Terahertz VO₂-Based Dynamic Coding Metasurface for Dual-Polarized, Dual-Band, and Wide-Angle RCS Reduction

Abstract

With the rapid development of terahertz radar technology, the electromagnetic device for terahertz radar cross-section (RCS) reduction is worth investigating. However, the existing research concentrates on the RCS reduction metasurface with fixed performance working in the microwave band. This paper proposes a terahertz dynamic coding metasurface integrated with vanadium dioxide (VO₂) for dual-polarized, dual-band, and wide-angle RCS reduction. The simulation result indicates that by switching the state of the VO₂ between insulator and metal, the metasurface can realize the effective RCS reduction at 0.18 THz to 0.24 THz and 0.21 THz to 0.39 THz under the left-handed and right-handed circularly polarized incident waves. When the polar and azimuth angles of the incident wave vary from 0° to 40° and 0° to 360° respectively, this metasurface can maintain a 10 dB RCS reduction. This work has potential value in the terahertz stealth field.

1. Introduction

The terahertz (THz) frequency band generally means 0.1 to 10 THz. Terahertz radar has attracted considerable attention recently for high resolution, small aperture, all-day, Doppler sensitivity, and anti-interference in detection and imaging [1]. Electromagnetic (EM) stealth technology aims to make the target undetectable and protect the target. It is essential in military and civilian fields. However, the rapid development of terahertz radar technology has threatened conventional stealth devices [2]. Radar cross-section (RCS) reduction is the most significant aspect of the EM stealth device [3]. Therefore, the terahertz EM device for RCS reduction is worth investigating.

The low-profile metasurface can efficiently manipulate EM waves’ amplitude, phase, and polarization. Metasurface-based EM devices, such as the absorber, polarization converter, metalens, orbital angular momentum multiplexer, and demultiplexer, have become a research highlight [4]. RCS reduction metasurfaces have made significant progress. Most research focuses on the metasurface-based low-RCS high-gain antenna [5,6,7,8,9,10]. This research introduces complex multilayer structures to reduce RCS and enhance the gain of the meta-antenna. Some of the studies work on realizing a simple structured RCS reduction metasurface [3,11,12]. Some research further optimizes the metasurface using the particle swarm optimization (PSO) algorithm, genetic algorithm (GA), and pseudorandom algorithm [13,14,15]. In addition, the conformal RCS reduction metasurface is also investigated to improve adaptability [16,17,18]. However, the existing research concentrates on the RCS reduction metasurface with fixed performance working in the microwave band.

The dynamic metasurface (reconfigurable or tunable metasurfaces) combined with active components is superior to the fixed metasurface in flexibility, such as graphene, positive–intrinsic–negative (PIN) diode, varactor diode, and liquid crystal [19,20]. The performance of the dynamic metasurface is tunable by controlling the active component. Some achievements have been made in the dynamic RCS reduction metasurface recently. Applying PIN and varactor diodes realizes the low-RCS and high-gain antenna with reconfigurable scattering patterns [21,22]. For the vertical incident wave, using graphene-based and PIN diode-based coding metasurfaces dynamically manipulates the scattering field [23,24,25,26]. To steer the scattering field, broadband, and wide-angle metasurfaces hybridized with graphene and PIN diode are investigated [27,28]. A wideband low-scattering metasurface with an in-band tunable transparent window is also studied by loading the PIN diode [29]. Nevertheless, there is little research on the terahertz dynamic RCS reduction metasurface.

