Tunable polarization-independent and angle-insensitive ultra-broadband terahertz absorber with vanadium dioxide

In this paper, a tunable ultra-broadband terahertz metamaterial absorber is proposed based on the phase transition material of vanadium dioxide (VO2). The absorber cell consists of a petal-like monolayer vanadium dioxide, a dielectric layer, and a metal layer. The terahertz absorption bandwidth of more than 90% absorptance reaches 4.2 THz, which covers from 1.99 to 6.19 THz, and a relative bandwidth attains to 102.7%. By changing the conductivity of VO2, the absorbance of this structure can be dynamically adjusted from 2.4% to 98.96%. The physical mechanism of the perfect absorption in this paper is investigated by the impedance matching theory and electric field distributions. The results show that the strong coupling effect in the petal-like structure contributes to the broadening of the absorption spectrum, and the absorber is polarization-insensitive and wide-angle incidence-insensitive due to the symmetry of the cell structure. The metamaterial absorber designed in this paper is expected to have a wide range of applications in the fields of terahertz imaging, stealth, sensing and detection.


Introduction
Terahertz (THz) waves are electromagnetic waves located in the frequency range of 0.1 to 10 THz, between microwave and infrared light [1,2].Due to their special optical properties, they have shown great potential in various fields such as broadband communication [3], biological imaging [4], and security detection [5].Metamaterials, as artificial materials, possess electromagnetic properties that can not be obtained by natural materials [6].In 2008, Landy et al successfully achieved strong plasmon resonance in the 9 to 14 GHz by periodically arranging split metal rings in the pattern layer, resulting in a single perfect narrowband absorption peak [7].This discovery inspires researchers to further develop millimeter and micrometer scale broadband and narrowband perfect absorbers by adjusting the structure and arrangement of pattern layers.At present, domestic and foreign researchers have designed various structures [8][9][10][11][12][13][14] for terahertz metamaterial absorbers, and single band [15,16], multi band [17,18], and broadband [19][20][21] designs through simulation have been verificated.However, these absorbers are relatively single in function, and their absorption performance is difficult to flexibly adjust according to actual needs, which to some extent limits their application range.Therefore, designing absorbers with adjustable operating frequency has become a current research hotspot.In order to achieve broadband absorption, researchers usually use two main methods: material tuning and geometric tuning [22].In terms of material tuning, materials such as liquid crystals [23], graphene [24], and vanadium dioxide [25] have been widely studied; on the other hand, geometrical tuning involves physically altering the geometry of microstructures to adjust their equivalent parameters [22].However, due to the intricate design and complex preparation process of the unit structure, it is particularly difficult to achieve tunable broadband absorption by physically altering the structure.Therefore, combining metamaterials with materials with unique properties such as vanadium dioxide has become a promising method for achieving reconfigurable properties in the terahertz range [26].This combination can not only utilize the excellent properties of metamaterials, but also dynamically regulate the absorption characteristics of metamaterials through tunable materials such as vanadium dioxide.
With the continuous progress of technology, the emergence of new materials such as VO 2 has brought innovative possibilities for the development of tunable terahertz absorbers.VO 2 as a unique reversible phase change material, exhibits an insulating state at room temperature, but once the temperature rises to 68 °C, it will undergo a significant phase transition process and transform into a metallic state.This phase transition causes a significant change of almost four orders of magnitude in the conductivity of VO 2 , and when the temperature drops back to room temperature, VO 2 can naturally recover from a metallic state to an insulating state [27].The uniqueness of this material lies in its ability to trigger its phase transition process through various external excitation methods such as thermal [28], electricity [29], or light [30], greatly expanding the application prospects of VO 2 in various fields.In 2021, Wu et al [31].proposed a tunable broadband terahertz metamaterial absorber based on vanadium dioxide.Under normal incidence conditions, the absorber exhibits excellent performance, with an absorption bandwidth of up to 3.30 THz and an absorption rate exceeding 90% in the frequency range of 2.34 ∼ 5.64 THz.In 2022, Yang et al [32].designed a tunable broadband terahertz metamaterial absorber based on vanadium dioxide.When electromagnetic waves are normally incident, the absorber exhibits characteristics of wide frequency band and high absorption rate.Specifically, its absorption bandwidth reaches 3.78 THz, and the absorption rate exceeds 90% in the frequency range of 3.01 ∼ 6.79 THz.In recent years, many researchers have worked on realizing terahertz devices with broadband absorption capability and reconfigurable properties.To achieve broadband absorption, several resonant structures with different dimensions and dielectric layer structures with multilayer thickness have been proposed [8][9][10][11][12][13][14].However, the fabrication process of these structures is complicated and difficult to control.Therefore, there is still a need to design a broadband tunable absorber with monolayer substrate that is insensitive to polarization and wide-angle incidence.
In this context, a dynamically tunable broadband terahertz absorber is presented, which consists of three layers: two perpendicular VO 2 elliptical structures as the top layer, a polytetrafluoroethylene (PTFE) [33] dielectric layer in the middle, and a metal layer at the bottom.A broadband absorptance of more than 90% in the 1.99 ∼ 6.19 THz band (with a bandwidth of 4.2 THz) can be achieved for differently incident polarizations and wide incident angles.By changing the temperature, the conductivity of VO 2 can be varied from 2×10 2 S m −1 to 2×10 5 S m −1 , which results in metamaterial from a perfect reflector to a perfect absorber.The absorption peak intensity of the metamaterial structure can be continuously adjusted between 2.4% ∼ 98.96%.Moreover, the physical mechanism of broadband high absorption is analyzed and elucidated based on impedance matching theory and field distributions.Results show that the broad absorption can be obtained based on the combined effect of magnetic dipoles and electric dipoles from two orthogonal arranged vanadium dioxide elliptical structures.In addition, the absorption characteristics of the metamaterials under different polarizations and incidence angles are investigated in this paper.The ultra-wideband tunable metamaterial absorber proposed in this paper has a wide range of applications in the fields of electromagnetic stealth, mobile communication [34], medical diagnosis [35], imaging [36], and biosensor [37].

