterized by macroscopic electronics and microscopic photonics. Furthermore, the terahertz frequency range is 0.1–10 THz [1,2]. Terahertz waves are extensively used in security detection, biosensing, and wireless communication because of their good penetration and lower energy (compared with infrared light) [3,4,5,6]. The use of metamaterials and metasurfaces can be very good for the modulation of terahertz waves. With the artificial design, the metasurface can be constructed with arbitrary electrical and magnetic permeability to modulate the terahertz beam’s phase, amplitude, and polarization [7,8,9]. The electromagnetic metasurface is an artificially designed subwavelength array structure. It can be considered as the two-dimensional metamaterial [10,11,12]. The applications of metamaterials involve microwave devices, terahertz devices, electromagnetic stealth, sensors, antennas, and other research fields. The mass of metamaterial devices with different properties have been studied, including perfect absorbers [13,14,15,16,17,18,19,20], bound states in the continuum (BIC) [21,22,23,24], and electromagnetically induced transparency (EIT) [25,26,27].

In the application of metamaterials, stealth technology can be divided into two categories: transmissive wave stealth, and absorptive wave stealth. The essence of absorptive wave stealth technology is to design special metamaterial structures, use impedance matching between the metamaterial absorbing layer and the free space, significantly reduce the intensity of reflected waves, and exhibit strong absorption for electromagnetic waves, to realize the stealth effect. The conventional radome generally consists of a conventional frequency-selective surface, which is poorly conformal to the radome, so we choose to use a metasurface to make a frequency-selective surface, which not only can not change the radome shape but also can make the electromagnetic waves of specific frequencies pass through. The electromagnetic waves of other frequencies are absorbed and shielded. A perfect metamaterial absorber (PMA) based on electromagnetic metamaterials is fabricated according to the above principles [28,29,30,31]. When an electromagnetic wave is an incident on a PMA, the reflected and transmitted waves on the metasurface are both zero, indicating that the electromagnetic wave has been completely absorbed. The real part of the equivalent impedance of the metasurface is 1 and the imaginary part is 0, so it is consistent with the equivalent impedance of the environment.

The study on terahertz metamaterials shows that the electromagnetic response of metamaterials can be used to simulate the EIT in classical quantum physics. Electromagnetic-induced transparency (EIT) is a quantum coherent effect which occurs in a three-level atomic system. EIT media exhibit three energy level states, namely a ground state |1>, an excited state |3>, and a metastable state |2>. The particles absorb energy and jump directly from |1> to |3> when the EIT materials are illuminated by a probe laser, leading to a broad absorption valley in the transmission spectra. Furthermore, when a coupling laser is introduced to the above experimental system, the particles absorb energy and a jump from |1> to |3> can be realized by the following two routes: |1>→|3> or |1>→|3>→|2>→|3>. Interference between the two jump routes (|1>→|3> or |1>→|3>→|2>→|3>) leads to a cancellation effect on state |3>, accompanied by an enhanced transparency window within the broad absorption valley [32]. At present, metamaterial EIT is extensively used in band-pass filters, optical switches, slow optical devices, and sensors.

Furthermore, active control of EIT has a wider application prospect than passive modulation, and has become a research hotspot. Recently, only a few researchers have studied the transition from EIT devices to absorbers [33,34,35,36]. This is important for the design, research and integration of future terahertz communication devices. The first paper [34] investigates the effect of parameter variation on EIT, and the study of the generation and nature of the absorption peak after turning into an absorber by means of active control utilizes impedance matching theory. The other papers [35,36] analyzed the mechanism of EIT generation using TCMT and CMT, respectively, and also theoretically analyzed the generation of the absorption peak using impedance matching. The paper [37] uses equivalent refractive index theory to theoretically analyze the EIT and high absorption peaks. Furthermore, the paper [38] uses the LC equivalent circuit model for the EIT phenomenon is explained and the spectral lines of EIT are calculated. However, they just used different theories to explain the different phenomena. The impedance matching theory cannot explain which absorption peaks are from structural interactions and the effect of changes in structural parameters on the absorption peaks. The LC equivalent circuit model is not applicable to the analysis of metasurfaces in the case of oblique incidence, and it is not possible to reverse the design of metasurface structures by equivalent circuits. The coupled mode equation can not only calculate the spectral lines well, but the parameters in the equation are also almost all basic physical quantities (which can be obtained by simulating the separate structure). Furthermore, the changes in the structural parameters can correspond to the changes in the physical quantities, which is important for the generation of EIT and PMA, the effects of parameter changes, and the inverse design of the structure. Therefore it is important to derive a unified theory using the coupled mode equations, which is instructive for the design of EIT and PMA.

