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Abstract
In this paper, a hybrid mechanism metasurface (HMM) employing 1-bit random coding is proposed to achieve polarization-insensitive and dual-wideband monostatic/bistatic radar cross section (RCS) reduction under a wide range of incident angles. The anisotropic unit cell is designed by the combination of the multi-objective particle swarm optimization (MOPSO) algorithm and Python-CST joint simulation, which facilitates the rapid acquisition of the desired unit cell with excellent dual-band absorption conversion capability. The unit cell and its mirrored version are used to represent the units "0" and "1", respectively. In addition, the array distribution with random coding of the units "0" and "1" is optimized under different incident angles, polarizations and frequencies, which enables better diffusion-like scattering. Simulation results demonstrate that the proposed coding HMM can effectively reduce the monostatic/bistatic RCS by over 10 dB within the dual-band frequency ranges of 2.07-3.02 THz and 3.78-4.71 THz. Furthermore, the specular and bistatic RCS reduction performances remain stable at oblique incident angles up to 45° for both TE and TM polarizations.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent years, terahertz (THz) technology has gained substantial attention due to its unique advantages in terms of large bandwidth and high resolution, which has the potential for target detection [1–3], remote sensing [4,5] and environment monitor [6,7] in radar systems. With the rapid growth of THz radar technology, electromagnetic stealth has been drawing increasing interest to reduce the probability of target detection, particularly in military applications. Radar cross section (RCS) serves as a crucial physical parameter for evaluating target stealth capability under radar irradiation [8]. Effective RCS reduction (RCSR) can result in an improved stealth performance of the target. Therefore, it is necessary to investigate the mechanisms and implementations of RCSR.
Metasurfaces are typical 2D ultrathin planar structures capable of manipulating and controlling the phase [9–11], amplitude [12,13], and polarization [14–16] of electromagnetic (EM) waves with unparalleled simplicity and flexibility. With these capabilities, metasurfaces are envisioned as a promising solution for RCSR [17,18]. Traditional approaches employ a single mechanism to achieve RCSR, such as absorption [19,20], polarization conversion [21,22] and phase cancellation [23–26]. While these methods play a certain role in RCSR, their performances are not always satisfying due to limited bandwidth and sensitivity to angle. Fortunately, the hybrid mechanism metasurface (HMM) is an innovative metasurface that integrates the aforementioned mechanisms and can achieve superior RCSR performance [27,28]. Moreover, it should be noted that the HMMs have not been fully investigated, which motivates us to further explore the HMMs in RCSR.
The design can be divided into two components: unit cell and array distribution. For the unit cell design, we aim to adjust the topology of the unit cell to achieve favorable absorption and polarization conversion functionality within the operating frequency band to facilitate subsequent RCSR. Conventional manual-optimization methods heavily rely on the designer’s expertise and intuition [29]. In other words, the complexity of the unit topology makes it difficult to rapidly determine the parameters which play critical roles in the performance of the unit cell, thereby further complicating the design process. To address this issue, some evolutionary optimization techniques have been introduced for the rapid design of metasurface topologies, such as the genetic algorithm (GA) [30,31], particle swarm optimization (PSO) [32], and covariance matrix adaptation evolution strategy (CMA-ES) [33,34]. However, these optimizations all focused on implementing single-band functionality, with relatively less research on achieving dual-band functionality. One reason for this is that optimizing dual-band functionality is regarded as a multi-objective optimization problem, making it tough to obtain optimal solutions due to the mutual influence between objectives. Therefore, seeking ways to accelerate unit cell topologies’ design while optimizing and balancing dual-band performance remains a challenge. For the array distribution design, several coding methods have been proposed to reduce RCS. For instance, chessboard coding, as a periodic coding method, is capable of reducing monostatic RCS significantly, but the backscattered patterns have four strong beams that degrade the performance of bistatic RCSR [35–38]. To achieve a more uniform energy distribution, random coding methods have been devised [39,40]. Nonetheless, they only considered vertical incidence and focused on only a single frequency point, leading to degraded performances in terms of bandwidth and angular stability. Consequently, developing a more comprehensive coding strategy to realize wide-band, wide-angle and polarization-insensitive monostatic/specular and bistatic RCSR is regarded as another challenge.
