Adjusting the Metamaterial（MM）cell resonance structure may show many exotic electromagnetic properties，such as negative refraction^［1-2］，perfect absorption^［3-4］，electromagnetic stealth^［5-6］，and electromagnetic induction transparency^［7］. Because MM has the above-mentioned abnormal electromagnetic properties，it has gradually become a research hotspot，and has been widely used in national defense，communications，and biomedical sensing^.［8-10］.

The Metamaterial Perfect Absorber（MPA）has attracted widespread attention due to unprecedented characteristics compared to taper-like structure absorbers^［11］ or ordinary absorbers，such as high absorption efficiency，ultrathin thickness，and a scalable working wavelength^［12］. Since Landy et al. first proposed an MPA with perfect absorption characteristics^［3］，different types of MPAs have been proposed，and the absorption wavelengths over microwave^［13］，terahertz^［14］，infrared，^［15］ and visible bands have been identified^［16］. However，once the structural parameters of MPAs are fixed，their absorption characteristics are difficult to be tuned. On the other hand，demand on tunable MPA is increasing in many applications，such as modulators，optical switches，and smart reflectors.^［17］.

To realize the dynamic tunability of the absorption characteristics of MPA，many research groups choose to incorporate varactor diodes or graphene into the design of MPA. In the low-frequency band，diodes with changeable capacitance are generally used to change the equivalent capacitance of MPA to achieve dynamic tuning of MPA absorption wavelength and absorption efficiency^［18-19］. In the high-frequency band，graphene is used in MPA. By changing the chemical potential of graphene，one can achieve dynamic control of absorption wavelength，absorption efficiency，and even absorption bandwidth of MPAs^［20-21］.

In recent years，phase-changing material vanadium dioxide（VO₂）demonstrated outstanding optical and electrical properties，and can realize the transition between metallic state and dielectric state through external excitations，such as light，electricity，and heat^［22-23］. Because VO₂ has reversible phase-changing characteristics，it is an ideal material for preparing a tunable MPA，and many research work has been done on tunable MPAs based on VO₂. LEI L et al from Shenzhen University designed an absorption-bandwidth-tunable MPA based on VO₂ and metallic chromium materials^［24］. DAO Rina et al from Nanjing University of Posts and Telecommunications used VO₂ as a resonance unit material，and the absorption efficiency of MPA could be tuned by changing the temperature of the resonance unit ^［25］. Our research group also demonstrated tunable absorption wavelength and absorption efficiency of MPA by using VO₂ and graphene in MPA^［26］.

To the best of our knowledge，current VO₂-based MPA can realize tunable absorption efficiency，but the tuning of absorption bandwidth is rarely involved. Moreover，the tunable MPA bandwidth in visible and near-infrared bands is even less involved. However，at present，for the application of intelligent windows，intelligent reflectors，intelligent temperature control systems，and heat emitters，MPA absorption bandwidth is required to be tunable in the visible and near-infrared bands^［27-28］. Therefore，in this paper，a bandwidth-tunable VO₂-based MPA in visible and near-infrared bands is proposed and studied using Finite Difference Time Domain（FDTD）method. The simulation results showed that the bandwidth，W_a， of the tunable MPA proposed in this paper could reach 1.03 μm and 0.652 μm with absorption efficiency higher than 90% in the VO₂ dielectric and metallic state. By analyzing the electromagnetic field distribution of MPA，it was observed that as VO₂ was in the dielectric state，MPA achieved a wide bandwidth and high absorption owing to the Propagating Surface Plasmon（PSP），Localized Surface Plasmon（LSP），and the resonance of Fabry-Perot（FP）cavity.

The structure of the absorption-bandwidth-tunable MPA is shown in Fig. 1. Fig. 1（a）is overall view of the MPA structure，and Fig. 1（b）is zoom-in view of one MPA unit cell. The MPA unit cell is composed of an Au substrate and four cylindrical resonance units with different radii. The cylindrical resonance units are of two-layered structure，with VO₂ as bottom layer and Au as top layer. The structural parameters are as follows：P is the period of the MPA unit cell；r₁，r₂，r_3， and r₄ are the radii of the four cylindrical resonance units respectively；h_m=0.03 μm and h_v=0.11 μm are the thickness of Au and VO₂ in the cylindrical resonance unit respectively；w₁，w₂，w₃ and w₄ are spacing between different cylinder resonant elements. In this work，the thickness of the Au substrate is 0.2 μm，which is thick enough to block the incident light effectively，and the transmission of the structure is nearly zero.

