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Abstract
In this paper, a polarization modulated metasurface to improve the magnitude and expand the bandwidth of radar cross section (RCS) reduction is presented. Two physical mechanisms are responsible for the reflection diffusion of the proposed metasurface. One is the functionality of controlling the spatial distribution of polarization response, and the other is the capability of spanning the entire 2π phase range by making full use of the variable sizes and height difference of unit cells to achieve superwideband phase cancellation. A 10 dB monostatic RCS reduction is obtained from 3.87 to 92.89 GHz (a ratio bandwidth of 24:1) for both polarizations under normal incidence by simulation, which is identical to experimental results and theoretical analysis. The proposed method for suppressing vector fields in an extremely wide band may hold promising potentials for suppression of acoustic, electromagnetic, optical and other elastic waves.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials, which can be applied to transmit, reflect and absorb electromagnetic (EM) waves, have been extensively studied in recent years [1,2]. Metasurfaces are thin planar metamaterials that can control EM characteristics by placing subwavelength elements into a 2D pattern [3,4]. In the microwave regime, devices based on metasurfaces have been explored and proved to be available in the designs of antennas, frequency selective surface (FSS) and sensors [5–7]. In the case of reflection, metasurfaces provide the freedom to manipulate the amplitude, phase and polarization mode of EM waves, so they offer a good platform to realize scattering-signature reduction. The radar cross section (RCS) reduction techniques typically make objects transparent to EM waves so as not to be detected by enemy radar. Conventionally, it can be achieved by coating the targets with a material that can absorb the undesired scattering [8] or by optimizing their shapes so that the reflected wave changes its scattering direction [9]. The FSS absorber is a kind of functional material that can effectively absorb the incident EM waves and significantly reduce the intensity of the target echo to improve its stealth performance [10]. Multilayer FSS resistances were introduced in [11,12], which come at the expense of high thickness and large weight in exchange for broadband absorption features. For materials applied to stealth targets, the metasurface using artificially designed structures suffers from the advantage of light weight and low cost compared to absorbing materials. The reflection amplitude property of the meta-atom is controlled to realize different energies being transmitted into the multiple beams [13–15]. The abrupt phase on the interface can be introduced by changing the geometric parameters to realize the phase regulation of the EM waves [16–18]. Loading appropriate meta-atoms with two unit cells equal in amplitude and a phase difference of 180° can realize opposite phase cancellation (OPC) [19,20], however these metasurfaces are incapable of reducing the RCS in a wide band. In [21], the concept of coding metasurfaces is proposed, which assigns each unit cell a binary digit and the reflection phase is quantized and replaced with a coding sequence, then diffuse scattering of EM waves is realized by randomly arranging the sequence [22]. A checkerboard metasurface based on optimized multielement phase cancellation is designed in [23] and a 10 dB RCS reduction from 5.5 to 32.3 GHz (a bandwidth ratio of 5.87:1) under normal incidence is observed, in which the range of phase shifting can be further extended by combining multi-element in a wide band. The absorptive coding metasurfaces that reduce the backscattering in wideband is another approach to diffuse the reflected energy [24–26]. A triple-layer FSS absorbers structure based on high capacitance conductors is designed to achieve low backscattering in [27], which exhibits -10 dB reflection loss with a bandwidth ratio of 12.4:1. Polarization state is an intrinsic property of EM waves [28] and polarization conversion metasurface (PCM) is very highly desirable for stealth due to its capacity for polarization rotation to its orthogonal direction. Many PCMs have been designed to realize RCS reduction in narrow single-band or multi-band [29–31]. It is hard enough to design a unit cell with higher polarization conversion ratio (PCR), and even more difficult to select an element that achieves a higher conversion ratio in a wide band [32–34]. By changing one or more physical dimensions of EM waves, including time, amplitude, phase, and polarization, metasurfaces can be employed to achieve desired functions [35–38]. To date, the RCS reduction-related technologies have problems such as bandwidth expansion difficulty, reduction magnitude limitation, angle and polarization instability, etc. Increasing the phase control range and simultaneously adjusting the magnitude of the element's reflection coefficient to expand the bandwidth of RCS reduction become particularly feasible.