In this paper, we use a phase-changing material vanadium dioxide (VO₂) to design a multilayer metasurface structure to achieve this ingenious conversion. At room temperature, due to the coupling effect between the bright and dark modes (cut wire (CW) is the bright mode and a pair of split-ring resonators (SRRs) is the dark mode in this paper), a transparent window is created in the transmission spectrum, generating the EIT phenomenon. The peak of EIT will appear near 1.138 THz. With a gradual increase in temperature, the conductivity of VO₂ changes from 10 S/m to a high-temperature metal state (conductivity is 2 × 10⁵ S/m) [39,40,41], leading to the formation of a reflective layer-like structure in the middle layer of the multilayer structure, where the wave transmission is weakened and reflection suddenly and sharply increases, thereby realizing the transition from a transmission device to a reflector, and achieving two perfect absorption peaks at 1.19 and 1.378 THz, respectively. This abrupt change from the transmission to absorption peaks in a frequency band could enable active modulation of the terahertz spectrum, which would be of great importance for modulators, switches, sensors, etc.

We use coupled mode equations to explain the EIT phenomenon and PMAs, and verify the simulation results through theoretical calculations. The theoretical analysis results are consistent with the simulation results. As far as we know, few academic researchers have studied the conversion between the EIT and PMA before [34,35,36]. Although the original studies on EIT mostly employed coupled mode equations, this is the first time that the coupled mode equations are used for the theoretical calculations of two absorption peaks in a PMA [42,43,44]. Lastly, we also analyze the effects of PMA structure parameters on absorbance amplitude.

2. Structure Design and Method

We employ the CST Microwave Studio to perform numerical simulations and study the transmission and absorption properties of structures. Figure 1 shows a unit cell of the structure we designed. The structure consists of a 200-nm-thick gold CW and a pair of 200-nm-thick gold SRRs. The terahertz beam is normally incident on the metamaterial array, with polarization parallel to the CW, as shown in Figure 1a. The dielectric constant of VO₂ with a thickness of 1.2 µm and that of the sapphire is set to 9 [32] and 9.67, respectively. For the polyimide material, we set the relative dielectric constant as ε = 3.1 and loss as tan δ = 0.07 [45].

3. Coupling Mode Theory for Metasurface

As shown in Figure 2, by separately simulating the spectral lines of the metal CW and the double SRRs, we can judge that CW is the bright mode and the two SRRs are the dark mode. Therefore, the coupled mode equation can be written as follows (in the coupling mode equation, we do not consider the coupling between the two SRRs in the adjacent unit cell, because the distance between the two SSRs is large, and the coupling between CW and SRR is significantly larger than that between the two SRRs, so the coupling between the SRRS could be neglected):

$$\left[\begin{array}{cc}w-w_1-i({\gamma }_1+{\gamma }_a)& g\\ g& w-w_2-i{\gamma }_2\end{array}\right]\left[\begin{array}{c}a\\ b\end{array}\right]=\left[\begin{array}{c}\sqrt{{\gamma }_1}E\\ 0\end{array}\right],$$

(1)

$$\left[\begin{array}{c}{S}_r\\ S_t\end{array}\right]=\left[\begin{array}{cc}r& t\\ t& r\end{array}\right]\left[\begin{array}{c}E\\ 0\end{array}\right]-\left[\begin{array}{cc}\sqrt{{\gamma }_1}& 0\\ \sqrt{{\gamma }_1}& 0\end{array}\right]\left[\begin{array}{c}a\\ b\end{array}\right],$$

(2)

The parameters ${\omega }_1$, ${\omega }_2$, ${\gamma }_1$, and ${\gamma }_2$ represent the amplitudes and the damping rates of the bright and dark modes, respectively. The parameter ${\gamma }_a$ denotes the absorptive losses of the bright mode, and g represents the coupling coefficient between the two modes. $\left[\begin{array}{cc}r& t\\ t& r\end{array}\right]$ is the scatter matrix, $S_r$ and $S_t$ denote reflected and transmission terahertz waves, respectively. Here a represents the amplitude of the bright mode, and b represents the amplitude of the dark mode.

$$T=\mid \frac{S_t}{E}{\mid }^2;R=\mid \frac{S_r}{E}{\mid }^2$$

(3)

T and R denote transmission and reflection spectra, which are related to the amplitudes of the incident wave (E), reflected wave ($S_r$), and transmitted wave ($S_t$).