This paper offers a terahertz dynamic coding metasurface integrated with vanadium dioxide (VO₂) for dual-polarized, dual-band, and wide-angle RCS reduction. Considering the influence of the incident wave’s polar and azimuth angles, an RCS reduction formula that covers the incident angle is derived first. Then, a coding metasurface with the whale optimization algorithm (WOA) is designed. The top metal resonator embedded with VO₂ and a middle dielectric and bottom metal plate forms the meta-atom of the metasurface. VO₂ undergoes the insulator-to-metal transition at around 68 °C [30]. Thus, regulating the VO₂ state can effectively change the performance of the meta-atom. The Pancharatnam–Berry (PB) phase (geometric phase) is applied to obtain the required abrupt phase under a circularly polarized (CP) incident wave [31,32]. As the meta-atom rotation angle is limited to 0° and 90°, the metasurface is valid for both left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) incident waves. The simulation result demonstrates that the metasurface can achieve a 10 dB RCS reduction from 0.18 THz to 0.24 THz (the relative bandwidth is 28.6%) and 0.35 THz to 0.43 THz (the relative bandwidth is 20.5%) under LCP and RCP incident waves. When the polar and azimuth angles of the incident wave vary from 0° to 40° and 0° to 360°, the metasurface can generally maintain the 10 dB RCS reduction. Therefore, the terahertz VO₂-based dynamic coding metasurface can effectively implement the dual-band, dual-polarized, and wide-angle RCS reduction. This work owns potential value in the terahertz stealth field.

2. Design Principle

First, consider a coding metasurface arranged in a rectangular grid on the xoy plane. There are N_x and N_y elements in the x- and y-directions, respectively. The distances between the elements are D_x and D_y in the x- and y-direction. The metasurface is excited by a plane wave with a polar angle θ_i and azimuth angle φ_i. According to the phased array theory [33,34], and simultaneously considering the influence of the incident wave’s angle, for the radiated field at a point in space (θ,φ), the phase difference between elements consists of three parts: the abrupt phase ϕ₁ introduced by the element, the phase delay ϕ₂ caused by the element’s spatial position, and the phase delay ϕ₃ caused by the incident wave. For the n_xn_yth element, ϕ₂ and ϕ₃ can be written as:

$${\varphi }_2\left(n_x,n_y\right)=k_0\sin \theta \left(\frac{2n_x-1}{2}{D}_x\cos \phi +\frac{2n_y-1}{2}{D}_y\sin \phi \right)$$

(1)

$${\varphi }_3\left(n_x,n_y\right)=k_0\sin {\theta }_i\left(\frac{2n_x-1}{2}{D}_x\cos {\phi }_i+\frac{2n_y-1}{2}{D}_y\sin {\phi }_i\right)$$

(2)

Therefore, take the amplitude A(n_x,n_y) in each element into consideration and write the array factor F_a of the metasurface as:

$$F_a\left(\theta ,\phi \right)={\displaystyle \sum _{n_x=0}^{N_x}{\displaystyle \sum _{n_y=0}^{N_y}A\left(n_x,n_y\right)\exp j\left[{\varphi }_1\left(n_x,n_y\right)+{\varphi }_2\left(n_x,n_y\right)+{\varphi }_3\left(n_x,n_y\right)\right]}}$$

(3)

The wave number k₀ = 2πC/f₀, C is the wave velocity in free space, and f₀ is the frequency.

Then, to optimize the RCS reduction effect, the WOA [35] is employed. The fitness function F_fit is the maximum value of F_a. Express F_fit as:

$$F_{fit}=\max \left[F_a\left(\theta ,\phi \right)\right]$$

(4)

Figure 1 shows the WOA-based optimization process. Firstly, set the number of search agents N_se, the number of variables N_dim = N_x × N_y, and the maximum number of iterations N_it. Then, initialize the whale population with a random coding matrix X_ini (i = 1, 2, …, N_se). X_ini contains N_dim elements. The elements are 0 or 1. Initialize the best search agent X_be to null matrix and the best score S_be to positive infinity. Next, perform iterative optimization. Calculate the F_fit of each search agent using Equations (3) and (4) and update X_be and S_be if there is a better solution. Update the position of the search agent by encircling prey, spiral bubble-net attacking method, and search for prey. Finally, terminate the loop when the number of iterations reaches the maximum. Obtain the optimized coding matrix X_be and minimum value of S_be.