With the development of material preparation technology and nanofabrication technology，the current micro-nano machining technology can fully meet the requirements of MPA processing as shown in Fig. 1. Therefore，the MPA structure proposed in this paper is easier to realize in an actual experiment. The proposed structure in Fig. 1 can easily be realized by current nano-fabrication technology. Firstly，a continuous VO₂ layer is prepared on the Au substrate by the lower-cost sol-gel method ^［29］，then a thin Au layer was sputtered on the VO₂ layer by magnetron sputtering，finally the required cylindrical resonance units are patterned by electron beam lithography and ion beam etching.

The refractive index n，and coefficient k of Au for different light wavelengths could be obtained from Ref.［30］，as shown in Fig. 2. According to the Bruggeman's effective medium theory^［31］，The dielectric constant of VO₂ could be calculated by Eq.（1）. In Eq.（1），ε_i≈9 is the dielectric constant of VO₂ in the dielectric state，ε_m is the dielectric constant of VO₂ in the metallic state，and f represents the volume ratio of VO₂ in the metallic state in the entire VO₂. Moreover，ε_m could be obtained by Eq.（2）. In Eq.（2），ω_p is the plasma frequency，ω is the incident light angular frequency，τ=2 μm_e/e is the relaxation time，m_e is the mass of free electrons，u≈2 cm²/V. s is carrier mobility，and e is the amount of free electron charge. Furthermore，f could be obtained by Eq.（3），where T represents the environment temperature，T₀=68°C represents the VO₂ phase transition temperature，and ΔT=6°C is the transition width. Eqs.（1）~（3）could be combined to obtain the refractive index，nVO2_， and the extinction coefficient，kVO2_， of VO₂ for different wavelengths at different temperatures，as shown in Fig. 3.

The characteristics of proposed MPA is studied by FDTD simulation. Since the MPA is of periodic structure，by carefully setting boundary conditions，it is feasible to only simulate the unit structure as shown in Fig. 1（b）in FDTD software. A periodic boundary condition was added in the x- and y-directions. A perfect match layer was added in the z-direction as the boundary condition. The polarization of the incident light was set to be TM polarization（Along the x axis）. Incident light was perpendicular to the surface of the structure，which indicated the incident angle θ is 0. To ensure that the simulation results were closer to reality，the grid type was auto non-uniform during simulation，and the grid accuracy was set to the maximum value of 8. The details are shown in Fig. 4.

Fig. 5 shows FDTD simulation results of absorption spectra of MPA at different temperatures. As Fig. 5 shows，at T=80°C，the MPA could maintain more than 90% absorption efficiency between 0.505 μm and 1.157 μm，and the absorption bandwidth W_a could reach 0.652 μm. When the temperature T dropped from 80°C to 25°C，the MPA could maintain more than 90% absorption efficiency between 0.505 μm and 1.535 μm，and the absorption bandwidth，W_a reached 1.03 μm. These findings indicate that the MPA proposed in this paper can realize the tuning of absorption bandwidth by changing the VO₂ temperature，and the tuning range of absorption bandwidth can reach 0.378 μm. In addition，the results show that the absorption spectrum of MPA covers both the visible and near-infrared bands.

To explore the internal physical mechanism of the MPA with tunable absorption bandwidth，the electromagnetic field distribution of MPA at different resonance wavelengths is simulated and calculated at low temperature. Fig. 6 shows the electric field distribution of MPA in the x-z plane（y=-0.125 μm，e.g. the center plane of cylinders with radii r₃ and r₄）under different resonance wavelength conditions（T=25°C）. As shown in Fig. 6，under different resonance wavelength conditions，the electric field is basically concentrated between the gaps of the cylindrical resonance units and the corners of the Au cylinder，which indicates the incident light excites the surface plasmon polaritons（SPPs）in the MPA. Therefore，from the electric field distribution，it can be concluded that the high absorption of the MPA at each resonance wavelength is due to SPP resonance^［24］.