In this work, a metasurface is proposed to realize RCS reduction more than 10 dB in extremely-wideband (the fractional bandwidth (FBW) of 184%). Specifically, this metasurface is designed by considering two aspects. Meta-atoms with polarization conversion function are adopted to reduce the reflection energy of co-polarization. A physical mechanism of the multivariate phase destructive interference is proposed for low RCS in wider bandwidth. The metasurface formed by the selected unit cells of multiple geometry parameters can realize variable phase difference between them, thereby achieving a significant improvement in the bandwidth of destructive interference. The measurements of the proposed metasurface have been carried out to validate the effect of the RCS reduction in ultra-wideband, which agree well with the theoretical analysis and simulations.
2. Design and analysis of the metasurface
Figure 1 schematically illustrates the mechanism of the designed metasurface to regulate EM waves in the polarization domain combined with the multivariate phase destructive interference. The metasurface is composed of an array of polarization conversion unit cells with variable geometry parameters. The two degrees of freedom of the polarization conversion and the variable phase difference between elements are fully exploited, which exhibits much stronger control capabilities on EM waves and overcomes the issues of narrow bandwidth for RCS reduction. Specifically, the co-polarized RCS reduction is partly achieved by controlling the spatial distribution of polarization response. When the size and thickness of the diverse meta-atoms are carefully tuned, the variable phase differences between them will be generated to increase the ability to achieve extremely wideband phase cancellation, that is, the destructive interference compensates for the strong reflection characteristics due to the low polarization conversion ratio. A flow chart for designing the metasurface is depicted in Fig. 2. First, the polarization conversion unit cells with variable geometry parameters, correspondingly with different polarization conversion capabilities and varying reflection coefficients is selected. Second, the array pattern synthesis theory combined with the PSO algorithm is employed to optimize and determine the geometric parameters of the unit cells for the maximum RCS reduction in extremely wideband. Then the metasurface is modeled and simulated numerically. Finally, the RCS reduction performance of the metasurface is validated by experiments.
Fig. 1. The conceptual sketch of the proposed metasurface with modulation of EM waves in the polarization domain combined with the multivariate phase destructive interference.
2.1 Polarization domain manipulation
By rotating the polarization of the incident wave by 90° to the cross polarization, the polarization conversion metasurfaces can be used to reduce the reflected energy of co-polarization. This kind of structure as a spatial converter of EM waves can be used to control the scattered waves by changing the amplitude of the reflection coefficient of the unit cells. The unit cell of the proposed metasurface is composed of a metal patch, a substrate, and a metal coating as ground, as shown in Fig. 3(a). The substrate has a thickness of h, a relative permittivity of 6 and a loss tangent of 0.001. The period of the unit cell is p = 10 mm, and the width of the metal patch is w = 0.4 mm. The inside length of the unit cell is L. The full-wave simulation software CST Microwave Studio (by frequency domain solver) is used, and periodic boundary conditions are applied to the unit cell to generate an infinite structure. Parameter sweeping simulation results show that unit cells with various geometric parameters are endowed with different reflection coefficients. And two unit cells with L = 2.2 mm, h = 0.93 mm (unit 1) and L = 4.8 mm, h = 3.93 mm (unit 2) are taken as examples respectively, whose PCR are shown in Fig. 3(b). It is worth mentioning that the fixed-size unit cell has resonance points at different frequencies, where the co-polarization energy is mainly reflected in the cross-polarization direction. As can be seen, the PCR of the unit 1 is higher than 95% at 15 and 34.5 GHz, which means that incident y polarized EM wave were converted to x polarized wave in reflection. The co-polarized RCS can be extremely reduced at these individual frequencies where the co-polarized reflection approaches 0. However, at non-resonant points, the co-polarization energy is still relatively high, which is not in accordance with the aforementioned criteria for converting the energy perfectly. Therefore, it is not feasible enough to achieve wideband RCS reduction solely relying on the polarization conversion characteristics of a certain unit cell. The combination of these two unit cells may have the potential to expand the bandwidth for RCS reduction, because unit 2 can realize polarization conversion at the frequency different from that of unit 1, that is, around 11.7 GHz. We proposed to combine polarization conversion with the multivariate phase destructive interference.