Furthermore, according to Equation (1), f₀ is a function of F_a. The coding sequence of the metasurface should change as f₀ varies. Therefore, apply VO₂ to tune the metasurface. Use the equivalent complex permittivity ε and conductivity σ to describe VO₂ [36,37]. Based on the Drude model, write ε and σ as:

$$\epsilon \left(\omega \right)={\epsilon }_{\infty }-\frac{{\omega }_p^2\left(\sigma \right)}{{\omega }^2+j\gamma \omega }$$

(5)

$$\sigma \left(\omega \right)=\frac{j{\epsilon }_0{\omega }_p^2\left(\sigma \right)}{\omega +j\gamma }$$

(6)

$${\omega }_p^2\left(\sigma \right)\approx \frac{\sigma }{{\sigma }_0}{\omega }_p^2\left({\sigma }_0\right)$$

(7)

ε_∞ is the permittivity at high frequency, ω_p (σ) is the plasma frequency, and the collision frequency γ equals 5.75 × 10¹³ s⁻¹. ω_p (σ₀) = 1.4 × 10¹⁵ rad/s with σ₀ = 3 × 10³ Ω⁻¹cm⁻¹ and ε_∞ = 12. σ are taken to 200 S/m and 2 × 10⁵ S/m with the insulating and metallic VO₂, respectively. Switching the state of the VO₂ can theoretically realize the dynamic regulation of the metasurface.

At last, apply the PB phase principle to realize the required coding metasurface [31,32,38]. Consider an x-polarized or y-polarized wave incident to the reflective meta-atom along the negative z-direction. Express the incident and reflected waves as:

$${\left[\begin{array}{c}{E}_x\\ E_y\end{array}\right]}_{\mathrm{out}}=\left[\begin{array}{cc}\cos \left(2{\phi }_{rot}\right)& -\sin \left(2{\phi }_{rot}\right)\\ -\sin \left(2{\phi }_{rot}\right)& -\cos \left(2{\phi }_{rot}\right)\end{array}\right]{\left[\begin{array}{c}{E}_x\\ E_y\end{array}\right]}_{\mathrm{in}}$$

(8)

E_x and E_y represent the linearly polarized (LP) waves. φ_rot is the rotation angle of the meta-atom. The CP wave can be composed of two LP waves:

$${\left[\begin{array}{c}{E}_L\\ E_R\end{array}\right]}_{\mathrm{in}}=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& -j\\ 1& j\end{array}\right]{\left[\begin{array}{c}{E}_x\\ E_y\end{array}\right]}_{\mathrm{in}}$$

(9)

$${\left[\begin{array}{c}{E}_L\\ E_R\end{array}\right]}_{\mathrm{out}}=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& j\\ 1& -j\end{array}\right]{\left[\begin{array}{c}{E}_x\\ E_y\end{array}\right]}_{\mathrm{out}}$$

(10)

E_L and E_R are the LCP and RCP waves, respectively. Combine Equations (8)–(10):

$${\left[\begin{array}{c}{E}_L\\ E_R\end{array}\right]}_{\mathrm{out}}=\left[\begin{array}{cc}{e}^{-j2{\phi }_{rot}}& 0\\ 0& e^{j2{\phi }_{rot}}\end{array}\right]{\left[\begin{array}{c}{E}_L\\ E_R\end{array}\right]}_{\mathrm{in}}$$

(11)

Therefore, there is a −2φ_rot (2φ_rot) phase difference between the LCP (RCP) incident wave and the corresponding co-polarized reflected wave. The phase difference, which relates to the incident wave’s polarization state, is the PB phase. φ_rot is limited to 0° and 90° to acquire the same PB phase under LCP and RCP waves.