For the transmissive structure, we approximate the substrate as a fully transparent structure. Thus, we let $r=0$ and $t=1$ in the scattering matrix and obtain

$$S_r=-\sqrt{{\gamma }_1}a;S_t=E-\sqrt{{\gamma }_1}a$$

(4)

The transmission spectrum becomes

$$T=\mid \frac{(w-w_1-i{\gamma }_a)(w-w_2-i{\gamma }_2)-g^2}{(w-w_1-i({\gamma }_a+{\gamma }_1))(w-w_2-i{\gamma }_2)-g^2}{\mid }^2$$

(5)

The absorption spectrum is calculated as $A\left(w\right)=1-R\left(w\right)-T\left(w\right)$, where $R\left(w\right)=|S_{11}{|}^2$ is the reflectance, and $T\left(w\right)=|S_{21}{|}^2$ is the transmission. $S_{11}$ and $S_{21}$ are the reflection parameters and transmission parameters obtained from the simulation, respectively. For metal–media–metal structures, terahertz waves do not pass through the metal-like surface, so the transmission coefficient T of the absorber is set to 0. For the scattering equation, we let $\left[\begin{array}{cc}r& t\\ t& r\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, the absorption spectrum formula is simplified to $A=1-R$. At this point, the absorbance spectrum formula of the absorber is

$$S_r=E-\sqrt{{\gamma }_1}a;S_t=-\sqrt{{\gamma }_1}a$$

(6)

$$A=1-R=1-\mid \frac{(w-w_1-i{\gamma }_a)(w-w_2-i{\gamma }_2)-g^2}{(w-w_1-i({\gamma }_a+{\gamma }_1))(w-w_2-i{\gamma }_2)-g^2}{\mid }^2$$

(7)

In the process of fitting the curves, the resonant frequency w and the magnitude of the loss $\gamma$ can be obtained by simulating the bright and dark mode structures separately. The coupling coefficient g and the loss ${\gamma }_a$ of the absorption are obtained by fitting them to the spectral lines. For the coupling of two bright modes, we simply change the number 0 in the right-hand term of Equation (1) to $\sqrt{{\gamma }_2}E$. For the uncoupled structures, it is only necessary to let the coupling coefficient be zero. Therefore, the theory applies to other structures.

4. Numerical Calculations for EIT and PMA

4.1. Electromagnetically Induced Transparency (EIT) without Phase Changing

At low temperatures, the conductivity of the VO₂ is so poor that the incident terahertz light can pass through the VO₂ layer, producing the EIT phenomenon. The gold CW will resonate at 1.1 THz and is considered the bright mode, whereas the SRRs will not resonate in the 0.1–2.1 THz interval and are considered the dark mode. When THz light is incident on the surface of the structure, the CW will be excited and the SRRs will not respond. However, due to the coupling effect between CW and SRRs, energy exchange occurs (part of the energy of the CW is transferred to the SRRs), which produces a transparent window in the spectral line and generates the EIT phenomenon.

For this EIT phenomenon, we approximate the substrate as a fully transparent structure. We use Equation (5) to fit the spectral lines obtained from the simulation, and we can obtain the fitted EIT spectral lines. The theoretical calculation and simulation results of the spectral lines are in good agreement, as shown in Figure 2b.

To further discuss the coupling effect of the EIT structure, we change the size of the coupling strength between the structures by changing the distance between the CW and SSRs. For the EIT structure, when the distance d between the SRRs and CW changes, the size of d is inversely proportional to the peak value of the transparent window. As the value of d increases, the peak value decreases, and the transmission rate lowers. As varying the size of d changes the value of the coupling strength, the larger the d, the greater the decrease in the coupling strength, as shown in Figure 3. Therefore, the energy transfer between the bright and dark modes starts to decrease, and the transparent window becomes smaller, demonstrating the phenomenon in Figure 3a.

4.2. Perfect Metamaterial Absorber (PMA) with Phase Changing

When the temperature increases, VO₂ changes into a metal-like state, and the structure model changes into a metal -media -metal-like structure, which transforms into an absorber. The simulation spectrum is depicted in Figure 4. The structure will produce two absorption peaks above 99.5% at 1.19 and 1.378 THz. To simplify the theoretical analysis, we consider that the transmission coefficient is approximated as 0 and use the coupling mode Equation (7) to calculate the absorbance of the structure. The fitting results almost agree with the simulation results, as shown in Figure 4c.

For the coupling effect in absorbers, the conductivity of VO₂ is 2 × 10⁵ S/m at this time, the absorption efficiency of the two absorption peaks reaches the maximum. At 1.19 and 1.378 THz, the absorbers can reach 99.7% and 99.8% absorption rates, respectively. As d increases, the absorption efficiency of the two absorption peaks begins to decline and red-shift. Although the absorption efficiency of both peaks decreases as d increases, the absorption efficiency of the first absorption peak decreases the fastest in Figure 5 due to the coupling between the CW and SRRs. Thus, we can further infer that when the coupling is very weak or there is no coupling, the peak will disappear. We fit the spectral lines for different values of d and obtain the variation trend of the coupling strength, as shown in Figure 5.

If other phase change materials replace the VO₂ in this paper, the effect on the structure also changes from a transmissive to a reflective structure, affecting only its transmission matrix, and the theory still applies If the phase change material is added to the structure, it will cause the change in the resonant frequency and loss of the structure in the equation, which still applies to the theory. Therefore, the theory is equally applicable to other phase change materials.

