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Abstract
This paper proposed a high angle stability polarization convert metasurface element. The element has one dielectric substrate with the bending lines on the top layer and metallic ground on the bottom layer. A method of priority optimize polarization conversion ratio(PCR) under oblique incident angle based on impedance analysis is proposed to realize high angle stability. And the proposed element can convert linear polarization to orthogonality polarization at 60° incident angle with 17.8% relative bandwidth with more resonances compared with normal incident. Both the PCR and bandwidth of the proposed element increase from 0° to 45° incident angle which different with traditional polarization convert elements. A metasurface with the high angle stability element is fabricated and the measured results are in good agreement with simulated results.
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1. Introduction
With the recent development of microwave field applied for various cases, there is a rapidly increase demand for polarization control which has the function of sensing, radar cross section reduction, the polarization convert of antenna and so on [1–4]. Most traditional polarization manipulation devices utilizing the phase accumulation to obtain polarization change with the principle of birefringence behaviors in crystals, which lead the bulky devices and difficult to satisfy the requirement of lightweight and ultrathin [5,6]. Metamaterial not only has functions in manipulating electromagnetic waves such as beamforming [7], wave absorbing [8], polarization control [9] and filtering [10], but also has advantages of thin thickness, low cost and easy fabrication [11–15]. A number of polarization convert designs have been proposed using effects of anisotropic metamaterials [16], which lead to narrowband and limited the application. Thus there are many elements have been proposed to extend the bandwidth of polarization converters [17–20]. Except considering the bandwidth, the efficient of polarization manipulation has been researched. Although two or more layers or via holes is required for high polarization conversion ratio(PCR) for most polarization converters [21–23], the designs with one layer and none via holes are proposed [24].
However, the wide bandwidth character is only for normal incident and shows rapidly decrease under high oblique incident angle. Also, most high efficient converters cannot maintain the high PCR from 0° to high incident angle. Compare with the study on wide bandwidth and high PCR, the angle stability of polarization convert element is few but valuable because of the potential applications in particular cases. A three metallic layers element with patch, slot and microstrip lines is introduced in [25] with 40° angle stability (PCR > 0.85). The high angle stability is realized by coupling of the patchs and microstrip lines microstrip lines which indicates that more than one layer and via holes are demanded. A single dielectric substrate polarization converter with metallic lines on the top is proposed in [26]. It can achieve 45° angle stability because of the high dielectric constant and large thickness. [27] design a linear convert polarization element loaded slotted patch with one layer. Because of the high dielectric constant, large thickness and the slots on the top patch, the element is miniaturized which lead to high angle ability. The bandwidth of the element is 7.5% at 60° incident angle.
In this paper, a high angle stability polarization convert metasurface element with bending metallic lines is designed. The method to priority optimize PCR under middle oblique incident angle based on and impedance theory is proposed. The PCR and bandwidth reach best at 45° incident angle, which different from most polarization convert elements. The performance at 60° incident angle is good with multi-resonances whereas rarely other elements can achieve. The simulated relative bandwidth of the element is 17.8% under 60° incident angle at Ku band and has a valuable agreement with measurement results.
2. Element structure
Fig 1 shows the configuration of the proposed polarization convert metasurface element with the size of 0.43λ×0.43λ×0.027λ. It composed of a structure with bending lines on the top layer and a metallic ground on the bottom. The Rogers 5880 dielectric substrate(${\varepsilon _r} = 2.2,\; tan\delta = 0.0009$) with 1.524 mm thickness is adopted. Structure parameters of the element are chosen as follows: P = 8 mm, d = 0.3 mm, d1 = 0.7 mm, d2 = 0.5 mm, L = 8 mm, l = 3.6 mm, l1 = 2.5 mm, g = 0.3 mm. The u- and v-axis are defined by rotating the x- and y-axis by 45° respectively and mutually to each other. In order to design the element with the same polarization rotation characteristic for co- and cross-polarized incident waves, the symmetrical of the element along both u- and v-directions is designed. The main structure of the top layer is two parallel narrow lines(PNL) with the distance of d4 along u-axis. On the basis of main structure, two T-shape lines(TSL) are loaded on the middle of the main structure. Also, another bending lines on side(BLS) are placed on both sides of the main structure.