3. Results and Discussion

3.1. Meta-Atom

Figure 2 displays the structure schematic diagram of the proposed metasurface’s meta-atom. Figure 2a,b indicate the metal-VO₂ resonator, dielectric layer, and metal plate form the meta-atom. The resonator consists of two split-ring resonators (SRRs) labeled SRR 1 and SRR 2. The SRRs embed two patches of VO₂, labeled VO₂ 1 and VO₂ 2. The metal is gold (Au, σ = 4.561 × 10⁷ S/m) with a thickness t_m of 0.2 μm. The VO₂ patch has two states: insulator (σ = 200 S/m) and metal (σ = 2 × 10⁵ S/m). The thickness t_v of the VO₂ is 0.2 μm. The dielectric is silica (SiO₂, ε_r = 3.8) with a thickness t_s of 120 μm. In Figure 2c, the period P of the meta-atom is 280 μm. The radii r₁ and r₂ of SRRs are 120 μm and 80 μm, respectively. The line widths g₁ and g₂ are 10 μm. The angles α₁ and α₂ of arc-shaped VO₂ patches are 5°. The angles between VO₂ patches and the positive x-axis are φ₁ and φ₂, respectively. Owing to the different states of the VO₂ patch, the Au-VO₂ resonator can exhibit various performances. As Figure 2d suggests, when VO₂ 1 and VO₂ 2 are in the insulating and metallic states, respectively, the Au-VO₂ resonator is approximately equivalent to an SRR with a rotation angle φ₁ and a complete ring labeled State 1. SRR 1 works, while SRR 2 is invalid. The meta-atom rotates φ₁. For State 2, the Au-VO₂ resonator is approximately equivalent to an SRR with a rotation angle φ₂ and a complete ring. SRR 1 does not work, while SRR 2 is effective. The meta-atom rotates φ₂. Thus, in theory, switching the state of VO₂ patches can tune the working frequency and the PB phase of the meta-atom under a CP incident wave.

CST Studio Suite 2022 was used to simulate the designed meta-atom. The Frequency Domin Solver and Tetrahedral mesh type were selected. The unit cell boundary condition was applied in the x and y-directions and the open (add space) in the z-direction. The Floquet boundary was set in the z-direction with CP excitation. The Drude dispersion model was adapted to simulate VO₂ with different states. φ₁ and φ₂ were restricted to 0° and 90° to introduce the same PB phase under LCP and RCP waves. For the meta-atom in State 1, Figure 3 and Figure 4 exhibit the simulation result. According to Figure 3a and Figure 4a, for the LCP and RCP normal incident waves, the magnitudes of the co-polarized reflection coefficients R_LL and R_RR are above −1 dB and the cross-polarized reflection coefficients R_RL and R_LR are less than −10 dB in the frequency ranging from 0.18 THz to 0.24 THz. For the LCP incident wave, take φ₁ changes from 0° to 90° with φ₂ = 0° as an example. Figure 3b indicates a phase difference of 180°. For the RCP incident wave, take φ₁ = 0° with φ₂ = 0° and φ₁ = 90° with φ₂ = 90° as an example. The phase difference is also about 180° based on the Figure 4b. It is thus clear that for the meta-atom in State 1, most of the CP incident wave converts into a co-polarized reflected wave within 0.18 THz to 0.24 THz. Furthermore, rotating VO₂ 1 from 0° to 90° can introduce the same phase difference of 180° under LCP and RCP waves.

For State 2 with metallic VO₂ 1 and insulating VO₂ 2, Figure 5 and Figure 6 exhibit the simulation result. According to Figure 5a and Figure 6a, for the LCP and RCP normal incident waves, the magnitudes of R_LL and R_RR are above −2 dB, while R_RL and R_LR are less than −10 dB within 0.35 THz to 0.43 THz. For the LCP incident wave, take φ₂ varies from 0° to 90° with φ₁ = 0° as an example. While for the RCP incident wave, take φ₁ = 0° with φ₂ = 0° and φ₁ = 90° with φ₂ = 90° as an example. Figure 5b and Figure 6b suggest a phase difference of approximately 180°. Therefore, when the meta-atom is in State 2, most of the CP incident wave is converted into the co-polarized reflected wave in the frequency range of 0.35 THz to 0.43 THz. A same phase difference of 180° can be acquired by rotating VO₂ 2 from 0° to 90° under LCP and RCP waves.

For the meta-atom in State 1 and State 2, Figure 7 shows the corresponding electric field distributions at 0.21 THz and 0.39 THz. The resonant structure switches between SRR 1 and SRR 2 by varying the states of VO₂ 1 and VO₂ 2. Moreover, there is a strong field at the opening of the SRR with different φ₁ and φ₂.

