Jiu-Sheng Li(李九生) and Zhe-Wen Li(黎哲文)

Centre for THz Research,China Jiliang University,Hangzhou 310018,China

Keywords: metasurface,switchable terahertz absorber,electromagnetically induced transparency

1. Introduction

Vanadium dioxide (VO2) and graphene have attracted much attention due to their excellent external control properties. VO2can switch to different phase transition states as the temperature changes.[1,2]Moreover, the phase transition process can be accomplished by thermal,[3,4]electrical[5,6]or optical control.[7]When working at room temperature,the lattice structure of VO2is monoclinic(the insulating state).When the temperature reaches 68°C,the lattice of VO2is distorted into a tetragonal structure(the metallic state).This state is reversible,and the electromagnetic properties of VO2will change significantly during this process.[8]In the terahertz region, VO2is usually embedded in a metasurface to achieve dynamic regulation. In 2019, Liuet al.[9]proposed an adjustable absorber based on VO2. With a change in the phase transition state,the absorber is converted from low absorption to broadband high absorption. When the temperature exceeds 70°C,the absorption bandwidth reaches 2 THz. In 2020, Donget al.[10]proposed a chiral metasurface composed of hybrid gold-VO2structures, and realized the switching on or off of asymmetric transmission by adjusting the phase of VO2from the insulating state to the metallic state and vice versa. Based on the transition of VO2,Denget al.[11]investigated a switchable metamaterial. Their device behaves as a cross converter when the VO2is metallic, while it behaves as an analog with electromagnetically induced transparency when VO2is switched to the insulating state.

Graphene is composed of carbon atoms in a planar hexagonal lattice. As a two-dimensional monolayer material,[12]a graphene surface can excite surface plasmons from the midinfrared to terahertz bands. Compared with traditional metals, graphene has fewer free charges, and its free charge concentration can be changed by chemical doping or a bias voltage. Hence, the conductivity of graphene can be manipulated by changing the chemical potential. In 2019, Xianget al.[13]investigated a tunable dual-band perfect absorber based on graphene. With an increase in the Fermi energy, the amplitude and frequency band of the absorption peak could be controlled. In 2020,Sunet al.[14]proposed a novel multifunctional device based on a hybrid metal-graphene metamaterial with electromagnetically induced transparency in the terahertz band. An ultra-broadband transmission window with a bandwidth of 1.23 THz can be obtained and the spectral extinction ratio can be tuned from 26% to 98% by changing the Fermi level of graphene. Moreover,metasurfaces based on VO2and graphene are increasingly being reported in the literature. In 2020, Zhuet al.[15]presented a switchable and tunable terahertz absorber based on the Fermi energy level of graphene and the phase transition properties of VO2.When VO2is in the insulating state,broadband absorption properties are achieved.When VO2is in the metallic state,the device acts as a tunable multi-band absorber. In 2021, Liuet al.[16]proposed a bifunctional metamaterial which can realize a dynamic switch between beam steering and broadband absorption as the phase state of the VO2changes. By changing the Fermi energy level of graphene,the incident wave is scattered in different patterns and the absorptance can also be gradually changed.

In this paper,we design a dual-function terahertz metasurface by utilizing the dynamic properties of graphene and VO2.When the bottom VO2is in the metallic state,the metasurface can be switched between a single-band and dual-band absorber under different states of the top VO2patches (i.e., when the top VO2is in the metallic state,the designed metasurface behaves as a single-band absorber with an absorptance of 99.7%at 0.736 THz and when the top VO2is in the insulating state,the proposed metasurface acts as a dual-band absorber with an absorptance of 98.9%at 0.894 THz and 99.9%at 1.408 THz).When the bottom VO2is in the insulating state, the metasurface achieves electromagnetically induced transparency(EIT),and dynamic control of the transparency window and group delay can be manifested by changing the chemical potential of graphene. The designed metasurface shows the advantages of function switching and dynamic control.

2. Structure design

Figure 1 shows a three-dimensional (3D) structure diagram of the multifunctional terahertz metasurface, which consists of a gold pattern layer, a SiO2layer, a VO2layer,graphene and a SiO2bottom spacer substrate. The gold pattern is composed of four split rings and a cross. The gap is embedded with eight VO2patches. The optimized structure parameters are as follows:P=120μm,l=20μm,a=32μm,s=8μm,w=8μm,g1=8μm,andg2=21.2μm(the symbols are defined in Fig.1). The thicknesses of the gold layer,SiO2spacer substrate, VO2film layer, graphene film layer and SiO2bottom spacer substrate are 0.5μm, 7.5μm, 1μm,0.01μm,and 3μm,respectively. Numerical simulations were performed using the finite difference frequency domain solver of CST Microwave Studio, for which the unit cell boundary conditions were set along thex-andy-directions,and the open boundary conditions were applied in thez-direction.

