1. Introduction

Metamaterials are the artificially periodic structure materials with sub-wavelength scale, which have attracted substantial attentions owing to the unique features in the past decades [1–3]. Recently, metasurfaces (MSs) with ultra-thin thickness and in-plane design were proposed as an approach to realize full controls of the electromagnetic (EM) waves [4–8], which break the theoretical limitation of the quarter wavelength of traditional absorbing materials [9,10]. As two-dimensional metamaterials, MSs show several functions including polarization conversion, anomalous reflection/refraction, subwavelength focusing, perfect absorption, and so on, which have been fully demonstrated [11–15].

Numerous efforts have been made on developing radar stealth MSs based on EM resonance, polarization conversion and energy scattering [16–18]. Since the first perfect metamaterial absorber was proposed by Landy et al. [19], EM resonance MSs have been applied to dissipate the incident EM energy based on the EM coupling characteristics, aiming to realize the low-frequency and high-efficiency microwave absorption [20,21]. Recently, phase gradient MSs have been gradually used in the field of radar stealth, which can be applied to realize the polarization conversion and energy scattering of EM waves [22,23]. Both can reduce the probability of being detected by the radar. Li et al. proposed the design of hybrid surface composed of a frequency selective surface on the bottom and a checkerboard MS on the top, which shows that the RCS can be reduced by more than 10 dB at 4.1-7.7 GHz and the insertion loss in the transmission window is lower than 1 dB at 11.3-13.3 GHz [24]. Chen et al. proposed the polarization conversion MS based on diagonal phase gradient design. This double-layer MS shows an ultra-wide frequency band of polarization conversion from 3.5 GHz to 16.6 GHz [25]. Ji et al. presented a broadband MS by using a combination of phase cancellation and absorption mechanisms, this MS realize the RCS reduction over a wide frequency band ranging from 13 GHz to 31.5 GHz [26]. The reports mentioned above mainly realize radar stealth by manipulating the polarization mode and transmission direction of EM waves [27,28]. As we know, no MS with the properties of EM wave imprisonment has been proposed. Currently, Shen et al. designed an asymmetric split ring structure, which can realize asymmetric EM wave transmission. This design provides an approach for the EM control of MSs and is expected to be applied to EM imprisonment [29].

In this work, we propose an approach to obtain the radar trap model, which can imprison the EM waves and greatly reduce the detectability of radar. This three-layer radar trap model is composed of upper-layer transmission polarization converter, middle-layer dielectric substrate and lower-layer reflection polarization converter. Taking Jones calculation as a guide, then optimizing geometric parameters to design the trap models that meets actual requirements. The transmission polarization converter is designed to realize asymmetric polarization conversion, which means that the EM waves of a single polarization mode can only pass through the converter from a single side. The reflection polarization converter can convert the polarization state of the EM waves passing through upper and middle layers. Due to the asymmetric transmission characteristics of upper layer, the reflected EM waves cannot enter the free space through the upper layer in opposite direction subsequently. The middle dielectric substrate can be seen as an EM wave channel and a supporting bridge, which also reduce the EM coupling effects between the upper and lower layers to a certain extent. On this basis, we analyze and verify the feasibility of our investigations through two kinds of radar trap model designs based on linear and circular polarization conversion MSs. Experimental results are in accordance with the simulated ones. The key of this work is not to broaden the stealth performance, but to offer a novel strategy for radar trap model design.

2. Designs and methods

2.1 Model design principle

The stealth principle of the radar trap model is shown in Fig. 1, we named the EM waves of two polarization states Mode-1 waves and Mode-2 waves. Design concept is as follows: the incident Mode-1 waves pass through the upper layer and are converted to the transmitted Mode-2 waves. Subsequently, the transmitted Mode-2 waves are further converted to the reflected Mode-1 waves by interacting with the lower layer. The reflected Mode-1 waves can hardly enter the free space due to the antisymmetric transmission characteristics of the upper layer. As a result, the EM wave energy is finally imprisoned in the radar trap model. Figure 1 only represents the basic diagram of the trap structure, we present different explanations for the EM imprisonment mechanism under linear and circular polarization incidence conditions subsequently. Our design breaks the traditional research mode and aims to broaden the vision of EM wave manipulation and radar stealth application.

 

Fig. 1. Stealth principle of the radar trap model.

