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

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.


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, First, consider a coding metasurface arranged in a rectangular grid on the xoy plane.There are N x and N y elements in the xand y-directions, respectively.The distances between the elements are D x and D y in the xand 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 ϕ 1 introduced by the element, the phase delay ϕ 2 caused by the element's spatial position, and the phase delay ϕ 3 caused by the incident wave.For the n x n y th element, ϕ 2 and ϕ 3 can be written as: 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: The wave number k 0 = 2πC/f 0 , C is the wave velocity in free space, and f 0 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: 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 .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 Ffit is the maximum value of Fa.Express Ffit as: Figure 1 shows the WOA-based optimization process.Firstly, set the number of search agents Nse, the number of variables Ndim = Nx × Ny, and the maximum number of iterations Nit.Then, initialize the whale population with a random coding matrix Xini (i = 1, 2, …, Nse).Xini contains Ndim elements.The elements are 0 or 1. Initialize the best search agent Xbe to null matrix and the best score Sbe to positive infinity.Next, perform iterative optimization.Calculate the Ffit of each search agent using Equations (3) and ( 4) and update Xbe and Sbe 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 Xbe and minimum value of Sbe.Furthermore, according to Equation (1), f0 is a function of Fa.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: ε∞ is the permittivity at high frequency, ωp (σ) is the plasma frequency, and the collision frequency γ equals 5.75 × 10 13 s −1 .ωp (σ0) = 1.4 × 10 15 rad/s with σ0 = 3 × 10 3 Ω −1 cm −1 and ε∞ = 12.σ are taken to 200 S/m and 2 × 10 5 S/m with the insulating and metallic VO2, Furthermore, according to Equation (1), f 0 is a function of F a .The coding sequence of the metasurface should change as f 0 varies.Therefore, apply VO 2 to tune the metasurface.Use the equivalent complex permittivity ε and conductivity σ to describe VO 2 [36,37].Based on the Drude model, write ε and σ as: ε ∞ is the permittivity at high frequency, ω p (σ) is the plasma frequency, and the collision frequency γ equals 5.75 × 10 13 s −1 .ω p (σ 0 ) = 1.4 × 10 15 rad/s with σ 0 = 3 × 10 3 Ω −1 cm −1 and ε ∞ = 12.σ are taken to 200 S/m and 2 × 10 5 S/m with the insulating and metallic VO 2 , respectively.Switching the state of the VO 2 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: 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: E L and E R are the LCP and RCP waves, respectively.Combine Equations ( 8)-( 10): 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.

Meta-Atom
Figure 2 displays the structure schematic diagram of the proposed metasurface's meta-atom.Figure 2a,b indicate the metal-VO 2 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 VO 2 , labeled VO 2 1 and VO 2 2. The metal is gold (Au, σ = 4.561 × 10 7 S/m) with a thickness t m of 0.2 µm.The VO 2 patch has two states: insulator (σ = 200 S/m) and metal (σ = 2 × 10 5 S/m).The thickness t v of the VO 2 is 0.2 µm.The dielectric is silica (SiO 2 , 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 r 1 and r 2 of SRRs are 120 µm and 80 µm, respectively.The line widths g 1 and g 2 are 10 µm.The angles α 1 and α 2 of arc-shaped VO 2 patches are 5 • .The angles between VO 2 patches and the positive x-axis are φ 1 and φ 2 , respectively.Owing to the different states of the VO 2 patch, the Au-VO 2 resonator can exhibit various performances.As Figure 2d suggests, when VO 2 1 and VO 2 2 are in the insulating and metallic states, respectively, the Au-VO 2 resonator is approximately equivalent to an SRR with a rotation angle φ 1 and a complete ring labeled State 1. SRR 1 works, while SRR 2 is invalid.The meta-atom rotates φ 1 .For State 2, the Au-VO 2 resonator is approximately equivalent to an SRR with a rotation angle φ 2 and a complete ring.SRR 1 does not work, while SRR 2 is effective.The meta-atom rotates φ 2 .Thus, in theory, switching the state of VO 2 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 VO 2 with different states.φ 1 and φ 2 were restricted to 0 • and 90 • to introduce the same PB phase under LCP and RCP waves.For the meta-atom in State 1, Figures 3 and 4 exhibit the simulation result.According to Figures 3a and 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 φ 1 changes from 0 • to 90 • with φ 2 = 0 • as an example.Figure 3b indicates a phase difference of 180 • .For the RCP incident wave, take φ 1 = 0 • with φ 2 = 0 • and φ 1 = 90 • with φ 2 = 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 VO 2 1 from 0 • to 90 • can introduce the same phase difference of 180 • under LCP and RCP waves.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, Figures 3 and 4 exhibit the simulation result.According to Figures 3a and 4a, for the LCP and RCP normal incident waves, the magnitudes of the co-polarized reflection coefficients RLL and RRR are above −1 dB and the cross-polarized reflection coefficients RRL and RLR 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 VO 2 1 and insulating VO 2 2, Figures 5 and 6 exhibit the simulation result.According to Figures 5a and 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 φ 2 varies from 0 • to 90 • with φ 1 = 0 • as an example.While for the RCP incident wave, take φ 1 = 0 • with φ 2 = 0 • and φ 1 = 90 • with φ 2 = 90 • as an example.Figures 5b and 6b  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 VO 2 1 and VO 2 2.Moreover, there is a strong field at the opening of the SRR with different φ 1 and φ 2 .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 φ2.0° and 90° respectively, the phase of RRR.
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.

