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Abstract
A linear-to-linear polarization conversion metamaterial is proposed with a water-metal structure. The simulation results show that the proposed metamaterial design can achieve ultra-broadband and high-efficiency polarization conversion within the frequency range from 7.46 GHz to 14.84 GHz with a polarization conversion ratio over 90%. This metamaterial exhibits sensitivity to the incidence angle but not to and temperature. The physical mechanism of polarization conversion is analyzed based on the distributions of the surface current and the magnetic field. An experimental sample of the designed metamaterial is fabricated, assembled, and measured in such a way as to realize reflective polarization conversion. This work provides a significant stepping stone for water-based metamaterial design and polarization control.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Polarization is a key aspect of investigating the propagation of electromagnetic waves [1,2], especially in the microwave, terahertz, and optical frequency bands. In particular, polarization manipulators have received considerable attention for numerous applications in communications [3], imaging [4], and remote sensing [5]. Although natural anisotropic materials can be used for manipulating electromagnetic wave polarization, these materials can’t satisfactorily achieve polarization conversion in the microwave frequency band. The emergence of metamaterials provides a novel and convenient alternative for polarization conversion in that band. Metamaterials [6,7] are artificial materials that are composed of subwavelength resonators with appropriate periodic arrangements. These materials exhibit different sophisticated electromagnetic characteristics that are hard to attain by natural materials. These characteristics include those of the negative refractive index [8,9], superlens [10,11], and asymmetric transmission [12,13].
Specifically, metamaterials generally show high capabilities for polarization control. Thus, polarization conversion in metamaterials has been recently receiving considerable research attention [14–19], with different proposals for conversion schemes such as the linear-to-linear, linear-to-circular, and circular-to-circular types. In the microwave, Long et al [20]. utilized two twisted 90° multigap rings in order to achieve polarization conversion for wideband transmission, with a conversion ratio exceeding 93% for the frequency range from 12.7 GHz to 17 GHz. Lavesh et al [21]. achieved dual-band reflective linear-to-circular polarization conversion, in which the two frequency bands from 8.34 GHz to 8.71 GHz and from 10.3 GHz to 14.73 GHz, respectively. Ahmad et al [22]. designed a hollow rhombus-shaped unit cell to achieve a linear to linear and linear to circular polarization conversion in the broad frequency spectrum of 13 GHz to 26 GHz. When it comes to terahertz range, Nathaniel et al [23]. created a linear polarization conversion at 0.4 THz to 2.0 THz with two rotating metal lines. Li et al [24]. introduced a stereo-metamaterial to control polarization conversion for terahertz waves, and they demonstrated linear polarization conversion for the range from 1.0 THz to 1.6 THz. Barkabina et al [25]. proposed an ultra-thin linear-to-circular polarization conversion metasurface with a conversion ration exceeding 99% in the frequency range from 0.83 THz to 0.92 THz. Cheng et al [26]. achieved a broadband reflective linear to linear polarization conversion between 356.5 THz to 536.5 THz, while linear to circular polarization conversion between 336.5 THz to 544.5 THz based on all-metal anisotropic metasurface. Nevertheless, to the best of our knowledge, polarization conversion with water-based metamaterials has been largely overlooked in the literature. Obviously, water naturally exists as a cheap, abundant and environmentally friendly resource, is widely exist in nature. Due to its low microwave band dispersion and high dielectric loss, water is a highly attractive component in the design of perfect absorption metamaterials [27–29]. For instance, Pang et al [30]. developed a sandwich structure with a metal pattern, water, and a metal plate. This structure achieves absorption above 90% in the frequency band of 4-20 GHz. Moreover, water can be used to acquire other electromagnetic properties. For example, Stenishchev et al [31]. realized a toroidal dipole response on clusters of cylindrical particles, formed with water cubes.