In this work, to overcome the above two challenges, a fast and effective solution for RCSR within the desired dual-wideband frequency range is provided by the 1-bit random coding HMM. Owing to the integration of polarization conversion, absorption and phase cancellation mechanisms, both suppression of the reflection amplitude and uniform distribution of the energy can be achieved. Firstly, a method combining the multi-objective particle swarm optimization (MOPSO) algorithm with the Python-CST joint simulation is proposed to enable quick design of the unit cell incorporating both the absorption and polarization conversion mechanisms. Specifically, the MOPSO algorithm could avoid the hassle of manual tuning of the structure parameters, while ensuring the widest bandwidth of absorption conversion rate (ACR) exceeding 0.9 simultaneously in both frequency bands. Secondly, units "0" and "1" are adopted to respectively represent the unit cell and its mirrored version. The bistatic RCSR is then comprehensively optimized for various polarizations, incidence angles and frequency points during the optimization of array distribution while considering the integrated effect of absorption and phase cancellation mechanism. The schematic diagram for this work is demonstrated in Fig. 1. This study would inspire further research in the design and optimization of metasurfaces for dual-wideband monostatic/bistatic RCSR with angular stability and polarization insensitivity, and have great application prospects in shape stealth.
Fig. 1. The steps of the proposed HMM design. Firstly, a theoretical absorption prediction is provided from the equivalent circuit model. Secondly, the unit structure is optimized based on the combination of the MOPSO algorithm and Python-CST joint simulation to achieve excellent dual-band absorption conversion capacity. Finally, the array distribution is optimized with random coding, which allows the HMM to exhibit a diffusion-like scattering, ultimately resulting in remarkable RCSR.
2. Theoretical analysis
This section aims to elaborate on the theoretical aspects applied to our design, which is divided into three parts. Firstly, the operating principle of HMM is introduced. Secondly, an equivalent model is established for the proposed four-layer unit structure. By analyzing the equivalent model, the theoretical absorption rate can be predicted, thereby providing theoretical guidance for optimizing the topology structure of subsequent unit cell. Finally, to further illustrate the effects of absorption and phase cancellation on RCSR for the proposed HMM, we give the RCSR mechanism based on array antenna theory, which can be applied in the optimization of the array distribution.
2.1 HMM operating principle analysis
When electromagnetic waves impinge upon the surface of the metamaterial, a portion of the energy is reflected, while the remaining energy is transmitted. Therefore, the absorption of the metamaterial absorber can be expressed as
where $R(\omega )$ and $T(\omega )$ represent the reflectivity and transmissivity, respectively. $S_{11}$ and $S_{21}$ represent the reflection coefficient and transmittance, respectively.Reflective-type unit cells typically have almost perfect reflection characteristics, resulting in an extremely low transmission coefficient that is almost zero. Thus, Eq. (1) can be simplified as
Note that $S_{11}$ in Eq. (2) contains both the co-polarized and cross-polarized parts. When the designed structure uses both absorption and polarization conversion mechanisms, the absorption in Eq. (2) can be expanded as
where $S_{11}^{xx}$ and $S_{11}^{yx}$ represent the reflection coefficient of their co- and cross-polarization for the $x$-polarization incident wave, respectively.To assess the performance of the HMM, the absorption conversion ratio (ACR) is employed, which contains both absorption and polarization conversion. The ACR can be defined as
The polarization conversion can be defined as
2.2 Equivalent circuit model and analysis
As shown in Fig. 1, the designed HMM consists of indium tin oxide (ITO) and polyethylene terephthalate (PET). With a thickness of 0.185 $\mu m$ and a square resistance of 8 $\Omega /\rm {sq}$, the ITO layer resembles a metallic thin film and exhibits excellent surface resistance properties, enabling the structure to demonstrate a high absorptivity performance. PET is selected as a dielectric material (${\varepsilon _r}=3.05$ and $\tan \delta$=0.006).