Structure design and simulation analysis
As shown in figure 1, the ultra-wideband terahertz absorber designed in this article adopts a unique unit structure, which includes two perpendicular VO 2 elliptical structures, a polytetrafluoroethylene [33] (PTFE, 2. 1 dielectric layer in the middle, and a metal gold layer at the bottom.It is worth noting that we chose PTFE as a dielectric material because its various superior properties, such as excellent high-temperature

( ) w s =
´-At normal temperature, VO 2 is in an insulated state, and the conductivity of VO 2 is set to 200 S m −1 in the simulation.When the temperature increases to 68 °C, VO 2 changes from an insulating state to a metallic state [40,41], and the conductivity also changes with this process by 4 to 5 orders of magnitude.At this time, the conductivity of vanadium dioxide could be changed from 200 S m −1 to 2 × 10 5 S m −1 .The electromagnetic simulation software of CST STUDIO SUITE is used to simulate the absorber structure in this paper.Open boundary conditions are set in the z-direction, and periodic boundary conditions are set in the x and y directions.In this paper, the optical properties of the VO 2 metamaterial absorber are studied by simulation, and the reflection and absorption spectra of the absorber are obtained in both the insulating and metallic states.Since the thickness of the metal is much larger than the skin depth at the operating frequency, thus the transmittance T ( ) w is zero.Therefore, the absorbance A( ) w is calculated as where R ( ) w is the reflectance and S 11 ( ) w is the reflection coefficient in the S parameters.

Results
The reflection and absorption spectra of the absorber are shown in figure 2(a) when the VO 2 is in the metallic state with a conductivity of 2 × 10 5 S m −1 .The results demonstrate an absorption bandwidth exceeding 90% absorbance, spanning from 1.99 THz to 6.19 THz under normal incidence.This performance surpasses that of previously reported MPAs [8][9][10][11][12][13][14], as shown in table 1. Comparing the results with the data in [8][9][10][11][12][13][14], our design exhibits superior performance in terms of bandwidth and tunable range.Traditional designs typically rely on a single magnetic resonance or electric resonance, thus their bandwidth are limited.In contrast, our design incorporates two mutually perpendicular ellipsoidal structures of vanadium dioxide and successfully combines the resonant effects of magnetic dipoles and electric dipoles through careful structural design, thereby achieving a broader bandwidth absorption.The absorber has two absorption peaks located at 2.41 THz and 5.57 THz, respectively.The frequency interval between the two peaks is 3.99 THz. Figure 2(b) shows the metamaterial absorption spectra for normal incidences of different polarized electromagnetic waves when VO 2 is in the metallic state.It can be seen from the figure that the absorption spectrum of the designed absorber hardly changes when the polarization angle is varied between 0°and 90°.This is because the absorber structure is central symmetry and axial symmetry, therefore, the absorber exhibits the insensitive property to the angle of polarization of the incident wave.
Next, the tunable characteristics of the metamaterial absorber are analyzed in this paper, and the results are shown in figure 3. When the conductivity changes from 200 S m −1 to 2 × 10 5 S m −1 , the reflection and absorption spectra of the absorber also change accordingly.With the increase of conductivity, the absorption rate of the absorber grows significantly, jumping dramatically from 2.4% to 98.96%, while the center frequency of the absorber remains basically stable, as shown in figures 3(a) and (b).This phenomenon is mainly attributed to the corresponding change of the dielectric constant of VO 2 with the change of conductivity.Actually, by precisely regulating the phase transition temperature of VO 2 , employing doping or alloying techniques, and incorporating advanced thin film preparation processes, we are able to stably regulate the conductivity of VO 2 .The real and imaginary parts of the vanadium dioxide dielectric constant respectively based on the formular (1) can be obtained [38,39].Figures 3(c) and (d) present the trend of the real and imaginary parts of the vanadium dioxide dielectric constant as a function of conditions.The real part shows a negative value, and at a certain frequency, the real part decreases while the imaginary part increases as the conductivity increases.With increasing frequency, the real part increases while the imaginary part decreases significantly.These results indicate that vanadium dioxide possesses dynamic tuning properties in the terahertz band.