3. Results analysis

3.1. Switching between single-and dual-band absorption

The absorptance of the proposed metasurface is written as follows:

whereRandTrepresent reflectance and transmittance, respectively,whileS11andS21represent reflection and transmission parameters,respectively. Figure 2(a)shows the different states of the absorption curve of the top VO2patch through phase transition while the bottom VO2film is in the metallic state. When the top VO2patches are in the insulating state,the metasurface behaves as a dual-band absorber, and the absorptances at 0.894 THz and 1.408 THz are 98.9%and 99.9%,respectively. When the temperature rises to 68°C, the bottom VO2film becomes metallic, and the designed structure is converted to a single-band absorber with an absorptance of 99.7% at 0.736 THz. The impedance matching theory[20]is introduced to analyze the structure,as follows:

whereZ1represents the equivalent surface impedance of the proposed device andZ0is the free space impedance. When the effective impedance matches the free space impedance,the relative impedanceZis close to 1, which realizes perfect absorption. The real and imaginary parts of the relative impedance of the designed metasurface are shown in Figs. 2(b) and 2(c). At 0.894 THz, the real and imaginary parts of the impedance are of 0.845 and 0.111,respectively.At 1.408 THz,the real and imaginary parts of the impedance are 1.035 and 0.034, respectively. Moreover, the real and imaginary parts of the impedance are 1.099 and-0.028, respectively,at 0.736 THz. This indicates that the designed structure has low reflectivity and high absorptance at the three frequencies. From Fig. 2(a), one can see that the perfect absorption is close to 100%. In addition, due to its symmetrical structure,the designed structure is polarization insensitive and can achieve the same absorption effect regardless of the incident waves being TE or TM.

In order to introduce the absorption mechanism at different frequencies, figure 3 illustrates the electric field distribution at the top and bottom of the switchable absorber at different resonant frequencies. One can see from Figs.3(a)and 3(b)that pairs of induced charges gather at the top and bottom layers of the metasurface pattern,which indicates a dipole excited on the metal and VO2layer. At the same time,the direction of flow of charge in the VO2layer is opposite to that in the top metal layer. Therefore, the strong coupling between the two layers leads to magnetic resonance,and the electric and magnetic dipole resonances give rise to a perfect absorption peak at 0.736 THz. Similarly,figures 3(c)and 3(d)display that the top charges are mainly concentrated at the crossing ends,and the direction of charge flow is opposite to that of the bottom VO2layer.The absorption peak at 0.894 THz is also caused by the electric dipole resonance and magnetic dipole resonance.In Figs. 3(e) and 3(f), the result show that the positive and negative charges are mainly concentrated at the two ends of the four split rings,and four dipole-like pairs are accumulated.The electric octopoles between the top and bottom layers can be clearly observed; these are opposite to each other. Due to the strong interaction of the electric octopole mode, a fourharmonic magnetic resonance is formed.

Fig. 2. (a) Absorption curves of VO2 in the metallic and insulating states.(b)Real and imaginary parts of the impedance of a single-band absorber. (c)Real and imaginary parts of the impedance of a dual-band absorber.

We also studied the relationship between absorption and the terahertz wave angle. Figures 4(a) and 4(d) show the absorption spectra with different polarization angles for singleband and dual-band absorbers with vertically incident terahertz waves. When the polarization angle changes from 0°to 90°,the terahertz absorption spectra reveal polarizationinsensitive characteristics,caused by the symmetry of the structure. Figures 4(b)and 4(c)show the absorption spectra of the single-band absorbers with the angle of incidence changing under TE and TM modes. For the TE mode, the angle of incidence varies from 0°to 60°, and the absorptance remains above 0.8. The peak absorption rate decreases with increasing angle of incidence. That is to say, the direction of the electric field changes with the angle of incidence, which results in a decrease in the intensity of electric resonance. For the TM mode,the electric field does not change direction. In this case, when the angle of incidence is 70°, the absorption peak also maintains a high absorption rate above 0.9. It is worth noting that when the angle of incidence is above 40°,some undesirable absorption peaks appear in the absorption spectrum. This is because with an increase in the angle of incidence some parasitic resonances in the metasurface increase sharply. Figures 4(e)and 4(f)display the absorption spectra of the dual-band absorber with change in the angle of incidence for TE and TM modes. For the TE mode, when the angle of incidence varies from 0°to 40°,the two absorption peaks are above 0.8. In particular, the first absorption peak can remain at 0.9 when the angle of incidence reaches 70°. For the TM mode,when the angle of incidence is 60°,the two absorption peaks remain above 0.9. Similarly, absorption peaks caused by high resonance modes can be observed in the TM mode.This confirms that when the designed metasurface is used as switchable absorber it is insensitive to the polarization angle and can still maintain high absorption under a large angle of incidence.

Fig.3.Electric field distribution:at the top layer at 0.736 THz(a),0.894 THz(c)and 1.408 THz(e)and at the bottom layer at 0.736 THz(b), 0.894 THz(d)and 1.408 THz(f).

Fig.4. Absorption spectra of single-band(a)-(c)and dual-band(d)-(f)absorbers with different polarization angles and incident angles.