Compared with the conventional sandwich structure, the four-layer structure has an additional dielectric layer, which can be converted to the corresponding equivalent circuit model, as depicted in Fig. 1. Owing to its exceptional surface resistance properties, the bottom layer ITO can be treated as a perfect electric conductor (PEC), obstructing the propagation of incident electromagnetic waves effectively and thereby resulting in a near-zero $T(\omega )$. Hence, this structure can be equivalently represented as a single-port network according to transmission line theory. The top ITO layer can be modeled as a series connection of resistance $R$, inductance $L$ and capacitance $C$, while the bottom layer ITO can be modeled as the equivalent resistance ${R_g}$. Furthermore, the PET layer can be modeled as a transmission line with corresponding characteristic impedance and electrical length. By the analysis of this model, it becomes feasible to quantitatively evaluate the matching degree between the input impedance ${Z_{in}}$ and the free space impedance ${Z_0}$, thereby enabling the quantitative assessment of absorption.
The impedance ${Z_a}$ and ${Z_b}$ can be expressed as
where ${\beta _1} = \frac {{2\pi f\sqrt {{\varepsilon _ {r}}} }}{c}$, ${Z_1}=\frac {{{Z_0}}}{{\sqrt {\varepsilon _{r}}} }$ and ${t_1}$ represent the propagation constant, the characteristic impedance and the thickness of the PET dielectric layer. $f$ is the frequency of incident electromagnetic waves, and $c$ is the speed of light.Owing to the properties of the bottom layer ITO similar to PEC as mentioned earlier, ${R_g}$ can be approximated as zero. Hence, ${Z_b}$ can be simplified as
The impedance ${Z_c}$ observing from the top ITO layer can be expressed as
Based on the aforementioned derivation, the input impedance ${Z_{in}}$ of the entire HMM when viewed from port 1 can be calculated as
In order to maximize the absorption of HMM, it is crucial that the overall input impedance $Z_{in}$ should be matched to the characteristic impedance $Z_{0}$ of free space, i.e., $Z_{in}=Z_{0}$. Once this condition is met, the values of $R$, $L$, and $C$ can be determined, which can be given by
Thus, exploiting the values of $R$, $L$, and $C$ associated with the equivalent circuit model, the expression for $Z_{in}$ can be derived. From Eq. (2), we can calculate the theoretical absorption $A(\omega )$ as follows:
2.3 RCSR mechanism analysis
The RCSR mechanism can be explicated through a theory akin to that of antenna arrays. Employing the theory in [41], the metasurface’s array factor ($AF$) of the far-field pattern can be mathematically represented as
When analyzing the RCSR of specular direction, the $AF$ can be simplified as
Due to 1-bit coding adopted in the design of the metasurface (MS), with the assumption of the equivalent number of the units "0" and "1", the specular RCSR of oblique incidence compared with equal-sized metal plate can be expressed as
According to Eq. (16), the amplitudes and the phase difference, i.e., $A_0$, $A_1$ and $\Delta \varPhi$, rather than the array distribution of the units, determine the specular RCSR. However, it should be noted that the spatial scattering pattern is predominated by the array distribution of the units. Thus, the bistatic RCSR is introduced to facilitate the subsequent optimization of the distribution of units "0" and "1", which can be expressed as
3. HMM design and analysis
The HMM design comprises two optimization modules, namely the unit and array optimizations. For the optimization of the coding unit, we employ the MOPSO algorithm to optimize the unit structure parameters to achieve excellent dual-wideband ACR. For the optimization of the array distribution, random coding is utilized to optimize the distribution of units "0" and "1", resulting in optimal suppression of bistatic RCS. A flowchart depicting the entire design process is illustrated in Fig. 2.