We identify a reflective linear-to-linear polarization converter, whose main structure consists of water and metal. This metamaterial achieves high-efficiency polarization conversion in the frequency region of 7.46 GHz to 14.84 GHz, through which the polarization conversion ratio is over 90%. The physical mechanism of polarization conversion in the proposed metamaterial design is the coupling between the electric and magnetic resonators, which can be explained by the distributions of surface currents, as well as electric and magnetic fields. This paper seeks to set a new direction to study water-based metamaterials, and motive research investigation of water-based metamaterials with polarization conversion.
2. Unit cell design
Figure 1(a) shows a profile chart of the designed unit cell, with five parts and six layers, as follows: a metal pattern, a dielectric substrate, a top layer of the container, a water layer, a bottom layer of the container, and a metal plate. This structure can be called metal combination water structure (MCWS). It should be pointed out that the container has a middle layer to encase the water layer. However, in order to better observe the water layer, a middle layer of container is ignored. The metal pattern and the metal plate are created with 0.035-mm-thick copper, which has an electrical conductivity of 5.96${\times} $107 S/m. The dielectric substrate is made of a 1 mm thickness layer of FR4 with a permittivity of 4.3 and a loss tangent of 0.025 [32]. The container layer is built by 3D printing using a photosensitive resin material, with the corresponding permittivity and loss tangent being 3.5 and 0.001, respectively. The water is well described by the following Debye formula, which indicates that the water dispersion at different frequencies is given by [33]:
Fig. 1. The schematic diagram of the unit cell (a) the side view of the whole structure, (b) the top view of the metal pattern, (c) the top view of the water layer.
The copper strip (CS) is etched on the FR4 with a 45° rotation about the x-axis, as shown in Fig. 1(b). The water layer is inside the container, as shown in Fig. 1(c). The water rectangular ring (WRR) rotates in the same direction and at the same angle with the CS. The detailed geometric parameters are as follows: the length of FR4 and container (L) is 10 mm, the length of the CS (l) is 8 mm, the width of the CS (n) is 2 mm, the length of the WRR (g) is 10 mm, the width of the WRR (q) is 3 mm, the thickness of the WRR (g) is 0.5 mm, the height of the WRR (h) is 1 mm, and the thickness of photosensitive resin (t1 and t2) is 0.5 mm.
3. Simulation results, discussion, and analysis
The MCWS structure is modeled and the reflection spectra are simulated by CST Microwave Studio, a high-performance 3D EM analysis software package, based on the finite-integration time-domain (FITD) method. The boundary conditions consider a unit cell in the x and y axes, and this amounts to mimicking an infinite periodic structure. In the z-axis, the open (add space) is applied to the boundary conditions. This shows that the electromagnetic wave is incident to the MCWS from the z-direction. To analyze the reflective polarization conversion, the reflection coefficient can be defined as rji. This indicates that the incident wave is an i polarization wave and the reflected wave is a j polarization wave. Meanwhile, there are three electric fields Ein, Eir, and Ejr, respectively. wherein Ein denotes the incident electric field, while Eir, and Ejr are the reflected electric fields with i and j polarizations, respectively. Therefore, the co-polarization and cross-polarization reflection coefficients are defined as [34]:
Firstly, we simulate the reflection spectra of each of the CS and WRR geometries with an incident x-polarized wave. For the sake of comparison, all geometric parameters are the same as those in Fig. 1. To evaluate the polarization conversion performance, the polarization conversion ratio (PCR) is computed as follows [35]: The simulation results of the reflection spectrum with the CS is shown in Fig. 2(a), which indicates the existence of a reflection resonance point at 9.06 GHz, and also asserts that the values of the co-polarization reflection coefficient (rxx) is 0.27, and that of the cross-polarization reflection coefficient (ryx) is 0.72. Figure 2(b) presents the results calculated for the PCR, and reaches up to its highest value at a frequency of 9.06 GHz, at which 87% of the x-polarized wave is reflected to a y-polarized wave. Figure 2(c) displays the WRR reflection spectrum. The two curves of rxx and ryx have no intersection. The corresponding PCR is exhibited in Fig. 2(d), and the value is lower than 0.4 in the whole frequency band. The results of Fig. 2 indicate that the CS has a certain polarization conversion property, and that the WRR cannot realize polarization conversion.Fig. 2. The simulation results of reflection spectra (a) CS, (c) WRR; the calculation results of PCR (b) CS, (d) WRR.