3.2. Dynamic control of electromagnetically induced transparency

When both the bottom and top VO2patches are in an insulating state,the metasurface converts from terahertz absorption to EIT. Figure 5 depicts the transmission curves of the split rings, cross and their combination under normally incident terahertz waves when the electrochemical potentialμcof the graphene layer is set to 0 eV.It can be concluded that the resonant peak at 1.04 THz is generated by the cross while the resonant peak at 1.58 THz is generated by the four split rings.Therefore, the bright mode induced by the four split rings and the bright mode induced by the cross produce destructive interference between adjacent resonators, which induces a transparent window in the opaque band. In order to clarify the physical mechanism of EIT,figure 6 shows the electric field distribution of the metasurface. At 1.04 THz,the cross is strongly excited by the incident terahertz wave while the four split rings are weakly excited. However, the electric field is mainly concentrated in four split rings at 1.58 THz. At a frequency of 1.24 THz,the cross and four split rings are excited at the same time,and the destructive interference caused by the hybrid coupling of the two bright modes inhibits the radiation loss and allows transmission of the incident wave.

Fig.5. Transmission curves of the split rings,cross and their combination.

wherem1(m2), ˙x1(˙x2), ¨x1(¨x2),ω1(ω2),γ1(γ2),andg1(g2)are the effective mass,the first derivative of displacement,the second derivative of displacement, resonance frequency, loss factor and the coupling strength of the two particles with the incident terahertz wave, respectively.κrepresents the coupling coefficient between the two particles. The following equations can be derived from formulae(10)and(11):

whereKis a coefficient of proportionality. The real part of the effective susceptibility represents the dispersion characteristics and the imaginary part represents the absorption of the proposed metasurface. Figure 7 demonstrates the simulation curve and parameter fitting of the designed metasurface.The fitting parameters areA=0.59,B=0.72,κ=0.65 THz,γ1=1.05 rad·ps-1andγ2=1.45 rad·ps-1. It can be observed that the calculation and simulation curves show good agreement.

Fig.6. Electric field distribution of the proposed metasurface: (a)1.04 THz,(b)1.24 THz,(c)1.58 THz.

Fig.7. Comparison of the calculated and simulated curves.

Fig.8. Transmission curve(a)and group delay(b)of the designed metasurface for a graphene layer under different chemical potentials.

In order to realize dynamic control of the EIT phenomenon, the transmission curves of the graphene layer under different chemical potentials were calculated,as shown in Fig. 8(a). When the chemical potential of the graphene layer is 0 eV,the transmission amplitude of the designed structure is 82% at 0.24 THz. As the chemical potential of the graphene layer gradually increases from 0 eV to 0.5 eV, the transmission amplitude of the EIT peak decreases from 82% to 39%.As an important phenomenon accompanying the EIT effect,a slow light is produced by the strong dispersion of the EIT window. The group delay(τg=-dφ/dω)is introduced to analyze the slow light capability of the designed metasurface. In this formula,φandωrepresent the phase shift and angular frequency, respectively, of the transmission spectrum. Since the transparent window is adjustable, active control of the group delay can also be achieved by changing the chemical potential of the graphene layer, as depicted in Fig.8(b). When the chemical potential of the graphene layer is set as 0 eV, the maximum positive group delay is 1.83 ps at the transparent window. With an increase in the chemical potential, the device gradually loses the slow light effect, showing that active control group delay can be realized by changing the chemical potential of graphene. This has great significance for the design of slow light equipment.

4. Conclusion

In this paper,a dual-function terahertz metasurface based on VO2and graphene is proposed. It is composed of a gold layer embedded with VO2patches,a SiO2layer,a VO2layer,a graphene layer and a SiO2spacer substrate.When the top VO2patches and bottom VO2are in the metallic state,the designed metasurface can be used as a single-band absorber with a terahertz absorptance of 99.7%at 0.736 THz. When the top VO2patches are in the insulating state and the bottom VO2is in the metallic state,the designed metasurface behaves as a dualband absorber, and the absorptance rates at 0.894 THz and 1.408 THz are 98.9% and 99.9%, respectively. The absorber is insensitive to polarization and maintains perfect absorption under large angles of incidence. When the bottom VO2layer is in the insulating state, the designed metasurface achieves electromagnetically induced transparency. When the chemical potential of graphene is varied from 0 eV to 0.5 eV, the transparent window can be dynamically regulated. Changing the chemical potential of the graphene layer can also realize active control of group delay. In summary,the designed terahertz device shows good prospects for application in tunable terahertz optoelectronic systems.

Acknowledgments

Project supported by the National Natural Science Foundation of China(Grant Nos.61871355 and 61831012),the Talent Project of Zhejiang Provincial Department of Science and Technology(Grant No.2018R52043),Zhejiang Key Research and Development Project of China (Grant Nos. 2021C03153 and 2022C03166),and Research Funds for the Provincial Universities of Zhejiang(Grant No.2020YW20).