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Abstract
A multifunctional metamaterial to realize broadband x-to-y cross-polarization conversion (CPC) and the absorption of electromagnetic waves is proposed in this paper. The presented multifunctional water-based metamaterial (MWM) consists of the top metallic dielectric substrate, the middle 3D printed container, and the bottom metal backplane. When the container is filled with water, the polarization conversion ratio (PCR) reaches more than 90% at 5.8-9.4 GHz, and the excellent absorption performance is achieved in the frequency band of 16.1-16.9 GHz. In addition, the CPC is achieved in two frequency bands (5.9-10.0 GHz and 14.3-16.4 GHz) without water injection. The unique properties of the proposed design are validated by experiments. As expected, the MWM simultaneously achieves polarization conversion and absorption functions, which is meaningful and consequential for multifunction and conformal stealth applications.
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1. Introduction
Electromagnetic metamaterials [1,2] have been widely investigated due to their extraordinary physical properties in the civilian and military fields. These properties such as phase, polarization, amplitude, and absorption of electromagnetic waves can be manipulated and determined by artificially designed subwavelength structures [3]. Therefore, different artificial materials are designed for different functions, such as polarizer [4,5,6], circular dichroism(CD) [7,8], and perfect absorber [9,10,11].
Water [12], as an abundant and environmentally friendly natural resource on earth, also has the characteristics of high dielectric constant [13], high-frequency dispersion [14], and optical transparency [15], so it is widely used in research of broadband absorption [16,17,18,19]. For example, Pang et al. [20] designed a composite structure with water and metal to achieve thermal adjustability. Chen et al. [21] introduced low backscattering at 2.8-80 GHz based on absorption-diffusion-integration design, and Li et al. [22] achieved wide incidence angle stability and polarization insensitivity within 6.5-21.4 GHz by designing a genuinely all-dielectric water absorbing structure. In line with the transparency of the water, Kwon et al. [23] created an optically transparent microwave absorber based on moth-eye metamaterial structures, which realizes ultra-wideband absorption in the frequency domain from 4 to 120 GHz. In addition, Wang et al. [24] proposed reconfigurable water wire antenna where wide frequency tuning range and stable broadside radiation are both achieved. However, most of the previous studies reported mainly concentrate on the radar absorbing properties [25,26,27,28] and less attention has been paid to the multifunctional application.
With the development of the metamaterials [29], the single-function model design has been unable to adapt to the complex electromagnetic environment, and integrated multifunction structures are constantly proposed. In recent years, some multifunctional designs [30,31,32] [33] have already been reported. Particularly, [34] has proposed a highly integrated lightning-type metasurface, which can realize the functions of CD, absorption of electromagnetic waves, polarization conversion function and asymmetric transmission. In [35], by combing a band-pass frequency selective surface with a polarization converter, a novel dual-polarized frequency-selective polarization converter with low-backward scattering has been designed. [36] has a switchable metasurface with electromagnetically induced transparency and absorption, while simultaneously achieving circular polarization-insensitive and circular-to-linear polarization conversion. Based on a switchable metasurface through the insulator-to-metal phase transition of vanadium dioxide, the bifunctional design of a broadband absorber and a broadband polarization converter in the same terahertz frequencies has been presented [37]. A switchable absorber/reflector with a dual-polarized wideband has been given in [38]. Nevertheless, the versatility of water-based metamaterials has been neglected in research.
This study proposes a water-based metamaterial with both cross polarization conversion and absorption functions for the first time. Multifunctional water-based metamaterials (MWM) consist of a metallic dielectric layer and a 3D-printed container. The MWM can realize the cross polarization conversion of 5.8-9.4 GHz with the polarization conversion rate over 90%. Due to the large permittivity and loss coefficient of water at the microwave frequency band, perfect absorption at 16.1-16.9 GHz can be achieved and the proposed MWM has polarization-insensitive characteristic. When the designed structure is not injected with water, efficient cross-polarization can be achieved in the frequency bands of 5.9-10.0 GHz and 14.3-16.4 GHz. The physical mechanism of polarization conversion is the coupling between the electric resonator and the magnetic resonator, which can be analyzed in detail by the surface current and the distribution of electric and magnetic fields. To verify the simulation results through measurement, the experimental results are in good agreement with the simulation results, which indicates that the design has great potential applications in the fields of adjustable and electromagnetic absorption.