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 φ 1 = 0 • and State 2 with φ 2 = 0 • represents "0", while the meta-atom in State 1 with φ 1 = 90 • and State 2 with φ 2 = 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 f 0 = 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 f 0 = 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 Figures 8a and 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 VO 2 -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 f 1 , polar angle θ 1 , and azimuth angle φ 1 .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 f 2 , θ 2 , and φ 2 .
optimal Coding Sequences 1 and 2 at 0.21 THz and 0.39 THz are shown in Figure 8a and 8b, respectively.Figure 8c displays the optimal fitness Curve 1 at 0.21 THz and Curve 2 at 0.39 THz.Ffit 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, Ffit equals 25 theoretically.Therefore, using the optimal coding sequence can significantly reduce Ffit.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, Figures 10e,f and 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 θi = 0° and φi = 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.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 f 1 = 0.21 THz, θ 1 = 0 • , and φ 1 = 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 f 2 = 0.39 THz, θ 2 = 0 • , and φ 2 = 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 VO 2 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  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 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, f 1 is in the range of 0.18 THz to 0.24 THz.θ 1 and φ 1 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 φ 1 = 0 • and θ 1 = 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 θ 1 = 40 • and φ 1 = 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 φ 2 = 0 • with θ 2 changing from 0 • to 40 • and θ 2 = 40 • with φ 2 varying from 0 • to 360 • , the metasurface can maintain a 10 dB RCS reduction from 0.35 THz to 0.43 THz.
Nanomaterials 2024, 14, x FOR PEER REVIEW 12 is in the range of 0.18 THz to 0.24 THz.θ1 and φ1 vary from 0° to 60° and 0° to 360° spectively.Figure 12 shows the simulation result.Figure 12a suggests that for the oblique incident wave with φ1 = 0° and θ1 = 0°, 20°, and 40°, the RCS reduction is abov dB from 0.18 THz to 0.24 THz. Figure 12b indicates that when the LCP wave with θ1 = and φ1 = 0°, 30°, 120°, 210°, and 300° obliquely incidents on the metasurface, the RC duction is also generally not less than 10 dB at 0.18 THz to 0.24 THz.For the metasur in State 2, taking the RCP incident wave as an example, Figure 13 reveals that when 0° with θ2 changing from 0° to 40° and θ2 = 40° with φ2 varying from 0° to 360° 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 a and the azimuth angle ranging from 0° to 40° and 0° to 360°, respectively, the effec RCS reduction can be realized at 0.18 THz to 0.24 THz and 0.21 THz to 0.39 THz by tu VO2.Table 1 shows a comparison of this work with previous works.Comparison it include dynamicity, polarization, 10 dB RCS reduction bandwidth (BW), fracti Nanomaterials 2024, 14, x FOR PEER REVIEW 12 is in the range of 0.18 THz to 0.24 THz.θ1 and φ1 vary from 0° to 60° and 0° to 360° spectively.Figure 12 shows the simulation result.Figure 12a suggests that for the oblique incident wave with φ1 = 0° and θ1 = 0°, 20°, and 40°, the RCS reduction is abov dB from 0.18 THz to 0.24 THz. Figure 12b indicates that when the LCP wave with θ1 = and φ1 = 0°, 30°, 120°, 210°, and 300° obliquely incidents on the metasurface, the RCS duction is also generally not less than 10 dB at 0.18 THz to 0.24 THz.For the metasur in State 2, taking the RCP incident wave as an example, Figure 13 reveals that when 0° with θ2 changing from 0° to 40° and θ2 = 40° with φ2 varying from 0° to 360°, 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 a and the azimuth angle ranging from 0° to 40° and 0° to 360°, respectively, the effec RCS reduction can be realized at 0.18 THz to 0.24 THz and 0.21 THz to 0.39 THz by tu VO2.Table 1 shows a comparison of this work with previous works.Comparison it include dynamicity, polarization, 10 dB RCS reduction bandwidth (BW), fracti 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 VO 2 .Table 1 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 VO 2 -based dynamic coding metasurface can realize the terahertz dual-polarized, dual-band, and wide-angle RCS reduction.