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2.2 Jones calculation of linear polarization conversion

The Jones matrix of the reflection polarization converter and the transmission polarization converter follows the same calculation rules. Therefore, we just need to analyze the transmission process by the Jones calculation method, the general transmission matrix of linear polarization waves can be expressed as [30]:

From the Lorentz reciprocity theory, the Jones matrix for the backward propagation direction has the following form:

The asymmetric transmission characteristics of linear polarization waves are usually characterized by Δ parameter, which represent the difference of transmittance between forward and backward propagations. Here, Δ can be defined as follows:

In order to realize perfect asymmetric transmission, the spatial symmetry of the MSs along the propagation direction should be broken. The transmission coefficients should satisfy ${T_{xx}} = {T_{yy}} = 0$ and $|{{T_{xy}}} |- |{{T_{yx}}} |= 1$. The linear polarization conversion ability of designed MSs can be defined as polarization conversion ratio [31]:

Here, r_xx, r_xy, r_yx and r_yy are the reflection coefficients. γ^x and γ^y represent the polarization conversion ratio of x- and y- polarized waves, respectively. This calculation is used to guide the design of chiral MSs, aiming to realize the asymmetric transmission and polarization conversion of linear polarization waves.

2.3 Jones calculation of circular polarization conversion

Since Pancharatnum-Berry phase principle deals with the circular polarization characteristics, the general transmission matrix of circular polarization waves can be obtained as follows [30]:

Here, ${\wedge} $ is the circular polarization transformation matrix, the transmission coefficient relation between circular polarization waves and linear polarization waves can be derived as:

3. Results and discussion

3.1 Radar trap model composed of linear polarization converter

We propose a radar trap model based on linear polarization conversion MSs. First, an asymmetric split ring (ASR) structure is proposed as the transmission polarization converter, which can realize the cross polarization conversion of linear polarization waves. This ASR converter is composed of FR4 substrate (dielectric constant ɛ=4.3, loss tangent tanδ=0.025) and split-ring metal etched on both sides of it. Figure 2(a) and 2(b) show the top view and side view of the unit cell, respectively. For unit cell with the periodicity of p_l1=10 mm: the thickness of middle-layer FR4 is h_l1=1.5 mm, and the thickness of metal patterns is 0.035 mm, other geometrical parameters are as follows: r_l1=4.5 mm, s_l1=1 mm and w_l1=0.2 mm. Since the unit cell is symmetric under π/2 rotation about z-axis followed by π rotation about y-axis with D_z(π/2)D_y(π). The backward Jones matrix T_li^b is equal to the forward Jones matrix after two rotated operation according to Formulas (2) and (3):

 

Fig. 2. (a) Top view and (b) side view of the ASR converter. (c) Transmission coefficient and (d) linear polarization conversion ratio of the ASR converter under x- and y-polarized incidence.

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The matrix described by Formula (14) satisfies T_xx=T_yy in the whole frequency range. Jones calculation guides the rotation design of ASR converter. Subsequently, we may realize effective linear polarization conversion through further geometric parameter optimization.

Under the condition of x- and y- polarized incidence, the simulated transmission coefficients are shown in Fig. 2(c). The cross polarization transmission coefficient T_xy reaches maximum value of 0.77 at 8.7 GHz, while both T_xx and T_yy are decreased to minimum value of 0.09 and T_yx is about 0.01. The results show the characteristics of the asymmetric transmission and polarization conversion, the difference between two cross polarization transmission components comes from the asymmetric design of ASR converter. The y-polarized waves can be converted into x-polarized waves due to mutual coupling between upper and lower pattern layers. The x-polarized waves hardly interact with the ASR converter, resulting in poor transmission efficiency. According to Formulas (5) and (6), we further analyze the polarization conversion ratio as shown in Fig. 2(d), which presents 99% polarization conversion at resonance frequency under y-polarized incidence. Meanwhile, the reflection coefficients of the ASR structure under front and back incidence are related to each other. The characteristics of forward x(y)-polarized waves are consistent with the one of backward y(x)-polarized waves, which further verifies that ASR converter has unidirectional polarization conversion characteristics.

To intuitively clarify the characteristics of asymmetric transmission and polarization conversion, we simulate the electric field distribution of unit cell at different positions at 8.7 GHz, which is shown in Fig. 3. It is clear that whether the polarization direction of incident EM waves is along x- or y- axis, the polarization direction of transmitted EM waves is always along x-axis, mainly due to the selectivity of ASR converter. From Fig. 3(a), when incident y-polarized waves pass through the metal pattern, the electric field direction changes sharply, resulting in a changed mode of the transmitted EM waves. The electric field strength under y-polarized incidence is shown in Fig. 3(b), the lower-layer pattern has a significant resonance effect, which further verifies that the EM waves pass through the ASR converter to realize polarization conversion. From Fig. 3(c), when the polarization direction of incident EM waves is along x-axis, the direction of electric field distribution is not changed. The electric field strength under x-polarized incidence is shown in Fig. 3(d), the lower-layer pattern has almost no resonance effect, which further verifies that the EM waves are forbidden to pass ASR converter. Here, we present the electric field distribution of ASR converter under the x- and y- polarized incidence to verify the theoretical analysis and simulation.