Fig. 3. (a) The schematic diagram of the PCM with EM waves control in the polarization domain and the perspective view of the geometry of the designed unit cell, (b) the PCR of the two unit cells.
2.2 Multivariate phase destructive interference
The process of OPC can be represented by a vector, which is the superposition of the scattered fields of equal amplitude and opposite phases of two elements. To realize the suppression of the broadband backscattered fields, we propose the multivariate phase destructive interference, which adopts the unit cell of various heights and sizes to extend the cancellation process of the scattered fields to the 2-D plane. The manipulation of EM waves can be described by the operation of phasors. The EM waves can be expressed mathematically in terms of time-varying electric fields. Assuming that the EM wave propagates along the positive z direction and the polarization direction is along the x axis, and in the plane where z is equal to a constant, the instantaneous expression of the EM wave can be abbreviated as [39]
where the Exm is the amplitude of scattered field and ϕx is the corresponding phase information, ω and t are angular frequency and time respectively. This paper uses the phasor method to represent the phase relationship of scattered waves, that is, the regulation of EM waves can be converted to the frequency domain to explain.The phasor representation of Eq. (1) is written as
The scattered waves at the same frequency can be superimposed using phasors, and its process of superposition and cancellation can be represented by a phasor diagram. For example, for a meta-atom with a certain size in the upper metal layer and a fixed reference surface, when substrates adopt different heights to form a metasurface, here the time delay tn is introduced due to the wave path difference, and EM wave is expressed as
For example, when the amplitudes of the scattered fields of two lattices are equal (${E_{1m}} = {E_{2m}}$) but the phase difference between them does not satisfy 180°, for $\dot{{E_2}}= {E_2}\angle {\phi _2}$, the delay caused by the height difference can be introduced, and the corresponding phasor after delay adjustment is
and the phase relationship can be regulated to satisfy ${\phi _2} + {\omega _1}{t_1} - {\phi _1} = 180^\circ $. This process can be expressed as phase rotation in the phasor domain so that the two have opposite phases. Then $\cdot{{E_1}}+ \dot{E_2^{\prime}} = 0$, and this is also an example of OPC, whose phasor diagram is shown in Fig. 4, through the time delay t1, the EM waves are regulated to achieve destructive interference. However, wideband RCS reduction cannot be achieved due to the problems of grating lobes and high-order resonances.Fig. 4. The regulation of EM waves of OPC. (a) The introduction of time delay, (b) the phasor representation.
When it comes to multi-element (N > 2), this situation is here called the multivariate phase destructive interference. As long as the phasor cancellation is satisfied, the scattered fields can be canceled, and the possibility of phase cancellation in the ultra-wideband is considered as much as possible, which greatly enhances the ability of destructive interference. Instead of the conventional OPC that accomplishes vector cancellation based on only two elements, the multivariate phase destructive interference extends the superposition of scattered fields into the 2-D plane and can handle nonlinear problems better than OPC. Here, taking the ternary phase cancellation as an example, the process is represented by a phasor diagram in Fig. 5(a) and (b), after the two time delays t2 and t3, the combination of various thicknesses and sizes of elements can achieve destructive interference at another frequency point.
Fig. 5. The regulation of EM waves in the 2-D plane of the multivariate phase destructive interference. (a) The introduction of time delays and (b) the phasor representation of the ternary phase cancellation, (c) phasor representation for destructive interference.