2. Structural design and theoretical analysis
2.1 Structural design and performance
As shown in Fig. 1(a), the unit cell of the MWM is a sandwiched structure consisting of a dielectric substrate, a container layer, and a metallic backplane. FR-4, with a permittivity of 4.4 and a loss tangent of 0.02, is used as the substrate material. The upper metal structure is composed of two half rings, and the water layer structure is a cross-cylinder, which facilitates the flow of water. The optimized geometrical dimensions of the unit cell are listed below: p = 10 mm, r1 = 3.5 mm, r2 = 4 mm, r3 = 3 mm, d = 1.4 mm, and w = 1 mm, as shown in Fig. 1(b). In Fig. 1(c), the thickness of the FR4 substrate, the container part, and the water layer is h3 = 2 mm, h2 = 1.5 mm, h1 = 0.5 mm, and h0 = 0.5 mm, respectively. The total thickness of the structure is 4.07 mm.
Fig. 1. (a) Layer-by-layer view of its unit cell; (b) Cross-sectional view of the unit cell; (c) Side view of the unit cell.
To investigate the microwave characteristics, the CST software based on the finite integration method is used to simulate the structure's response under normal incidence. In the simulation, periodic boundary conditions are used in the x and y directions, and an open (add space) boundary is added in the z-direction. When planar electromagnetic wave incidents on the proposed design along the negative z-axis, it is reflected on the surface of the structure. Through our simulation, the conductivity of the metal is $5.8 \times {10^7}S/m$, assuming the thickness of the metal is 0.035 mm. Since the permittivity and the loss tangent of water constantly change with frequency, it is explained in detail by the Debye formula.
2.2 Working mechanism
2.2.1 Working mechanism of MWM
Water with high permittivity and high-frequency dispersion plays a prominent role in applying broadband absorption. For the MWM, we consider full-space analysis from absorption and reflection to verify the advantages of various functions. Polarization is an important property of light, and only a y-polarized incident wave is considered for metasurface symmetric along the diagonal direction. And the absorption properties of meta-surface composed of sub-wavelength periodic structure can be analyzed by effective medium theory. Correspondingly, the polarization conversion rate (PCR) and absorption rate ${\Lambda }(\omega )$ can be calculated by the following equations [39]:
Fig. 2. (a) Co- and cross-polarized reflection coefficients under y-polarized incident wave; (b) PCR and Absorption rate varies with frequency.
2.3 Polarization conversion mechanism
To analyze the working mechanism of polarization conversion, an axis is established in Fig. 3(a) to decompose the incident electric field into the u-v axis with reference to x-y axis at ±45°. Due to mirror symmetry in the element design, the designed unit cell has the same behavior for x and y polarizations. The y-polarized incident wave is decomposed along the u-v axis to obtain $\overrightarrow {{E_u}} $ and $\overrightarrow {{E_v}} $, and ${\; }\overrightarrow {{E_u}} = \overrightarrow {{E_v}} $. In this way, the incident wave and reflected wave can be indicated as (7) and (8), respectively.
The amplitudes of the x- and y-polarized components in the reflected wave can be obtained,
And the cross- and co-polarization coefficients can be figured up as:
To verify the performance of the proposed polarization converter by theoretical analysis, numerical simulations are carried out for the incidence of u-polarization and v-polarization, respectively, which can be seen that the coordinate axes are established in Fig. 3(a). As depicted in Fig. 3(b), the simulated magnitudes of ${r_u}$ and ${r_v}$ are very close to 1.0, there is a slight difference, which should come from dielectric and conduction losses. Figure 3(c) shows the data curve of the phase difference Δφ between reflection coefficient ${r_u}$ and ${r_v}$. It can be seen that Δφ is close to 180° in the frequency range of 6.2-9.2 GHz. If ${r_u}\; $ is equal to ${r_v}$, and Δφ is 180° (or its even times), the incident electromagnetic wave is completely transformed into the reflected cross-component.
Fig. 3. (a) New coordinate system u-v axis; (b) Magnitude of the u- and v-polarized components; (c) Phase difference between u- and v-components.
Equations (2) and (11) are used to calculate ${R_{xy}}$, ${R_{yy}}$, and PCR, the theoretical calculation results are plotted in Fig. 4, which are consistent with the simulation results at the incidence of y-polarization. In a word, the anisotropy of the unit cell structure is the fundamental cause of the polarization conversion, which leads to the phase difference Δφ. For any polarization incident, Δφ can determine the magnitude of cross- and co-polarization reflections. By analyzing the reflection amplitude and PCR results, the expected polarization rotation is achieved at the incidence of y-polarization.
Fig. 4. (a) Comparison of simulated and calculated reflection coefficients; (b) Comparison of simulated and calculated PCR results.
In addition, for a more particular knowledge of the polarization conversion band of the polarization converter, Fig. 5 shows the surface currents at the two resonance frequencies of 6.302 and 8.3 GHz on the two half rings and the metal ground at the incidence of y polarization. As presented in Fig. 5, at two resonance frequencies, the induced surface current on the metallic bottom ground and the double half-rings are anti-parallel, indicating that the two resonances are caused by the magnetic resonance.