Unlike the electric field distribution，the magnetic field distribution（T=25°C）of the MPA under different resonance wavelength conditions is very different. As shown in Fig. 7（a）and 7（b），LSP resonance is the mainreason for the high absorption efficiency of MPA at long wavelengths（1.4 μm and 1.2 μm）. Moreover，most of the magnetic field is confined to the VO₂ layer，which is between the Au cylinder and the Au substrate^［23］. Fig. 7（e）shows that the high absorption efficiency of MPA at a short wavelength（0.505 μm）is mainly due to PSP resonance，because only a small part of the magnetic field is restricted to the VO₂ layer，and most of magnetic field is located between adjacent cylindrical resonance units，which is a significant PSP resonance feature^［32-33］. The specific proof can also be seen in Fig. 9（a）. As for the resonance absorption of MPA at wavelengths of 0.8 μm and 1 μm，Fig. 7（c） and 7（d） show that it is not only caused by LSP resonance and PSP resonance，but is also mixed with FP cavity resonance，that is，the light wave oscillated back and forth between the Au cylindrical layer and the Au substrate. In this case，the Au cylindrical layer and Au substrate act as mirrors to form a FP resonator.

To understand the intrinsic physical mechanism of the high absorptivity of MPA in the VO₂ metallic state，the electromagnetic field distribution of MPA at the wavelength of 0.505 μm and 1 μm at T=80°C is calculated，as shown in Fig. 8. Fig. 8（a）shows the magnetic field distribution of the MPA at a wavelength of 0.505 μm. Compared with Fig. 7（e），the magnetic field distribution of VO₂ at the short wavelength is basically the same regardless of whether VO₂ is in the dielectric state or metallic state. That is，the physical mechanism leading to the high absorption efficiency of MPA at the short wavelength is the same，which is because of the PSP resonance.

Comparing Fig. 8（b）with Fig. 7（c），it can be seen that when VO₂ is in the metallic state，the high absorption efficiency of MPA at long wavelengths（1 μm）is not only caused by LSP or PSP resonance，but also mainly because of FP cavity resonance. The FP cavity resonance here is mainly composed of an adjacent cylinder resonance units and air gap ^［24］. The FP cavity length is the thickness of cylinder resonance unit（h_m+h_v）. The width of FP cavity is w₁. Owing to the formation of the FP cavity，more magnetic fields are concentrated between the air gaps of the adjacent cylinder resonance units. Figs. 8（c） and 8（d） show the electric field distribution of MPA at a wavelength of 0.505 μm and 1 μm when VO₂ is in a metallic state，respectively. It can be seen the high absorption efficiency of MPA at high temperature is also due to the SPP resonance.

To explore the influence of MPA structural parameters on its absorption characteristics at low temperature（VO₂ is in dielectric state，T=25℃），the MPA absorption spectra（T=25°C）under the conditions of different periods P and cylindrical resonance unit radius were simulated and calculated. Fig. 9（a）shows the influence of P on the absorption spectrum of MPA. As P increased，the absorption bandwidth of MPA gradually narrowed，and the absorption wavelength of MPA at the short-wavelength gradually showed redshift. When P increased from 0.5 μm to 0.6 μm，the initial wavelength of the MPA absorption spectrum shifted from 0.505 μm to 0.599 μm. It can be found that the absorption wavelength of MPA at short wavelengths is very close to P. This phenomenon is due to the fact that high absorption efficiency of MPA at short wavelengths is caused by PSP resonance. The PSP resonance wavelength，λ_PSP， is related to the MPA period， P，which can be seen in Eq.（4）^［32］. In Eq.（4），m is an integer，λ₀is the free-space wavelength. Because the incident light is perpendicular to the surface of the MPA，θ is 0，therefore λ_PSPequals to P.

As Fig. 9（a）shows，although the P of MPA gradually increased，there is no obvious redshift or blueshift at the MPA wavelength of 1.4 μm. This is because，as can be seen from Fig. 7（a），the high absorption efficiency of MPA at 1.4 μm is caused by LSP resonance，and period P has almost no effect on the LSP resonance wavelength.