Based on the above results, adjusting the states of VO₂ 1 and VO₂ 2 can effectively switch the working frequency band of the meta-atom between 0.18 THz to 0.24 THz and 0.35 THz to 0.43 THz. Controlling the rotation angles φ₁ and φ₂ can easily change the PB phase. In addition, limiting φ₁ and φ₂ to 0° and 90° can bring in the same PB phase of 0° and 180° under the LCP and RCP waves.

3.2. Coding Metasurface

Design a 1-bit coding metasurface for verification. The metasurface consists of 5 × 5 coding elements. Each element contains 4 × 4 meta-atom. PB phases of 0° and 180° denote codes “0” and “1”, respectively. That is, the meta-atom in State 1 with φ₁ = 0° and State 2 with φ₂ = 0° represents “0”, while the meta-atom in State 1 with φ₁ = 90° and State 2 with φ₂ = 90° represents “1”. In Equations (1)–(3), N_x = N_y = 5 and D_x = D_y = 4 × P. Take amplitudes A(n_x,n_y) of meta-atoms equal each other. When the meta-atom operates at 0.18 THz to 0.24 THz, take f₀ = 0.21 THz, θ_i = 0°, and φ_i = 0° as an example for optimization. While the meta-atom operates at 0.35 THz to 0.43 THz, take f₀ = 0.39 THz, θ_i = 0°, and φ_i = 0° as an example for optimization. According to the WOA-based optimization process, set N_se = 120, N_dim = 25, and N_it = 400. Use MATLAB R2017a software to optimize the coding sequence. The optimal Coding Sequences 1 and 2 at 0.21 THz and 0.39 THz are shown in Figure 8a and Figure 8b, respectively. Figure 8c displays the optimal fitness Curve 1 at 0.21 THz and Curve 2 at 0.39 THz. F_fit decreases from 8.21 to 6.58 in Curve 1 and from 10.56 to 7.63 in Curve 2. According to Equation (3), when all of the elements are “0” or “1” in the coding sequence, F_fit equals 25 theoretically. Therefore, using the optimal coding sequence can significantly reduce F_fit.

Figure 9 shows the schematic of the terahertz VO₂-based dynamic coding metasurface for RCS reduction. When the meta-atoms are in State 1, Coding Sequence 1 is activated, and the metasurface can realize effective RCS reduction under the LCP and RCP incident waves with the frequency f₁, polar angle θ₁, and azimuth angle φ₁. When Coding Sequence 2 is in an active state with the meta-atoms in State 2, the metasurface can attain the RCS reduction under the CP incident wave with f₂, θ₂, and φ₂.

CST Studio Suite 2022 was used to analyze the 1-bit coding metasurface. The Time Domin Solver and Hexahedral mesh type were selected. The open (add space) boundary condition was applied in the x, y, and z-directions, and, simultaneously, a metal plate of the same size as the metasurface was simulated for comparison. When the metasurface is in State 1, Figure 10 shows the far-field pattern under the CP incident wave with f₁ = 0.21 THz, θ₁ = 0°, and φ₁ = 0°. For Figure 10a–c, the maximum numbers are −35.5, −35.1, and −22.3. For the metasurface in State 2, Figure 11 shows the far-field pattern under the CP incident wave with f₂ = 0.39 THz, θ₂ = 0°, and φ₂ = 0°. For Figure 11a–c, the maximum numbers are −31, −31.2, and −16.9. In addition, Figure 10e,f and Figure 11e,f displace the corresponding array factor calculated in MATLAB. Figure 10a–d reveal that the metasurface can obtain about a 13 dB RCS reduction. Figure 11a–d exhibit an RCS reduction of 14 dB. Therefore, the simulation result demonstrates that for LCP and RCP waves with θ_i = 0° and φ_i = 0°, switching the state of the VO₂ patch can simultaneously realize an RCS reduction of no less than 10 dB at 0.21 THz and 0.39 THz.