Fig. 5. The surface current distribution of top layer and the bottom metallic ground at two resonance frequencies (a)6.302 GHz; (b)8.3 GHz.
2.3 Absorption mechanism
The absorption mechanism of MWM is analyzed by impedance matching theory, and the parameters extracted from CST are applied to the impedance matching formula:$Z = \sqrt {\frac{{{{(1 + {S_{11}})}^2} - {S_{21}}^2}}{{{{(1 - {S_{11}})}^2} - {S_{21}}^2}}}$, the real and imaginary parts of the relative impedance of MWM are shown in Fig. 6(a). It can be seen that in the 16.1-16.9 GHz frequency band, the real part of the relative impedance is close to 1, and the imaginary part is close to 0. Figure 6(a) indicates that the designed MWM matches well with the free-space impedance in this frequency band, effectively absorbs most of the energy, and exhibits good absorption performance.
Fig. 6. (a) Relative impedance matching results of the designed structure; (b) Simulation results of absorption spectra at different polarization angles.
The absorption rates of MWM are explored by rotating the fabricated structure around its axis from 0° to 45° in steps of 15°, and the explored response is shown in Fig. 6(b). By observing the curves, it can be found that the absorption curves change very little when the polarization angles up to 45°. The slight deviation may be due to water coupling with electromagnetic complexity and metal. In the 16.1-16.9 GHz frequency band, the absorption rate exceeds 90%, which demonstrates the polarization insensitivity of MWM.
2.2.2 Working mechanism of anhydrous structure
When there is no water in the designed structure, the cross-polarization of the dual frequency band is realized. It is depicted in Fig. 7 (a) that the incident y-polarization wave is used to simulate the reflection spectrum of an anhydrous structure. In microwave (5.9-10.0 GHz and 14.2-16.5 GHz) bands, the cross-polarization reflection coefficient ${R_{xy}}$ is lower than -10 dB. The co-polarization reflection coefficient ${\textrm{R}_{\textrm{yy}}}$ in the frequency band of 6.0-9.9 GHz is close to 0 dB. ${R_{yy}}$ is near to −2 dB in the frequency band ranging from 9.9 GHz to 16.0 GHz. Equations (2) and (3) are used to calculate the polarization conversion rate(PCR) and absorption rate of the structure without water. The corresponding spectrum is shown in Fig. 7 (b). In the two frequency bands of 5.9-10.0 GHz and 14.3-16.4 GHz, the polarization conversion rate exceeds 90%. In addition, the PCR of the three resonant points at 6.338 GHz, 8.804 GHz, and 14.978 GHz are respectively 99.8%, 99.9% and 99.6%, which indicates that the structure has a good polarization conversion effect in the corresponding frequency bands when the structure is no water. The absorptivity of the whole frequency band is lower than 60%. Compared with the MWM, the absorption curve of the structure without water drops from 98% to 53% at 16.5 GHz, which shows that the structure does not have efficient absorption performance.
Fig. 7. (a) The reflection coefficient of the structure without water; (b) PCR and absorption rate of the structure without water.
2.4 Parametric analysis
As expected in Fig. 8 and Fig. 9, the MWM performs effective polarization conversion and absorption in two separate bands. The parameters are studied by parameter scanning analysis based on the control variable method to obtain the appropriate parameter values for the structure. First, only the seam width of the double half-rings is changed, as shown in Fig. 8. With the increase of loop seam width, the frequency band exceeding 90% of PCR shifted to high frequency and slightly widened, while the absorption rate of the frequency band over 90% narrowed. Therefore, 1.4 mm is selected for d based on the influence of the two frequency bands. Next, adjust the radius of the water-layer cylinder. From Fig. 9, it can be seen that r3 = 3 mm is the best value to achieve both effects simultaneously. The influence of this radius is opposite to the width of the ring seam. As r3 varies from 2.0 to 4.0 mm, the working frequency band with the cross-polarization effect becomes narrower while the effective absorption bandwidth widens.
In order to estimate the dielectric constant of water at different frequencies and temperatures, according to Debye formula (Eq. (1)), the variation curves of PCR and absorptivity obtained by simulation are shown in Fig. 10. As the temperature rises, the absorption band narrows and the absorption peak moves to the high frequency, while there is no change in the frequency band of the polarization conversion, indicating that the model is insensitive to temperature in the low frequency part but sensitive to temperature in the high frequency part.