Fig. 9（b）shows the MPA absorption spectra versus the radii of different cylindrical resonance units. As can be seen from Fig. 9（b），with an increase in the radius of the resonance unit，the MPA absorption bandwidth，W_a， increased firstly and then decreased. In the short wavelength range between 0.5 μm and 1 μm，in all the 4 simulated conditions，the MPA could maintain a relatively high absorption efficiency（>75%）. The reason for this is that the high absorption efficiency of MPA at short wavelength is caused by the PSP resonance，as shown in Fig. 7（e）. From Eq.（4），we know the resonance wavelength of PSP is mainly determined by the period P，so as long as P did not change，the MPA could maintain the PSP resonance at the short wavelength. However，the absorption efficiency varied greatly at long wavelengths（>1 μm）. The reason for this is that the high absorption efficiency of MPA at long wavelength is caused by LSP resonance，as shown in Fig. 7（a） and 7（b）. According to Ref.［32］，LSP resonance is mainly affected by the shape and size of the MPA resonance unit. Therefore，when the radius of the resonance unit is small，the absorption efficiency of MPA is extremely low because it cannot meet the conditions to excite LSP resonance；when the radius of the resonance element increases，it gradually meets the excitation conditions of LSP resonance，and increases the absorption efficiency of MPA at the long-wavelength range.

In order to understand the influence of structural parameters on the absorption characteristics of MPA at high temperature（VO₂ is in metallic state，T=80℃），we changed the thickness of top Au layer h_m and the radius of the resonance units. Fig. 10（a）shows the influence of h_m on the absorption characteristics of MPA as VO₂ is in metallic state（T=80℃）. As can be seen from Fig. 10（a），when h_m increases，the absorption wavelength of MPA at short wavelength almost unchanged，but the absorption efficiency gradually declines. Refer to Fig. 8（a），when VO₂ is in metallic state，the high absorption efficiency of MPA at the short wavelength is caused by the PSP resonance. On the contrary，the absorption wavelength of MPA in the long wavelength is red-shifted. This is because when VO₂ is the metallic state（T=80℃），the high absorption efficiency of MPA at the long wavelength is due to the FP cavity resonance rather than LSP resonance. The relationship between the FP cavity resonance wavelength λ_FP and h_m is shown in Eq.（5）^［34］，where n_eff is the FP cavity effective refractive index. According to Eq.（5），with the increase of h_m，the resonant wavelength of FP cavity λ_FP will increase，resulting in the red shift of MPA at the long wavelength.

Fig. 10（b）shows the influence of the MPA resonance unit radius on the absorption characteristics of the MPA. Different from VO₂ in dielectric state，when VO₂ is in metallic state，the absorption efficiency of MPA at long wavelength gradually increases with the increase of the resonance unit radius. As comparison，when VO₂ is in dielectric state，as shown in Fig. 9（b），with the increase of the resonance unit radius，the absorption efficiency of MPA at long wavelength first increases and then decreases. This is mainly because when VO₂ is metallic state，the high absorption efficiency of MPA at long wavelength is due to the FP cavity resonance. With the increase of resonance unit radius，the FP equivalent refractive index gradually meets the resonance condition of long wavelength（see Fig. 11），so that the absorption efficiency of MPA at long wavelength is gradually improved.

The relationship between the width of FP cavity w and the equivalent refractive index of FP cavity n_eff can be obtained by Eqs.（6）~（8）. ε_m and ε_d=1 are the dielectric constants of Au and air respectively. k₀=2π/λ，where λ is the incident light wavelength. Fig. 11 shows the relationship between w and n_eff when the wavelength of incident light is 1 μm（ε_m=-47.84+3.11i）. It can be seen from Fig. 11 that as w decreases，that is，as the radius of the cylinder resonance unit increases，n_eff will gradually increase. Because the length of the FP cavity unchanged，the resonance wavelength λ_FP of the FP cavity will increase when the n_eff increases. Therefore，as shown in Fig. 10（b），when the radius of the cylindrical resonance unit increases，the absorption efficiency of MPA at the long wavelength increases.

We designed a MPA with high absorption efficiency and tunable absorption bandwidth in visible and near-infrared light bands. The simulation results indicate that by changing temperature，the absorption bandwidth W_a of the MPA can be tuned，and the tuning range can reach 0.375 μm. We also studied the effects of structural parameters on absorption bandwidth. By analyzing the electromagnetic field of the MPA at absorption wavelength，it can be found that when VO₂ is at a low temperature（T=25°C），the high absorption efficiency of the MPA in the near-infrared band is due to LSP resonance，and the high absorption efficiency of the MPA in the visible band is due to the PSP resonance. However，when VO₂ is at high temperature，the high absorption efficiency of the MPA in the near-infrared band is caused by FP resonance. The research in this paper can provide a theoretical basis for design and fabrication of a high-performance，dynamic，adjustable MPA in the future.