Further, the broadband and wide-angle characteristics of the metasurface were investigated. For the metasurface in State 1, taking the LCP incident wave as an example, f₁ is in the range of 0.18 THz to 0.24 THz. θ₁ and φ₁ vary from 0° to 60° and 0° to 360°, respectively. Figure 12 shows the simulation result. Figure 12a suggests that for the LCP oblique incident wave with φ₁ = 0° and θ₁ = 0°, 20°, and 40°, the RCS reduction is above 10 dB from 0.18 THz to 0.24 THz. Figure 12b indicates that when the LCP wave with θ₁ = 40° and φ₁ = 0°, 30°, 120°, 210°, and 300° obliquely incidents on the metasurface, the RCS reduction is also generally not less than 10 dB at 0.18 THz to 0.24 THz. For the metasurface in State 2, taking the RCP incident wave as an example, Figure 13 reveals that when φ₂ = 0° with θ₂ changing from 0° to 40° and θ₂ = 40° with φ₂ varying from 0° to 360°, the metasurface can maintain a 10 dB RCS reduction from 0.35 THz to 0.43 THz.

Based on the above results, for the LCP and RCP incident waves with the polar angle and the azimuth angle ranging from 0° to 40° and 0° to 360°, respectively, the effective RCS reduction can be realized at 0.18 THz to 0.24 THz and 0.21 THz to 0.39 THz by tuning VO₂.

Table 1. Comparison of this work with previous works.

Ref.	Dynamicity	Polarization	10-dB RCS BW	FBW (%)	Max. θi (°)
[12]	No	RCP	10–24 GHz	82.3	60
[3]	No	x-pol or y-pol	23.71–33.52 GHz (x-pol) 25–37.8 GHz (y-pol)	34.3 (x-pol) 40.8 (y-pol)	37
[13]	No	x-pol and y-pol	7.6–26.2 GHz	110.1	0
[14]	No	x-pol and y-pol	5–40 GHz	155.6	45
[15]	No	x-pol and y-pol	3.5–11.5 GHz	106.7	30
[27]	Yes	x-pol and y-pol	8.52–16.98 GHz	66.4	55
[28]	Yes	x-pol and y-pol	4.5–13.74 GHz	101.3	30
[29]	Yes	x-pol and y-pol	3.8–10.73 GHz	95.4	30
This Work	Yes	LCP and RCP	0.18–0.24 THz 0.21–0.39 THz	28.6 60	40

shows a comparison of this work with previous works. Comparison items include dynamicity, polarization, 10 dB RCS reduction bandwidth (BW), fractional bandwidth (FBW), and max incident angle θ_i. The existing research concentrates on the RCS reduction metasurface with fixed performance working in the microwave band. The proposed VO₂-based dynamic coding metasurface can realize the terahertz dual-polarized, dual-band, and wide-angle RCS reduction.

4. Conclusions

This paper exhibits a method for the terahertz VO₂-based dynamic coding metasurface. This metasurface can realize a dual-polarized, dual-band, and wide-angle RCS reduction. The meta-atom consists of the resonator, dielectric layer, and metal plate. Two SRRs embedded with two patches of VO₂ compose the resonator. The simulation results prove that adjusting the state of VO₂ can effectively change the working frequency band and PB phase of the meta-atom. In addition, limiting the rotation angle to 0° and 90° can introduce the same PB phase of 0° and 180° under the LCP and RCP waves. A 1-bit coding metasurface optimized by the WOA for verification was designed. The simulation results demonstrate that for LCP and RCP vertical incident waves, tuning VO₂ patches between insulating and metallic states can simultaneously realize an RCS reduction of no less than 10 dB at 0.21 THz and 0.39 THz. Furthermore, the simulation results indicate that for the LCP and RCP oblique incident waves with the polar angle, and the azimuth angle ranging from 0° to 40° and 0° to 360°, respectively, the metasurface can maintain the effective RCS reduction at 0.18 THz to 0.24 THz and 0.21 THz to 0.39 THz. This work has potential value in the terahertz stealth field. Moreover, Surface Micro-Electro-Mechanical Systems (MEMS) technology, micro-nano machining technology, and lithography technology could manufacture the proposed metasurface. Testing the far-field pattern in the THz chamber could verify the performance. Heating could induce the VO₂ state transition.