The above results manifest that the individual structure of either the CS or the WRR is unable to achieve good polarization conversion performance, in terms of the bandwidth and efficiency. When the electromagnetic wave is incident to the structure of the CS combined with the WRR, referred to herein as the MCWS, significant improvement in the performance of polarization conversion can be noted. This improvement can be specifically noted from Fig. 3(a) with an x-polarized incident wave, together with the corresponding reflection spectrum. Within the frequency range from 7.46 GHz to 14.84 GHz, the curve of ryx is higher than that of rxx. The curve of rxx forms a deep and broadband dip in this frequency region where the value of rxx remains below 0.2. On the other hand, the ryx reaches up to its highest value which is around 0.9. To show the performance of the polarization conversion more directly, Fig. 3(b) reports the PCR results, and asserts that the efficiency of linear-to-linear polarization conversion is over 90% between 7.46 GHz and 14.84 GHz. The polarization conversion bandwidth of the metamaterial is generally reflected by the relative bandwidth (RB), as follows: $RB = \frac{{2({f_h} - {f_l})}}{{{f_h} + f}}$, where fl and fh are the lowest and highest frequency of that the PCR over 90%. After calculating, the RB of the proposed metamaterial is 66%, which indicates ultra-broadband in the polarization conversion. At 8.02 GHz, the PCR value is 99% which means that almost all the x-linear polarized waves were reflected as y-polarized waves. For the results of Fig. 3, it can be concluded that the proposed MCWS exhibits an ultra-broadband and a high efficiency reflective polarization conversion characteristic.
In order to investigate the physical mechanism of polarization conversion, we observe the surface current distributions of the CS, and z-component distributions of the electric and magnetic fields on the WRR. Here, we choose a frequency of 8.02 GHz to analyze, which is the frequency of the highest efficiency of polarization conversion in the proposed MCWS. Figure 4(a) shows the surface current distribution of the CS and the copper plate. On the top layer, there is a current beam at the CS, which the direction is left to right at a 45-degree angle. Meanwhile, the intensity of surface current is stronger at the CS. It can be equivalent to an electric dipole resonance. This means that electric resonance is being excited. On the bottom layer, the surface current on the copper plate moves from right to left at a 45-degree angle and the intensity is weaker. However, the surface current beams on the two layers are anti-parallel, which excites a magnetic resonance. Because the surface current cannot exist in the water layer, the role of water is analyzed solely by the electric and magnetic field distributions, as shown in Figs. 4(b) and 4(c). It is observed that the intensity of the electric field is very weak in the WRR and that a strong intensity of the magnetic field concentrates on the center of the WRR. According to the intensity of the magnetic field and surface current, we consider that the magnetic resonance in the WRR is stronger than that of in the metal. Therefore, the magnetic resonance in the proposed metamaterial is originated from the WRR. The physical mechanism of the proposed ultra-broadband polarization conversion metamaterial is caused by the superposition between the electric resonance of the CS and the magnetic resonance of the WRR.
Fig. 4. (a) The surface current distribution at 8.02 GHz, (b) The electric field distribution at 8.02 GHz, (c) The magnetic field distribution at 8.02 GHz.