3.1 Optimization of the 1-bit unit cell based on MOPSO algorithm
Initially, we employ the equivalent circuit model presented in subsection 2.2 to conduct a theoretical calculation of the absorption for the designed metasurface. To enable the metasurface to have the capability of dual-band RCSR within the range of 2-5 THz, the thickness ${t_1}$ of two PET layers is selected as $50\mu m$, as shown in Fig. 1. Accordingly, the frequency response curve of the equivalent resistance $R$ calculated by Eq. (11) is presented in Fig. 3(a), which corresponds to the matching of HMM and free space impedance. It is obvious that double wideband equivalent resistance matching peaks exist within the range of 1.72-5.16 THz. Then, two frequencies are selected within the operating frequency range based on their identical equivalent resistance values from the curve presented in Fig. 3(a). The frequencies chosen are 2.27 THz and 2.88 THz, with corresponding equivalent resistance $R = 195.08 \Omega$. From Eq. (12), the $L$-$C$ curve at these two frequency points can be obtained, as depicted in Fig. 3(b). The intersection of the two $L$-$C$ curves is $(0.002pF,0.002nH)$. Thus far, the variable values required to calculate the theoretical absorption using Eq. (13) have been determined. The absorption curve obtained is illustrated in Fig. 3(c). As observed, the structure exhibits dual-wideband absorption capability within the range of 1.72-5.16 THz. Furthermore, the lower-frequency and higher-frequency bands feature a bandwidth of 0.92 THz and 0.91 THz, respectively, wherein the absorption rate exceeds 0.9.
Fig. 3. (a) Frequency response curves of the equivalent resistance $R$. (b) The equivalent inductance $L$ versus the equivalent capacitance $C$. (c) Absorption calculated by the equivalent circuit model.
According to the theoretical absorption curve presented in Fig. 3(c), the PET-ITO-PET-ITO metasurface structure with four layers has dual wideband absorption capabilities in theory within the range of 1.72-5.16 THz. In addition, it is noteworthy that our intended design aims to utilize a hybrid mechanism to achieve RCSR, where the top ITO layer will use an anisotropic structure with specific polarization conversion capabilities. The anisotropy of the unit cell geometry can convert the incident linearly polarized waves into their orthogonal components, which could rotate the $x$-or $y$-polarized incident waves into its cross-polarized one. Moreover, the symmetric nature of this structure guarantees the polarization insensitivity of the proposed HMM. When it comes to the additional effect of polarization conversion on RCSR, the factor that affects the RCSR transfers from absorption to ACR. Thus, our goal is to design a unit whose ACR can effectively approximate the theoretical values, which can be achieved by optimizing the topological shape and size of the top ITO layer. During the optimization process, it is crucial to consider the potential competition between the ACR of the two frequency bands, as improving the absorption conversion capacity of one frequency band may adversely affect the other frequency band. Therefore, the desire for the unit’s dual-wideband absorbing conversion performance can be treated as a multi-objective optimization problem. The formulated objective function can be expressed as follows:
To enhance and balance the absorption conversion capacity of the two frequency bands, a design scheme based on the MOPSO algorithm is proposed. The MOPSO algorithm is a metaheuristic algorithm designed to solve multi-objective optimization problems with conflicting objectives. The advantages of the MOPSO algorithm have been validated through a comparative analysis conducted between the MOPSO algorithm and three other prominent evolutionary multi-objective optimization (EMO) algorithms [42]. The MOPSO algorithm is the only one capable of covering the complete Pareto front of all the utilized functions. Additionally, it exhibits superior convergence efficiency, accuracy, and computational speed. The MOPSO algorithm consists of several steps, including parameter initialization, fitness evaluation, particle velocity and position calculation, non-dominated sorting and selection based on the Pareto principle and crowding distance calculation methods. Here we will further elaborate on the Pareto principle. This principle is commonly utilized in multi-criteria decision-making to determine whether solutions can be added in the Pareto front, which consists of the set of solutions that cannot be improved in one objective criterion without sacrificing performance in another objective.