There is a remarkable paper [46] on discussing the coupling effect of absorbers. It also analyses the PMA using the coupled mode equation. However, the ideas of this paper is quite different from our paper. This paper uses two layers of graphene bands coupled to each other to produce a perfect absorber and performs a theoretical analysis using the coupled mode equation. The case discussed in the paper is the coupling effect between the layers and only the perfect absorber is analyzed. In our paper, we consider the intra-layer coupling effect and make the EIT and PMA with a unified set of theories by coupled mode theory.

5. Discussion

The structural parameters in EIT have been discussed in great detail in our previous papers [32]. Compared with the effect of structural parameters on the absorber, the variation in the EIT transmission spectrum is relatively small. Thus, in this section, we only discuss the variation in the absorption spectrum of the absorber, i.e., the case of VO₂ conductivity of 2 × 10⁵ S/m.

Using the above structural parameters of absorber, when VO₂ is in a metal-like state, we can obtain the spectral lines of the double absorption peaks, which reach 99.7 % and 99.8% at 1.19 and 1.378 THz, respectively, as shown in Figure 4. We further study the influence of the absorption spectrum by changing the geometry of the absorber. First, we adjust the thickness of the PI layer, and the first absorption peak increased significantly with an increase in thickness, whereas the absorption peaks moved in the low-frequency direction. Because the upper metal and the lower metal-like layer generate localized surface plasmon (LSP), that is, a magnetic dipole on the YOZ plane, the LSP shifts to lower frequencies as the thickness increases [41]. The change in PI thickness mainly affects the change of resonant frequencies of bright and dark modes, as shown in Figure 6. As the PI thickness increases, the frequency of the bright mode (ω₁) and the frequency of the dark mode (ω₂) will shift to lower frequencies. This will directly affect the frequencies generated by the absorption peaks.

Then we discuss the effect of oblique incidence of terahertz waves on absorption efficiency. As the incidence angle increases, the absorption peak obtained gradually moves to high frequencies. When the oblique incidence angle is 43 degrees, the absorption efficiency of the first absorption peak drops to less than 90%, as shown in Figure 7a. So, the absorption efficiency can reach more than 90% within the incidence angle of 42 degrees.

Next, we discuss the periodic parameters of the structure, as shown in Figure 7b,c. By adjusting the size of P_y, we found that the absorption peak would barely change, but the dip around 1.3 THz would gradually become smaller. When P_y is 140 μm, more than 90% absorption could be achieved with 0.26 THz bandwidth. By varying the P_x parameter, the absorption peak at 1.2 THz almost does not change (the coupling strength does not change). With an increase in P_x, the equivalent refractive index of the whole structure also increases gradually, shifting the right resonant peak to the left. When P_x is 150 μm, more than 90% absorption could be achieved with 0.286 THz bandwidth. This is a very valuable and interesting phenomenon, and we can adjust the structural parameters, to produce a specific frequency of resonance absorption, we can also adjust the bandwidth of the absorption spectrum. Furthermore, We can optimize the parameters to achieve a better absorption effect. We can also scale the metasurface structure up or down to extend it to other frequency bands.

For the conversion between EIT and absorber at the same frequency, We can change the thickness of the PI layer. When the PI thickness is 5 µm or 115 µm, the frequency of the absorber peak and the EIT frequency are almost the same. When the PI thickness is 5 µm, the absorption peak frequency is 1.03 THz, and the absorption efficiency is 27%; at this time, the EIT frequency is 1.02 THz. When the PI thickness is 115 µm, the EIT frequency is 1.14 THz, the absorption peak frequency is 1.15 THz, and the absorption efficiency is 98%, which is not a perfect absorption peak. When the PI thickness is 115 µm, the modulation depth of absorbing waves at 0.9152 THz can reach 64%. Due to the limitations of the processing technology, errors in structural parameters and the uneven thickness of PI can have an impact on the spectral lines measured in future experiments.

6. Conclusions

In this study, we realize the conversion from the EIT phenomenon to an absorber by actively regulating the temperature of VO₂ in the terahertz band. When the temperature is room temperature, the structure designed in this paper produces the EIT phenomenon; when the temperature is increased by active modulation, the structure converts to a perfect absorber. Furthermore, for the first time, we realize the calculation of the fitting of two absorption peaks using coupled mode equations and verified the consistency of the EIT structure to the absorber structure through theoretical calculations. In future studies, discussing the effects of different structural parameters on the absorption efficiency of an absorber, we can change the structural parameters of the metasurface to adjust the broadband, the number of absorption peaks, and the absorption efficiency, which is important for the design of absorbers with different characteristics and different needs. This will be of great significance to the design and development of radomes in future stealth aircraft.