In fact, any number of phasors can be canceled as long as they meet end-to-end to form a closure, as shown in Fig. 5(c), and by analogy, there are diverse combination of unit cells to achieve destructive interference at different frequency points, which can reduce RCS in an ultra wideband. Its root cause is the variable phase difference caused by the variable sizes and the height difference of the unit cells, and the combination of multiple unit cells makes the control of EM waves more flexible.
2.3 Optimization design
The combination of the multivariate phase destructive interference in the 2-D plane and the polarization conversion greatly improves the degree of freedom of the regulation of EM waves. Instead of basing on only two elements with strict requirements on amplitude and phase, multiple of elements with unfixed geometries provide more options to reach the minimum RCS in ultra-wideband. The key is how to choose the best geometric parameters of the unit cells, that is, to find the best N sets of data from the reflection curve of the full-wave simulation. Due to the high computational complexity of the traversal method, the PSO algorithm is used here to quickly select the appropriate specific size of the N lattices. The PSO is a population-based optimization technique [40] and a combination of parameters L and h denotes a particle in a population. We consider multiple frequency points in the range from 2 to 100 GHz to achieve broadband RCS reduction. The side length L is set from 0.4 to 9 mm in the simulation, with a step size of 0.1 mm, and the corresponding layer thickness for the dielectric substrate h is set from 0.93 to 7.93 mm, with 1 mm as the step size. The process is that varying structural parameters L and h of the unit cells correspond to changing reflection coefficients, and then the reflection coefficients are used to calculate the backward RCS, which are mapped to evaluate fitness values of all selected frequency points. Until the sum of fitness values reaches the desired value, the update iteration is stopped, and the structural parameters of the entire metasurface are determined with the best RCS reduction. Here, we take a metasurface containing 5 × 5 lattices as an example, after 1000 iterations, the fitness function gradually converges to a stable value. And the obtained optimized geometric dimensions of the 25 unit cells with the lowest backward RCS are listed in Table 1. The frequency-dependent amplitude and phase response distributions of the 25 unit cells at corresponding positions on the metasurface are shown in Fig. 6. The amplitude range covers 0 to 1, and the phase changes continuously from 0 to 2π. The theoretical prediction of RCS reduction greater than 10 dB is realized in the frequency range of 3.75 to 92 GHz as shown in Fig. 7(a). It can be seen that the proposed technique combining the multivariate phase destructive interference with polarization conversion can greatly broaden the bandwidth of RCS reduction by adjusting the reflection amplitude and phase of the unit cells.
Fig. 6. Distributions of the (a) amplitude and (b) phase response of unit cells of the proposed metasurface.
Fig. 7. (a) The predicted monostatic RCS reduction. (b) Full model of the optimized metasurface. The inserted number is the lattice index shown in Table 1.
Table 1. Optimized geometrical parameters L and h of 25 lattices (unit: mm)
3. Simulation and measurement
To verify the theoretical analysis, full-wave simulations and prototype measurements were carried out to demonstrate the performance of the designed metasurface. The RCS reductions at both normal and oblique incidences are also analyzed.
3.1 Numerical simulation
A full structure of the proposed metasurface was simulated as shown in Fig. 7(b), which is composed of 900 unit cells in 25 lattices. To facilitate fabrication, we stack the unit cells with substrates of the same height together. The simulated monostatic RCS of the designed metasurface under the normal incidence of the x and y polarizations are shown in Fig. 8(a). Compared with the RCS value of a metallic plate of the same size, a 10 dB RCS reduction of the metasurface is obtained from 3.87 to 92.89 GHz (FBW of 184%) for both polarizations, where the ratio bandwidth (${f_H}/{f_L}$) reaches 24:1. The numerical simulation results coincide well with the theoretical analysis results in Fig. 7(a), and the subtle difference between them can be attributed to the coupling effects between the adjacent lattices not considered in the theoretical calculation. The results indicate that the proposed mechanism of combining polarization conversion and the multivariate phase destructive interference, can effectively broaden the bandwidth of RCS reduction to a super-wide band. It is worth mentioning that the metasurface is insensitive to the azimuthal angle of the incident polarization. To study the influence of variations in the incidence angle on metasurface performance, the specular RCS reductions under both TE and TM polarizations were also simulated. As we can see from Fig. 8(b), a remarkable RCS reduction is realized from 4 to 90 GHz under the wide-angle incidence (at an angle of 40°) for both polarizations, which confirms the good performance of RCS reduction under oblique incidences. Figure 9 shows the simulated 2-D far-field scattering patterns of the metasurface and the equal-sized metallic plate, in which Fig. 9(a-d) and (e-f) are the patterns of the TE- and TM-polarized waves at 10 and 20 GHz, respectively. Compared with the sharp scattering patterns of the metallic plate that the whole reflection of the EM waves along the normal direction, the side lobes of the metasurface are enhanced while the main lobe is suppressed obviously under normal illumination.