 

Fig. 3. Electric field distribution at 8.7 GHz. For y-polarized incidence: (a) Electric field direction at the upper, middle and lower position of the unit cell, (b) Electric field strength of the unit cell. For x-polarized incidence: (c) Electric field direction at the upper, middle and lower position of the unit cell, (d) Electric field strength of the unit cell.

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We further propose a reflection polarization converter with split ring structure named SR₁ converter. This SR₁ converter consists of FR4 substrate etched with a split-ring metal, which can convert the polarization states of transmitted EM waves (the EM waves passing through the ASR converter). Figure 4(a) and 4(b) show the top view and side view of the unit cell, respectively. For unit cell with the periodicity of p_l2=10 mm: the thickness of middle-layer FR4 is h_l2=0.5 mm, and the thickness of metal patterns is 0.035 mm, other geometrical parameters are as follows: r_l2=3.7 mm, s_l2=1 mm and w_l2=1.5 mm. The calculation of reflection matrix is similar to the one of transmission matrix. Since the unit cell is mirror-symmetric with respect to the voz plane, the symmetric matrix is ${D_v} = \left( {\begin{array}{cc} { - 1}&0\\ 0&1 \end{array}} \right)$. The Jones matrix for SR₁ converter reflected at that plane is identical to the original one. Therefore, we have [30]:

 

Fig. 4. (a) Top view and (b) side view of the SR₁ converter. (c) Reflection coefficients and phases of the SR₁ converter under u- and v-polarized incidence. (d) Reflection coefficients of the SR₁ converter under x-polarized incidence.

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Here, r_xx, r_xy, r_yx and r_yy are the reflection coefficients of linear polarization waves. We can clearly see that the $|{{r_{xx}}} |= |{{r_{yy}}} |= 0$, $|{{r_{xy}}} |= |{{r_{yx}}} |= {r_{uu}}$, which demonstrates an effective linear polarization conversion of EM waves. Meanwhile, the EM characteristics along x- and y- axes are the same due to the symmetry design of SR₁ converter along the uv-axis. Let us take x-polarized incidence as an example, Fig. 4(d) gives the reflection coefficients of SR₁ converter, r_xx=0.27 and r_vx=0.93 at 8.7 GHz. It is worth pointing out that the x-polarized waves are converted to y-polarized waves.

In general, ASR converter is able to convert y-polarized waves to x-polarized waves. Subsequently, the transmitted x-polarized waves are further converted to reflected y-polarized waves by interacting with SR₁ converter. The reflected EM waves are forbidden to enter the free space through ASR converter due to its asymmetric transmission characteristics. Then, the y-polarized waves reflected back by the back of ASR converter interact with the further reflected x-polarized wave of SR₁ converter, the phase gradient of the x- and y- polarized waves is 90°. The two EM waves form an approximately circular polarization waves in this region, which is difficult to enter the free space through the ASR converter. This cycle completely presents a method to imprison EM waves based on the dual-layer design of linear polarization conversion MSs.

3.2 Radar trap model composed of circular polarization converter

We propose another radar trap model based on MSs having function of linear-to-circular polarization conversion. First, the asymmetric staggered split ring (ASSR) structure is presented as the transmission polarization converter, which is C₄-symmetric with respect to z-axis [30]. This ASSR converter is composed of the FR4 substrate and the staggered split-ring metal etched on both sides of it. Four pairs of staggered split rings form an asymmetric structure, whose split direction is rotated by 90°, 180°, 270°. Figure 5(a) and 5(b) show the top view and side view of the unit cell, respectively. For unit cell with the periodicity of p_r1=14 mm: the thickness of middle-layer FR4 is h_r1=1 mm, and the thickness of patterns is 0.035 mm, other geometrical parameters are as follows: r_r1=2.8 mm, s_r1=1.6 mm and w_r1=0.4 mm. The linear transmission matrix of ASSR converter can be expressed as [30,33]:

 

Fig. 5. (a) Top view and (b) side view of the ASSR converter. (c) Transmission coefficients and phases under x-polarized wave incidence. (d) Transmission coefficients of the circular polarization waves under backward propagation direction. (e) Transmission coefficients and (f) ellipticity of the linear-to-circular polarization conversion.