Discussions
In this paper, we design a tunable metamaterial absorber based on the VO 2 phase transition, and the core physical mechanism for realizing high absorption lies in the impedance matching.For normally incident terahertz waves, the absorption rate of the absorber directly depends on the relative impedance between it and  free space.By finely tuning the electromagnetic properties of metamaterial to match its impedance with the free space impedance, the reflection of electromagnetic waves can be greatly reduced, and the absorption efficiency of the absorber can be significantly improved.The specific quantitative relationship of this process can be determined by the following formula [42]: where Z 377 0 = Wis the free space impedance, Z is the absorber effective impedance, and Z Z Z r 0 = is the relative impedance.Since the thickness of the metal ground plane is much larger than the skin depth of the electromagnetic wave generated in the metal, the electromagnetic wave is almost completely reflected when it contacts with the metal ground plane, resulting in a transmission coefficient that can be approximated as zero.Therefore, the impedance relationship between the relative impedances of the absorber and the free space can be described as: The relative impedance of the metamaterial absorber based on the phase transition of VO 2 is calculated by using equation (6) and the results are shown in figure 4. From the figure, it can be observed that when the conductivity of VO 2 reaches 2 × 10 5 S m −1 , the real part of the relative impedance of the absorber is close to 1 and the imaginary part is almost 0 in the frequency range from 1.99 THz to 6.19 THz.This result clearly shows that the impedance of the absorber has reached a state of almost perfect matching with the impedance of the free space in this frequency range [43], which minimizes the reflection and significantly improves the absorber's performance in absorbing electromagnetic waves [44].
In order to further study the physical mechanism of metamaterial absorbers in achieving broadband absorption, we plot the electric field distributions at two specific absorption peak positions of 2.41 THz and 5.57 THz through simulation, as shown in figure 5. Specifically, figures 5(a) and (b) illustrate the electric field distributions at 2.41 THz and 5.57 THz, respectively, under y-polarized electromagnetic wave excitation.Similarly, figures 5(c) and (d) present the distributions at these frequencies under x-polarized excitation.Taking y-polarization as an example, figure 5(a) shows that the electric field is mainly concentrated at the long axis on both side of the ellipse, triggering electric dipole resonance [38].In addition, the weak electric field existing at the edge of the inner circle, cooperates with the electric field in the long axis, producing magnetic dipole resonance [39].The similar electric field pattern is evident in the figure 5(b), promoting the coexistence of electric dipole resonance and magnetic dipole resonance.Therefore, the incident electromagnetic wave excites surface plasmon resonance in the vanadium dioxide structure, and at the area of the vanadium dioxide ellipse, the combined action of magnetic resonance and electric resonance significantly enhances the absorption capacity of the absorber, achieving effective broadband absorption [45].
Next, this paper gradually changes the structural parameters of the absorber while keeping other parameters unchanged, in order to independently study the impact of each parameter on the absorption performance.Figure 6 clearly illustrates how the absorption spectra of metamaterial undergo corresponding changes when parameters r 1 , r 2 , r 3 , and t 2 are adjusted.As shown in figure 6(a), the overall absorptivity of the absorber decreases with the gradual increase of the radius r 1 of the long axis of the ellipse, and the bandwidth of the absorber reaches 4.2 THz when r 1 is increased to 14 μm and the absorptivity stays above 90%.In figure 6(b), with the increase of radius r 2 , the absorption spectrum shows an obvious red shift, while the bandwidth of the absorber is also getting larger gradually.In figure 6(c), as the inner radius r 3 increases, the position of the absorption peak and absorption bandwidth are constantly changing, while the absorption rate will gradually decrease.As shown in figure 6(d), with the increase of the thickness of the intermediate dielectric layer PTFE, the absorption rate is significantly enhanced, and at the same time, accompanied by the redshift phenomenon, the intensities of the different absorption peaks also show changes.After simulation analysis, we further confirm the importance of the top vanadium dioxide elliptical resonance structure and the intermediate PTFE dielectric layer in optimizing absorber performance.By finely adjusting these parameters, we have successfully designed an efficient absorber with broadband absorption characteristics, significantly improving its absorption performance.
Due to the arbitrary incident direction of electromagnetic waves, it is necessary to consider the impact of different incident angles on the absorption rate of the absorber.When the incident electromagnetic wave is TE  (Transverse Electric ) mode, the results are shown in figure 7(a).When the incident angle changes from 0°to 50°, the absorption rate exhibited by the absorber can be stably maintained at a level of 80% or higher.After exceeding 50°, the absorption rate decreases.This paper also analyzes the case of incident electromagnetic wave with TM (Transverse Magnetic) mode, as shown in figure 7(b).Under TM incidence, when the incident angle gradually increases from 0°to 60°, the absorption rate within a specific frequency band can still exceed 90%, demonstrating the excellent absorption ability of the absorber for TM mode in a larger range of incident angles.This efficient absorption characteristic not only indicates the good stability of the absorber under TM polarization, but also implies its potential application value in scenarios where large incident angle for TM polarization needs to be processed.Taking into account both TE and TM polarization conditions, this absorber can maintain good absorption performance within the range of incident angle variation to 50°.This means that regardless of whether the incident light is TE polarization or TM polarization, as long as the incident angle does not exceed 50°, the absorber can maintain a high absorption efficiency.This characteristic enables the absorber to perform excellently in various polarization states of incident light environments, thereby expanding its application range in fields such as optics, optoelectronics, and solar energy.