Conclusions
This paper exhibits a method for the terahertz VO 2 -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 VO 2 compose the resonator.The simulation results prove that adjusting the state of VO 2 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 VO 2 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 VO 2 state transition.

Figure 2 .
Figure 2. The schematic diagram of the meta-atom: (a) Three-dimensional structure; (b) Side view; (c) Vertical view; (d) The approximate equivalent structure of the Au-VO 2 resonator.
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 VO 2 2 from 0 • to 90 • under LCP and RCP waves.

Figure 3 .
Figure 3.For the meta-atom in State 1 with φ1 and φ2 limited to 0° and 90°, the simulated co-polarized reflection coefficient RLL and the cross-polarized reflection coefficient RRL under the LCP normal incident wave: (a) The magnitude of RLL and RRL; (b) When φ1 changes from 0° to 90° with φ2 = 0°, the phase of RLL.

Figure 4 .
Figure 4.For the meta-atom in State 1 with φ1 and φ2 limited to 0° and 90°, the simulated co-polarized reflection coefficient RRR and the cross-polarized reflection coefficient RLR under the RCP normal incident wave: (a) The magnitude of RRR and RLR; (b) When φ1 changes from 0° to 90° with φ2 = 0° and 90° respectively, the phase of RRR.

Figure 3 . 15 Figure 3 .
Figure 3.For the meta-atom in State 1 with φ 1 and φ 2 limited to 0 • and 90 • , the simulated co-polarized reflection coefficient R LL and the cross-polarized reflection coefficient R RL under the LCP normal incident wave: (a) The magnitude of R LL and R RL ; (b) When φ 1 changes from 0 • to 90 • with φ 2 = 0 • , the phase of R LL .

Figure 4 .
Figure 4.For the meta-atom in State 1 with φ1 and φ2 limited to 0° and 90°, the simulated co-polarized reflection coefficient RRR and the cross-polarized reflection coefficient RLR under the RCP normal incident wave: (a) The magnitude of RRR and RLR; (b) When φ1 changes from 0° to 90° with φ2 = 0° and 90° respectively, the phase of RRR.

Figure 4 .
Figure 4.For the meta-atom in State 1 with φ 1 and φ 2 limited to 0 • and 90 • , the simulated co-polarized reflection coefficient R RR and the cross-polarized reflection coefficient R LR under the RCP normal incident wave: (a) The magnitude of R RR and R LR ; (b) When φ 1 changes from 0 • to 90 • with φ 2 = 0 • and 90 • respectively, the phase of R RR .

Figure 5 .
Figure 5.For the meta-atom in State 2 with φ1 and φ2 limited to 0° and 90°, the simulated co-polarized reflection coefficient RLL and the cross-polarized reflection coefficient RRL under the LCP normal incident wave: (a) The magnitude of RLL and RRL; (b) When φ2 changes from 0° to 90° with φ1 = 0°, the phase of RLL.