To further illustrate the principle of the polarization conversion, we opted to decompose the electric field (E-field) of the x-polarized wave into two orthogonal E-field components. As shown in Fig. 5, the incident E-field $(E_x^i)$ can be decomposed into two components along the u-axis $(E_u^i)$ and the v-axis $(E_v^i)$. Meanwhile, the reflected E-field $(E_x^r)$ has two components $(E_u^r)$ and $(E_v^r)$. The electric field equations are [36]:
Figures 6(a) and 6(b) show the simulation results of the amplitude and phase of the reflection coefficient along the u- and v- axes. Let the phase along the u and v directions be ${\varphi _{uu}}$ and ${\varphi _{vv}}$, respectively. Thus, the phase difference between $E_u^r$ and $E_v^r$ can be calculated as follows:
The x-polarized wave is converted to its orthogonal polarization wave as ${r_{uu}} = {r_{vv}}$ and $\varDelta \varphi = 0$ or $\pi $. Figure 6(a) shows that the amplitudes of ruu and rvv are close to each other at 6.02 GHz to 13.94 GHz. The frequency range of the 180° phase difference is 7.46 GHz to 14.84 GHz, as shown in Fig. 6(b). Thus, it is concluded that the E-field of the reflected wave rotates by 90° compared to the incident wave. On the other hand, the reflection coefficients of rxx and ryx can be calculated through the parameters of u and v directions, as follows: The calculation and simulation results of rxx and ryx are shown in Fig. 6(c). The calculation results of ryx are more ideal. The values of ryx are close to 1, while the simulation values of ryx are around 0.9. The calculated and simulated data of rxx are well in agreement with each other. In other words, the four curves exhibit the similar variation trends, and thus express the expected polarization characteristics.Fig. 6. (a) The simulation results about amplitudes of u- and v- axis, (b) The simulation results. about phase of u- and v- axis, (c) The simulation and calculation results of rxx and ryx.
In what follows, we investigate polarization conversion with different incidence angles (θ) in the proposed MCWS scheme. We do so because the electromagnetic waves are always incident with oblique angles in practical applications. The simulation results of reflection spectra are shown in Fig. 7(a) for θ varying from 0° to 45° with a step of 15°. As θ increases, the values of rxx and ryx are kept unchanged within the frequency between 2 GHz and 8 GHz. However, in the high frequency range the two curves vary clearly, where rxx gradually rises while ryx gradually declines. It can be inferred that the efficiency of polarization conversion decreases with θ increasing. The PCR results are exhibited in Fig. 7(b), which indicates that the PCR bandwidth (wherever it is over 90%) is changed from an ultra-broadband to a narrow-band. The proposed MCWS still reveals high-efficiency polarization conversion at 8.02 GHz, and has the characteristic of being sensitive to the incidence angle.
On the other hand, due to water dispersion, the water permittivity of water varies with increasing temperature according to Debye’s formula (Eq. (1)). The corresponding results for water permittivity at different temperatures are shown in Fig. 8(a). Obviously, the water permittivity decreases as the temperature increases. This phenomenon complicates the design of temperature insensitive water-based metamaterials. However, insensitivity to temperature can be achieved in the MCWS. The reflection spectrum at different temperatures with a step of 20°C is shown in Fig. 8(b), while Fig. 8(c) shows the PCR results at 20°C, 40°C, 60°C, and 80°C. In Fig. 8(b), the curves of ryx exhibit a little bit of a drop. But the ryx values are still over 0.8. As for rxx, the four curves are well coincident with each other with only a small frequency shift. Therefore, the PCR results show high-efficiency of polarization conversion at different temperatures for the frequency range from 7.42 GHz to 15.15 GHz. The PCR frequency shift is caused by the shift of rxx and ryx. However, this variation is weak, and the results still verify the temperature insensitivity.
Fig. 8. (a) The water permittivity with different temperature, (b) The reflection spectrum with different temperature, (c) The calculation results of PCR with different temperature.