Module I in Fig. 2 depicts a flowchart of utilizing the MOPSO algorithm proposed to optimize the unit structure. Based on the advantages of Python programming language such as open source and rich library resources, we choose to use the Python-CST interface supported by CST Microwave Studio. With MOPSO algorithm, the parameters can be updated continuously, which are subsequently utilized for the automatic calling of CST to model the unit cell by home-made code in Python 3.6. By simulating using the frequency domain solver of CST with periodic boundary conditions and Floquet ports, the values of $B_{Lmax}$ and $B_{Hmax}$ can be evaluated. Therefore the Pareto front can be updated until reaching the maximum number of iterations, i.e., $N_{max}$. At this time, we get a global Pareto set. Then we can choose a solution from the global Pareto set as the final solution $gbest$. The particle distribution state, the determined Pareto front, and selected $gbest$ at the last iteration are illustrated in Fig. 4. Additionally, Table 1 presents the unit structure parameters obtained through the optimization.
Fig. 4. The inferior solution, Pareto front and selected $gbest$ produced at the last iteration from the MOPSO algorithm.
Table 1. Optimized parameters of the top layer ITO based on MOPSO algorithm
For the final optimized unit structure, the absorption and polarization conversion mechanisms work together in tandem to minimize reflection upon incidence of waves. Figure 5(a) shows the comparison of theoretical absorption and the simulated ACR, where it can be observed that the unit possesses a maximum continuous bandwidth with an ACR exceeding 0.9 in the lower and higher frequency bands with bandwidths of 0.87 THz and 1 THz, respectively. It closely approximates the ideal absorption calculated from the equivalent circuit. Figure 5(b) provides further insight into the ratio of absorption, conversion, and reflection energies for dual bands. In the lower frequency range of 2.08-2.95 THz, the percentage of absorption and conversion is 71.2% and 24.0%, respectively, with reflection only accounting for 4.8%. Similarly, in the higher frequency range of 3.85-4.85 THz, absorption and conversion account for 74.7% and 20.3%, respectively, while reflection only makes up 5.0%.
Fig. 5. (a) Theoretical absorption, simulated ACR, Absorption and Conversion. (b) The average ratio of the Absorption, Conversion and Reflection for the lower frequency band (2.08-2.95 THz) and the higher frequency band (3.85-4.85 THz) with ACR exceeding 0.9.
To sufficiently describe the unit performance, Fig. 6(a) displays the simulated reflection amplitudes of the unit under $x$- and $y$-polarized normal incidences. The presented results illustrate that the unit is polarization-insensitive. The cross-polarized part’s amplitude is greater than zero, while the co-polarized part’s amplitude decreases, which aligns with our previous analysis that the unit comprises both absorption and polarization. Furthermore, we designate this unit as unit "0" and its mirror structure as unit "1". Figure 6(b) exhibits the reflection phases of cross-polarization as well as the phase difference between units "0" and "1". We observe that the phase difference remains approximately constant at $180^{\circ }$ across the entire frequency ranges, which is beneficial to employing the phase cancellation mechanism for RCSR. Additionally, to provide a more comprehensive and accurate evaluation into the impact of "0" and "1" unit arrangements on RCSR in subsequent array distribution, we provide simulation results of total reflection amplitude, phase, and phase difference in Fig. 6(c) and (d), which take both cross-polarization and co-polarization into account.
Fig. 6. (a) Reflection amplitudes of unit "0" under $x$- and $y$-polarized normal incidences. (b) Reflection phase of cross-polarization and phase difference. (c) Reflection amplitudes under $x$-polarized normal incidences. (d) Reflection phases and phase difference under $x$-polarized normal incidences.