Fig. 8. The simulated RCS reduction (a) under normal incidence for both polarizations, (b) in the specular direction under oblique incidence (40°) for TE and TM polarizations. TE/TM: direction of the electric/magnetic field is perpendicular to the plane of incidence.
Fig. 9. The simulated 2-D far-field scattering patterns at 10 (a)-(d) and 20 (e)-(h) GHz in x-axis (a)(c)(e)(g) and y-axis (b)(d)(f)(h) polarization of the equal-sized metallic plate (a),(b), (e),(f) and the proposed metasurface (c),(d), (g),(h).
3.2 Experimental verification
To confirm the performance of the proposed metasurface, a prototype as shown in Fig. 10(a) has been fabricated using the PCB process, which has an over-dimension of 300 mm × 300 mm. The experimental setup essentially features an anechoic and two adjacent horn antennas with a working band from 4 to 40 GHz acting as transmitter and receiver, respectively. The measurement was carried out for both the fabricated metasurface and equal-sized metallic plate using the compact antenna test range system. Figure 10(b) shows the backward RCS reduction of the measurable frequency band in the x and y polarizations. It could be seen that the RCS is reduced by more than 10 dB in the frequency band of 4 to 40 GHz for both x and y polarized incident waves, which has a good coincidence with the simulations shown in Fig. 8(a) in the measurable frequency band. The slight discrepancies between the simulation and measurement results should owe to the fabrication imperfections and assembling error of the prototype. All results indicate that the proposed metasurface can effectively modulate reflected EM waves and achieve ultra-wideband RCS reduction. The performance comparison between the existing research results and the work in this paper on the simulation results is shown in Table 2. It can be found that the proposed low-profile metasurface designed based on the multivariate phase destructive interference method of the polarization conversion unit cells has made outstanding progress in reducing the bandwidth of RCS compared with the other research.
Fig. 10. (a) Photograph of the prototype and measurement of the proposed metasurface. (b)Measured RCS reductions for x and y polarizations under the normal incidence.
Table 2. Comparison of our work and the previous research
4. Conclusions
In this paper, a metasurface is designed, fabricated, and tested for extremely-wideband RCS reduction. The unit cells with polarization conversion function are adopted as the basic meta-atoms of the metasurface, which regulates of EM waves in the polarization domain. In order to obtain low scattering in extremely wideband, the multivariate phase destructive interference method is presented, which combines unit cells of various thicknesses and sizes to realize variable phase differences to achieve destructive cancellation, and its physical mechanism is explained by a phasor representation. The control of the scattered fields is extended from the 2-D plane compared with the OPC. The monostatic RCS reduction of the metasurface in extremely wideband around 184% bandwidth is realized, and it has the characteristics of polarization insensitivity. Meanwhile, favorable effects of specular and bistatic RCS reduction of the metasurface are also demonstrated. The proposed metasurface has the advantages of low profile, low cost and easy fabrication, and it greatly expands the bandwidth of RCS reduction, which has potential engineering application value in broadband stealth.
Funding
National Natural Science Foundation of China (62101416, U2141233, U2241229).
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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