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Here, T_RL=T_LR=0. The transmitted circular polarization coefficients depend on the incident linear polarization coefficients. Jones calculation guides the rotation design of ASSR converter, we may realize effective linear-to-circular polarization conversion by further geometric parameter optimization.

For ASSR converter, it has the same transmission characteristics under x- and y-polarized incidence. Taking x-polarized incidence as an example, the transmission coefficients and phase gradient are shown in Fig. 5(c). The phase gradient of cross polarization EM waves is set as: $\triangle \varphi = {\varphi _{yx}} - {\varphi _{xx}}$. At 5.6 GHz, |T_xx| and |T_yx| are different, $\triangle \varphi = \frac{\pi }{2}$, it shows an approximately circular polarization conversion. At 8.2 GHz, $|{{T_{xx}}} |= |{{T_{yx}}} |$, $\triangle \varphi ={-} \frac{\pi }{2}$, which presents a purely circular polarization conversion. Due to the difference in $\Delta \varphi $ between 5.6 GHz and 8.2 GHz, ASSR converter generates circular polarization waves with different modes. As shown in Fig. 5(d), the transmission coefficients of circular polarization waves under backward propagation direction are presented. It is clear that the LCP waves and RCP waves cannot pass through ASSR converter in the opposite direction at 5.6 GHz and 8.2 GHz, respectively. Figure 5(d) demonstrates the backward transmission characteristics of ASSR converter, which would work with the reflection polarization converter subsequently to realize the imprisonment of EM waves. The transmission coefficients of linear-to-circular polarization conversion are shown in Fig. 5(e), which exactly correspond to Fig. 5(c). At low frequency 5.6 GHz, the transmission coefficients of LCP waves and RCP waves are 0.18 and 0.46, respectively. Meanwhile, the transmission coefficients are 0.58 and 0.04 at high frequency 8.2 GHz. The linear polarization waves are converted into approximately RCP waves and purely LCP waves at 5.6 GHz and 8.2 GHz, respectively. According to Formula (11), the ellipticity of transmitted EM waves is calculated as shown in Fig. 5(f). The ellipticity of 25° at 5.6 GHz indicates a right-hand elliptical polarization conversion, and the ellipticity of 42° at 8.2 GHz indicates an effective LCP conversion.

In order to clarify the polarization conversion mechanism of ASSR converter, the surface current distribution at 5.6 GHz and 8.2 GHz is simulated. The black solid arrow indicates the current direction of upper metal pattern, and the black dashed arrow indicates the current direction of lower metal pattern. Intuitively, the straight metal wire and the circular ring can be regarded as an electric dipole and a magnetic dipole, respectively. As shown in Fig. 6(a), the surface current direction of upper and lower metal patterns is the same at 5.6 GHz, which is equivalent to a straight metal wire and can be regarded as electric dipole resonance mode. As a comparison, the surface current direction of upper and lower patterns is opposite at 8.2 GHz depicted in Fig. 6(b), which is equivalent to a circular ring and indicates a magnetic dipole resonance mode. This ASSR converter mainly generates electric dipole resonance at low frequency, thereby converting linear polarization waves to right-hand elliptical polarization waves. At high frequency, a magnetic dipole resonance is induced to realize the polarization conversion of linear polarization waves to LCP waves. Until now, we perform a surface current distribution of the low-to-high frequency response to verify the theoretical analysis and simulation.

 

Fig. 6. (a) and (b) present the surface current distribution of ASSR structure at 5.6 GHz and 8.2 GHz, respectively.

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We further propose a split ring structure as the reflection polarization converter, namely SR₂ converter. This SR₂ converter can convert the polarization states of transmitted EM waves passing through ASSR converter and its composition is similar to the SR₁ converter. Figure 7(a) and 7(b) show the top view and side view of the unit cell, respectively. For unit cell with the periodicity of p_r2=7 mm: the thickness of middle-layer FR4 is h_r2=0.5 mm, and the thickness of metal patterns is 0.035 mm, other geometrical parameters are as follows: r_r2=3 mm, s_r2=1.6 mm and w_r2=0.6 mm. As shown in Fig. 7(c), the reflection characteristics of SR₂ converter along uv-axis are similar to the SR₁ converter. At 5.6 GHz and 8.2 GHz, $|{{r_{uu}}} |= |{{r_{vv}}} |$, ${\varphi _{uu}} - {\varphi _{vv}} = 2n\pi + \pi $. According to Formulas (7) and (16), the circular polarization reflection matrix R_cir of SR₂ converter can be derived as:

 

Fig. 7. (a) Top view and (b) side view of SR₂ converter. (c) Reflection coefficients and phases of SR₂ converter under u- and v-polarized incidence. (d) Reflection coefficients of SR₂ converter under RCP incidence.