3.2 Optimization of array distribution for coding metasurface
Our design aims to achieve 10 dB RCSR for wide frequency bands under different polarizations and incident angles. Based on the theoretical analysis presented in Subsection 2.3, it is feasible to achieve beam shaping for far-field scattering patterns using an appropriate coding sequence, which can redirect the reflected energy, resulting in the bistatic RCSR. Therefore, in order to scatter the incident EM waves into different main beams as many as possible, it is necessary to optimize the coding matrix.
The flowchart is displayed in Module II of Fig. 2. The proposed array is composed of $6 \times 6$ lattices, with each lattice being a subarray of $3 \times 3$ unit cells. The algorithm is utilized in the following manner:
Step 1: A set of $6 \times 6$ particles are randomly generated within the value range of 0-1. These values are then quantized to either "0" or "1", ensuring that the number of units "0" and "1" is equal. The resulting quantized matrix serves as the unit coding matrix for HMM.
Step 2: Taking into account the coupling effect between adjacent cells, the coding matrix is expanded to an $18 \times 18$ matrix based on the number of units in each lattice.
Step 3: By utilizing the pre-stored reflection amplitude and phase matrices of unit "0" and unit "1" under TE and TM polarized incident waves, with varying incidence angles ($0^{\circ }$, $15^{\circ }$, $30^{\circ }$, and $45^{\circ }$) at $P$ frequencies, the far-field scattering patterns $AF$ and bistatic RCSR of the $18 \times 18$ coding matrix can be calculated using Eq. (15) and Eq. (17). This results in a $P \times 8$ RCSR matrix, which can be represented as
Step 4: We quantize the values of the RCSR matrix obtained above into 0 or 1 based on their magnitude relationship with $-$10 dB, and thus obtain a new $P \times 8$ matrix. The summation of values in this matrix serves as a score for evaluating the bistatic RCSR of the corresponding coding sequence. A smaller score indicates more dispersed reflected energy. Therefore, the objective function can be expressed as
After the iterative optimization of steps 1-4, the optimal array distribution with random coding is obtained, as depicted in Module II of Fig. 2. To highlight the advantages of random coding, we compare it with several conventional coding methods by calculating their 2D far-field scattering patterns at 2.34 THz in theory from Eq. (15), as shown in Fig. 7. The results indicate that for both normal and oblique incidence, the main lobes of the uniform, interval, and chessboard arrays are concentrated into 1, 2, and 4 strong lobes, respectively. In contrast, the main lobes of the random coding array are dispersed in all directions, redirecting the incident electromagnetic waves uniformly in all directions, and forming diffusion-like scattering. As a result, there are no obvious strong lobes for bistatic detection. Additionally, we can observe that the interval, chessboard, and random coding arrays exhibit similar performance for monostatic RCS under normal incidence and specular RCS under oblique incidence. This similarity stems from the fact that these array distributions have an equal number of units "0" and "1", which corroborates our theoretical analysis in Subsection 2.3. Specifically, the arrangement of the units has a negligible effect on the monostatic or specular RCS but has a notable impact on the bistatic RCS.
Fig. 7. Different array distributions and their corresponding 2D far-field scattering patterns of theoretical calculation under normal and oblique incidences at the center frequency of 2.34 THz. (a)-(d) Schematic of array distribution. (e)-(h) 2D far-field scattering patterns under normal incidences. (i)-(l) 2D far-field scattering patterns when the incident angle is $45^{\circ }$.
4. Results and discussion
To visually demonstrate the RCSR performance of the HMM, a 2D bistatic RCS simulation comparison between the HMM and PEC of equal size at 2.34 THz and 3.85 THz under normal incidence is presented in Fig. 8. The results clearly show that the scattering field of the HMM is smaller than that of PEC, thereby indicating the HMM’s excellent capability for bistatic scattering suppression.