Conclusions
This paper introduces a design for a dynamically adjustable ultra-wideband terahertz absorber, which consists of a single layer of two perpendicular VO 2 elliptical structures, a PTFE substrate and a metal gold layer at the bottom.Numerical simulations show that when the conductivity of VO 2 increases to 2 × 10 5 S m −1 , this design achieves over 90% absorption in a 4.2 THz wideband under normal incidence, particularly reaching peak absorptions of 98.52% and 96.92% at 2.41 THz and 5.57 THz respectively.Conversely, when the conductivity decreases to 2 × 10 2 S m −1 , the reflectance in the same frequency band rises above 98%, showing a marked reflectivity.By adjusting the conductivity, the absorber's absorbing or reflecting behaviors can be flexibly controlled for various applications.The study also explores the wideband absorption mechanism, revealing the crucial role of combined effect of magnetic dipoles and electric dipoles from two orthogonal arranged vanadium dioxide elliptical structures.Moreover, this metamaterial absorber exhibits robust insensitivity to polarization and incidence angle, maintaining stable absorption performance under various conditions.In the follow-up work, we will conduct processing tests and prepare real materials to verify our design.This ultra-wideband terahertz absorber with tunable function shows great application potentials in the fields of terahertz technologies, such as modulators, sensors, optoelectronic switches, and optical devices.Its emergence opens up a new path for the continuous progress and innovative development of the technology, and heralds broader application prospects and possibilities.

Figure 1 .
Figure 1.(a) The top view schematic and (b) three-dimensional schematic of the absorber.

Figure 2 .
Figure 2. (a) The reflection and absorption spectra of the absorber.(b) the color diagram of the absorption spectra with different polarization angles of incidence.

Figure 3 .
Figure 3. (a) The reflection spectra and (b) absorption spectra of absorber with different conductivities of VO 2 .(c) and (d) are the real and imaginary parts of VO 2 relative permittivity under different conductivity, respectively.

Figure 4 .
Figure 4.The relative impedance of absorber with a conductivity of 2 × 10 5 S m s for VO 2 .

Figure 5 .
Figure 5.The electric field distributions of the absorber under y-polarized electromagnetic wave excitation at (a) 2.41 THz and (b) 5.57 THz; The electric field distributions of the absorber under excitation of x-polarized electromagnetic waves at (c) 2.41 THz and (d) 5.57 THz.

Figure 6 .
Figure 6.Absorbance of the absorber with different parameter conditions at a conductivity of 2 × 10 5 S m −1 .(a) Radius of the long axis r 1 .(b) Radius of the short axis r 2 .Effects of (c) the radius of circle r 3 and (d) the thickness t 2 of PTFE.

Table 1 .
Comparison of absorption performance of vanadium dioxide metamaterial absorbers.