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In general, ASSR converter can convert linear polarization waves to RCP waves and LCP waves at 5.6 GHz and 8.2 GHz, respectively. At 5.6 GHz, the transmitted RCP waves are converted to reflected LCP waves by interacting with SR₂ converter. The backward transmission characteristics of ASSR converter are shown in Fig. 5(d), T_LL^-=0.21 at 5.6 GHz, the reflected LCP waves can hardly enter the free space through ASSR converter. At 8.2 GHz, the transmitted LCP waves are converted to reflected RCP waves. T_RR^-=0.11 at 8.2 GHz as shown in Fig. 5(d), the reflected RCP waves are forbidden to enter the free space through ASSR converter. The cycle provides another method to imprison EM waves based on the dual-layer design of circular polarization conversion MSs, further verifying the feasibility of our investigations.

3.3 Simulation and experimental verification

The final radar trap models are shown in Fig. 8(a) and 8(b), named “linear polarization conversion trap model (LPC-model)” and “circular polarization conversion trap model (CPC-model)”, respectively. The upper and lower layers are polarization converters to realize specific polarization conversion function. The thickness of middle-layer FR4 substrates of LPC-model and CPC-model is 1 mm and 0.5 mm, respectively. This dielectric layer can be regarded as an EM wave channel and further reduce the EM coupling effects between the upper and lower layers. The two models can realize the radar stealth properties based on polarization conversion MSs. We prepare the samples through traditional printed circuit board (PCB) technology, which is composed of lossy FR4 as dielectric material, copper films as resonance patterns and reflection layer. As shown in Fig. 8(c), the three functional layers of LPC-model are placed alternately, with the area of 180×180 mm² and the total thickness of 3.14 mm. As shown in Fig. 8(d), the three functional layers of CPC-model are placed alternately, with the area of 182×182 mm² and the total thickness of 2.14 mm.

 

Fig. 8. 3D schematic diagram of (a) the LPC-model and (b) the CPC-model. Fabricated samples of (c) the LPC-model and (d) the CPC-model. Simulation and experimental reflection loss of (e) the LPC-model and (f) the CPC-model.

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Figure 8(e) and (f) show the reflection loss of two radar trap models. For LPC-model as shown in Fig. 8(e), the simulation and experimental results reach -19.0 dB and -15.6 dB at 8.9 GHz under y-polarized incidence, respectively. When the incident polarization direction is along x-axis, the reflection loss is almost zero. For CPC-model as shown in Fig. 8(f), under y-polarized incidence, the simulated reflection loss reaches -9.5 dB at 6.2 GHz and -18.6 dB at 8.9 GHz. Meanwhile, the experimental reflection loss reaches -11.7 dB at 6.0 GHz and -20.5 dB at 8.9 GHz. When the incident polarization direction is along x-axis, the simulated reflection loss reaches -12.0 dB at 6.2 GHz and -18.4 dB at 8.8 GHz. The experimental reflection loss reaches -9.5 dB at 6.0 GHz and -28.4 dB at 8.8 GHz. It is clear that the operating bandwidth of the complete radar stealth model is slightly different from the initial design depicted in Section 3.1 and 3.2. The simulation errors between the final model and each layer are attributed to the thin thickness of FR4 dielectric substrates, which cause the slight shift of resonant frequency of the final models. There are also some differences between simulation and experiment, mainly due to the preparation errors. In general, the experimental results agree well with the simulated ones, proving the effectiveness of our design method.

4. Conclusion

In this work, we propose the design concept of three-layer radar trap model, which can realize the imprisonment of EM waves between upper and lower layers. This model is composed of the transmission polarization converter, the FR4 dielectric substrate and the reflection polarization converter. Taking Jones matrix calculation as a guide, the transmission polarization converter can realize the function of polarization conversion and asymmetric transmission. The reflection polarization converter can realize the required polarization conversion, and the FR4 dielectric substrate is regarded as the support and matching layer. This precise EM control and combined design may realize a blackbody-like function. On this basis, we propose two kinds of radar trap models based on the linear and circular polarization conversion MSs, the numerical simulation and physical origin are performed to further verify the feasibility and correctness of our investigations. Experimental results are in accordance with the simulated ones. Our paradigm provides an entertaining approach that can imprison the EM waves in a thin layer, letting the EM waves are neither absorbed nor scattered into free space. Although the operating bandwidth is narrow due to the limited research of asymmetric polarization conversion MSs, it still opens up an avenue for realistic application of radar stealth technology.