3. Experimental results
To determine the performance of the proposed MWM, a prototype (200 mm × 200 mm) consisting of 20 × 20 unit cells is fabricated, assembled, and measured. In Fig. 11(a), the half-ring copper strips are etched on FR4 substrate with a thickness of 1.5 mm by printed circuit board (PCB) technology. The sample of the water layer is made of photosensitive resin by 3D printing, and the top is a transparent photosensitive resin, which can observe the internal structure of the water layer, as presented in Fig. 11(b). Cross-shaped pipes connect the unit cells of the cylindrical water layer to facilitate the flow of water. Figure 11(c) shows the front view of the microwave anechoic chamber test environment. A pair of horn antennas used as transmitter and receiver are connected to a vector network analyzer (Agilent PNA E8362B), and the experimental results of ${R_{yy}}$ and ${R_{xy}}$ are measured. Adjusting the horn antenna can select two types of polarization electromagnetic waves. During the experiment, the experiment is conducted at a room temperature of 25°C. Meanwhile, the angle between the illuminating beam and the reflected beam is about 5° to receive the electromagnetic wave better.
Fig. 11. Physical drawing of (a) the dielectric layer and (b) the water layer, (c) the front side view of the experimental environment.
The measurement steps are as follows: the co-components reflection ${R_{yy}}$ is measured at first, and then adjust the position of the horns to measure the cross component’ reflection ${R_{xy}}$, ${R_{yy}}$ and ${R_{xy}}$ are measured with and without water in the structure, respectively. The measured data is normalized and calculated.
The measured results are presented in Fig. 12. Figure 12(a) represents the reflection spectrum in the presence of water. The simulation results are plotted in dashed lines, and the solid line shows the measured results. In the frequency range of 5.54-8.95 GHz and 15.43-17.18 GHz, the reflection coefficient of ${R_{yy}}$ is lower than −10 dB. Compared with the simulation results, at 16.50 GHz, the value of ${R_{yy}}$ also reaches the lowest peak, while the value of ${R_{xy}}$ shows a deep depression at 16.97 GHz. It indicates that the goodness of the consistency between the experimental and the simulation results is carried out. Figure 12(b) presents the polarization conversion rate and absorption rate results after calculation. Evidently, the PCR is higher at 5.63-8.70 GHz, with the conversion rate exceeding 90%. At the same time, within the frequency of 16.35 GHz to 17.14 GHz, the absorption rate is over 90%, showing excellent absorption performance. The discrepancy between the experimental results and the simulation results is due to the fact that the water in the simulation is in a perfect state and fully conforms to Debye formula, while the water used in the experiment contains impurities and ions, and there are air bubbles in the structural water. On the other hand, the fabrication error also exist between the simulation model and the 3D printed experimental sample. With a similar frequency range in the simulation, the results exhibit that the proposed metamaterial can simultaneously achieve cross-polarization conversion and perfect absorption under anhydrous conditions.
Fig. 12. Physical drawing of the structure with water (a) experimental and simulated reflection coefficients, (b) experimental and simulated PCR and absorption; Physical drawing of the structure without water (c) experimental and simulated reflection coefficients, (d) experimental and simulated PCR and absorption.
The corresponding results are illustrated in Fig. 12(c) when there is no water in the designed structure. In the 5.46-8.33 GHz and 12.54-13.84 GHz bands, the reflection coefficient ${R_{yy}}$ value is less than −10 dB, while ${R_{xy}}$ value is close to 0. It embodies the perfect property of polarization conversion. The comparison of PCR and absorption rate between simulated and measured results are shown in Fig. 12(d). There are two frequency bands with PCR greater than 0.9, which are 5.53-8.12 GHz and 12.84-13.76 GHz, respectively. The weak absorption performance of the sample is below 0.6 in the entire band (4-18 GHz). Although there are some frequency offsets and resonance depth variations that can be attributed to manufacturing errors and tolerances for different material properties. Despite these deviations, a good agreement between the experiment and simulation results can be observed.
4. Conclusion
In summary, a multifunctional water-based metamaterial that integrates polarization conversion and absorption characteristics in different frequency bands is designed and experimentally verified in this paper. Based on water-based metamaterial, both cross-polarization conversion and absorption can be achieved, which is the greatest preponderance of the design. In addition, through the dynamic circulation of pure water, the reconfigurable function of switching between the absorption and polarization conversion of the high-frequency part can be realized without changing the effect of low-frequency cross-polarization. Compared with other studies, the proposed structure in this paper combines the strengths of multifunction and wideband microwave switching, which makes it promising for a wide range of applications in the fields of tunability and electromagnetic absorption.
Funding
Fundamental Research Funds for the Central Universities (No.2022CXZZ102, CCNU22JC018).
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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