4. Experimental results
A prototype containing 20 × 20 unit cells is fabricated, assembled, and measured, as shown in Fig. 9(a). The left side of Fig. 9(a) shows a picture of the CS, which is etched on FR4 through printed circuit board (PCB) technology. The experimental WRR sample is built by 3D printing by using the pellucid photosensitive resin on the top, as shown in the right side of Fig. 9(a). Therefore, we can clearly observe the inside structure of the WRR. There are four pipelines around the WRR, which lead to water connections among all unit cells. The complete prototype dimensions are 200 × 200 × 3.07 mm. The measurement setup is shown in Fig. 9(b). The experimental results of rxx and ryx are measured through a pair of linear horn antennas and a vector network analyzer (Agilent PNA E8362B). The linear horn antenna is able to excite two-types of polarization electromagnetic wave. This is selected by changing the placement mode of the horn antenna. The placement mode of a pair of horn antennas in Fig. 9(b) can acquire the results of rxx. In order to better receiving the electromagnetic wave, the angle between the illuminating and reflecting beam is about 5°. Meanwhile, the distance between antennas and experimental sample is 0.6 m, which can be satisfied the far-field in the measurement.
Firstly, we measured the reflection spectra with absence of water, as shown in Fig. 10(a). The curve of rxx forms a deep dip at 10.02 GHz, while the curve of ryx reaches up to highest value at the same frequency. Figure 10(b) is the PCR result, and this shows high polarization conversion at 10.02 GHz with over 90%. It indicates that the proposed metamaterial achieves narrow band polarization conversion without water. Then, when we added water to the structure, the corresponding results are shown in Fig. 10(c). The measured results are solid line while dash line represents simulated results. Within the frequency of 7.42 GHz to 14.37 GHz, the value of ryx is larger than 0.6, while the value of rxx is lower than 0.4 in the experiment results. Meanwhile, at 7.94 GHz, the reflection coefficient of rxx is 0.15 and that of ryx is 0.75. It reflects perfect property of polarization conversion. Nevertheless, the experiment results are well coincident with the simulation results. The comparison of PCR between simulated and measured is shown in Fig. 10(d). There are two frequency bands of PCR larger than 0.9 where 7.71 GHz to 9.89 GHz and 15.22 GHz to 16.75 GHz. Although, the value of PCR is lower than 0.9 within frequency between 9.89 GHz and 15.22 GHz. It is larger than 0.7 that still exhibits good polarization conversion. From Figs. 10(c) and (d), we infer that the proposed metamaterial is able to realize ultra-broadband polarization conversion in the experiment with the similar frequency range in the simulation. The discrepancy between experiment and simulation can be considered as the fabrication error of 3D printing and PCB technology between simulation model and experimental sample. On the other hand, the water in simulation is the perfect state, but in the measure, the water exists inpurity and ions.
Fig. 10. (a) the experiment results of the reflection spectra with absence of water, (b) the calculated results of PCR with absence of water, (c) the comparison between experiment and simulation results of reflection spectra with the proposed metamaterial, (d) the comparison between simulated and measured results of PCR with the proposed metamaterial.
5. Conclusion
In summary, we utilize water and metal to achieve an ultra-broadband and a high-efficiency reflective polarization conversion between 7.46 GHz and 14.84 GHz. The physical mechanism of polarization conversion is analyzed by distributions of the surface currents, the electric field and the magnetic field. This indicates that the polarization conversion is successfully explained by the coupling between the electric resonance of the CS and the magnetic resonance of the WRR. Meanwhile, the reflection spectra with different incidence angles and temperatures are simulated to show the incident angle sensitivity and temperature insensitivity in the polarization conversion. To verify the performance of the proposed design, the prototype is manufactured and measured, so as to verify that the MCWS achieves reflective polarization conversion. The MCWS can be potentially applied to the successful design of polarization converters.
Funding
Hubei Provincial Department of Education scientific research plan guiding project (B2021311).
Acknowledgments
Zhaoyang Shen thanks the Hubei Provincial Department of Education for help identifying collaborators for this work.
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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