Figure 5 .
Figure 5.For the meta-atom in State 2 with φ 1 and φ 2 limited to 0 • and 90 • , the simulated co-polarized reflection coefficient R LL and the cross-polarized reflection coefficient R RL under the LCP normal incident wave: (a) The magnitude of R LL and R RL ; (b) When φ 2 changes from 0 • to 90 • with φ 1 = 0 • , the phase of R LL .Nanomaterials 2024, 14, x FOR PEER REVIEW 8 of 15

Figure 6 .
Figure 6.For the meta-atom in State 2 with φ1 and φ2 limited to 0° and 90°, the simulated co-polarized reflection coefficient RRR and the cross-polarized reflection coefficient RLR under the RCP normal incident wave: (a) The magnitude of RRR and RLR; (b) When φ2 changes from 0° to 90° with φ1 = 0° and 90° respectively, the phase of RRR.

Figure 6 .
Figure 6.For the meta-atom in State 2 with φ 1 and φ 2 limited to 0 • and 90 • , the simulated co-polarized reflection coefficient R RR and the cross-polarized reflection coefficient R LR under the RCP normal incident wave: (a) The magnitude of R RR and R LR ; (b) When φ 2 changes from 0 • to 90 • with φ 1 = 0 • and 90 • respectively, the phase of R RR .

Figure 7 .
Figure 7.The electric field distribution of the meta-atom: (a) For meta-atom in State 1, the corresponding electric field distributions at 0.21 THz; (b) For meta-atom in State 2, the corresponding electric field distributions at 0.39 THz.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

Figure 7 .
Figure 7.The electric field distribution of the meta-atom: (a) For meta-atom in State 1, the corresponding electric field distributions at 0.21 THz; (b) For meta-atom in State 2, the corresponding electric field distributions at 0.39 THz.Based on the above results, adjusting the states of VO 2 1 and VO 2 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 φ 1 and φ 2 can easily change the PB phase.In addition, limiting φ 1 and φ 2 to 0 • and 90 • can bring in the same PB phase of 0 • and 180 • under the LCP and RCP waves.

Figure 9
Figure9shows 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.

Figure 9 .
Figure 9.The schematic of the terahertz VO 2 -based dynamic coding metasurface.

Figure 10 .
Figure 10.For the metasurface in State 1, the simulation result under the CP incident wave with f1 = 0.21 THz, θ1 = 0°, and φ1 = 0°.The far-field pattern simulated in CST: (a) The LCP incident wave; (b) The RCP incident wave; (c) The metal plate; (d) 2D far-field pattern; The array factor calculated in MATLAB: (e) Coding sequence 1; (f) The elements of the coding sequence are "1".

Figure 11 .
Figure 11.For the metasurface in State 2, the simulation result under the CP incident wave with f2 = 0.39 THz, θ2 = 0°, and φ2 = 0°.The far-field pattern simulated in CST: (a) The LCP incident wave; (b) The RCP incident wave; (c) The metal plate; (d) 2D far-field pattern; The array factor calculated in MATLAB: (e) Coding sequence 2; (f) The elements of the coding sequence are "1".

Figure 11 .
Figure 11.For the metasurface in State 2, the simulation result under the CP incident wave with f2 = 0.39 THz, θ2 = 0°, and φ2 = 0°.The far-field pattern simulated in CST: (a) The LCP incident wave; (b) The RCP incident wave; (c) The metal plate; (d) 2D far-field pattern; The array factor calculated in MATLAB: (e) Coding sequence 2; (f) The elements of the coding sequence are "1".

Figure 11 .
Figure 11.For the metasurface in State 2, the simulation result under the CP incident wave with f 2 = 0.39 THz, θ 2 = 0 • , and φ 2 = 0 • .The far-field pattern simulated in CST: (a) The LCP incident wave; (b) The RCP incident wave; (c) The metal plate; (d) 2D far-field pattern; The array factor calculated in MATLAB: (e) Coding sequence 2; (f) The elements of the coding sequence are "1".

Table 1 .
Comparison of this work with previous works.