Fig. 8. Simulated 2D bistatic RCS comparison between the proposed HMM and equal-sized PEC surface at 2.34 THz and 3.85 THz under normal incidence. (a), (e) $x$-polarized $xoz$-plane. (b), (f) $x$-polarized $yoz$-plane. (c), (g) $y$-polarized $xoz$-plane. (d), (h) $y$-polarized $yoz$-plane.
Furthermore, when the incident angles are $0^{\circ }$, $15^{\circ }$, $30^{\circ }$ and $45^{\circ }$, the 3D scattering patterns of the proposed HMM and equal-sized PEC surface at 2.34 THz are also simulated, as presented in Fig. 9. It is evident that the proposed HMM effectively reduces the amplitude of the scattering field compared with PEC, and redirects the energy in multiple directions with diffusion-like scattering, whether under normal or oblique incidence. Besides, the HMM exhibits polarization insensitivity.
Fig. 9. Simulated 3D scattering patterns comparison between the proposed HMM and equal-sized PEC surface at 2.34 THz when the incident angles are (a) $0^{\circ }$, (b) $15^{\circ }$, (c) $30^{\circ }$ and (d) $45^{\circ }$, respectively.
Figure 10 shows the simulated results of the monostatic/specular RCSR and bistatic RCSR of the proposed HMM compared with the equal-sized PEC under different incidences of $0^{\circ }$, $15^{\circ }$, $30^{\circ }$ and $45^{\circ }$ for both TE and TM polarization. As shown in the Fig. 10, the proposed HMM exhibits excellent dual-band RCSR capability. For both monostatic and bistatic RCSR under the normal incidence of TE and TM polarization, the dual-wideband RCSR over 10 dB is achieved in 2.07-3.02 THz and 3.78-4.71 THz. Additionally, the HMM maintains stable dual-wideband RCSR capability with incidence angle variation from $0^{\circ }$ to $45^{\circ }$. The proposed HMM could be fabricated with the standard photolithography techniques as demonstrated in [43] in practical applications. Finally, to show the advantages of the proposed HMM, Table 2 compares the performances with those of previous researches. It is apparent that the proposed HMM shows superior performance in terms of all listed metrics.
Fig. 10. Simulated monostatic and specular RCSR of the HMM under four different incident waves for (a) TE polarization and (b) TM polarization. Simulated bistatic RCSR of the HMM under four different incident waves for (c) TE polarization and (d) TM polarization.
Table 2. Performances comparison between this work and previous researches
5. Conclusion
In summary, a novel design is presented to obtain a 1-bit coding HMM with dual-wideband RCSR in THz band. To acquire a unit cell with dual-wideband ACR, the MOPSO algorithm and Python-CST joint simulation are combined to rapidly optimize the unit cell structure, which can enhance and balance the ACR in the two bands effectively. Moreover, we optimize the array distribution with random coding considering the integrated effects of absorption and phase cancellation under incidences of different angles and polarizations at different frequencies. This approach enables redirection and uniform distribution of energy, leading to outstanding bistatic RCSR performance. Simulation results show that the proposed HMM can achieve over 10 dB monostatic/bistatic RCSR within the dual frequency bands of 2.07-3.02 THz and 3.78-4.71 THz. Besides, it features angular stability and polarization insensitivity at oblique incident angles up to $45^{\circ }$ for both TE and TM polarizations. This work provides a solution to design low RCS metasurfaces, specifically for the dual-band requirement, with great potential in shape stealth in the THz regime.
Funding
National Key Research and Development Program of China (2022YFF0604801); National Natural Science Foundation of China (62171186, 62201037, 62271056); Beijing Municipal Natural Science Foundation-Haidian Original Innovation Joint Fund (L222042); Basic Research Foundation of Beijing Institute of Technology, China (BITBLR2020014); 111 Project (B14010).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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