The simulated cross- and co-polarization reflection coefficients ${r_{xy}}$ and ${r_{yy}}$ under different incident angles are shown in Fig. 2(a-b). Within the frequency of 13.5-14.7 GHz, the ${r_{xy}}$ is better than -1.5dB with incident angle from 0° to 60°. It can be observed that the ${r_{xy}}$ increases with the incident angle becomes larger and reaches best when the incident angle is 45° rather than 0°. The property is different with most polarization convert metasurface elements. At 60° oblique incident angle, the reflection coefficient decreases but still better than -1.5dB in the frequency range of 13.3-15.3 GHz, and has larger bandwidth compared with low incident angles. The co-polarization reflection coefficient ${\textrm{r}_{\textrm{yy}}}$ with incident angle from 0° to 60° is low and shows more resonances with the increase of incident angle, which beneficial to obtain wide bandwidth. It can be noticed that the element has three resonances at 13.5 GHz, 14.9 GHz and 15.3 GHz with 60° incident angle. It indicates that the element has better performance under oblique incident rather than normal incident, which has application prospects in the cases that require polarization convert function at high oblique incident angle or wide incident angle range.
Fig. 2. Simulated results of proposed element with different incident angles. (a) ${r_{xy}}$ . (b)${r_{yy}}$. (b) PCR.
Fig 2(c) shows the PCR of the element in the frequency band, which PCR is defined as $r_{xy}^2/({r_{xy}^2 + r_{yy}^2} )$. The PCR is higher than 0.85 under incident angle from 0° to 60° in the frequency range of 13.5-14.6 GHz with 7.8% relative bandwidth. The simulated results confirm that the metasurface element can convert the most energy of y-polarization wave to x-polarization and have good performance of polarization convert at Ku band. It should be mentioned that the bending structures are proposed to obtain miniaturization element to generate the character of high angle stability. Also, the complex bending lines of the element are beneficial to get more resonances to achieve wider bandwidth. The reasons of high angle stability with different methods especially for impedance analysis is studied as follows.
3. Design process
In order to further understand the high angle stability element which has wider bandwidth under oblique incident, the PCR of three initial structures as shown in Fig. 3 with 0° to 60° incident are simulated. As shown in Fig. 4(a), the PNL has a resonance at about 12.1 GHz and the bandwidth becomes narrower with the increase of incident angle, which performance as a traditional element. It relative bandwidth(PCR > 0.85) is 5.6% at 60° incident angle. The PNL with TSL has two resonances at the frequencies of 11.6 GHz and 15.0 GHz, as shown in Fig. 4(b). It indicates that the number of resonances can be increased by loading more proper structures. Although the resonances have narrow bandwidth and the difference between two resonance frequencies is large, it is potential to extend the bandwidth and adjust resonance frequencies by loading specific structures. It can be observed that the structure also a traditional element which has the property of the bandwidth decreases with the rise of incident angle. From Fig. 4(c), the PCR of PNL with BLS has one resonance at 12.7 GHz with wide relative bandwidth of 8.8% under normal incident. Its reflection character almost unchangeable with the various of incident angle from 0° to 45° although the bandwidth has rapidly decrease under 60° incident angle. It can be noticed that the coupling between the TSL and BLS lead to the multi-resonances merge and wideband can be obtained especially for 60° incident angle, which consist with the element property of proposed polarization convert element.
To further study the character of the designed element, the parameter analysis has been completed under normal and oblique incident waves. Fig 5(a) illustrates the simulation results of the PCR with the various value of l which express the length of TSL. It can be observed that the PCR increase from 0.72 to 0.98 when the l increases from 3.2mm to 3.8mm and the center frequency has slight decrease from 14.4 GHz to 13.8 GHz under normal incident. The trend of PCR under 60° oblique incident angle is similarity. These resonance frequencies become far away to each other which lead to the PCR between these frequencies become lower. That means although the performance becomes better with the increase of l at 0° incident angle, the PCR decreases in specific values of l at 60° incident angle. The PCR at 0° and 60° incident angle interacts with each other and appropriate parameter values could be chosen to obtain a balance between different incident angles. From Fig. 5(b), it clearly that the PCR is affect by the distance between the TSL and BLS which is expressed as parameter g. With the increase of the g from 0.1mm to 0.5mm, the PCR under 0° incident angle has a brief increase from 0.96 to 0.99 and the center frequency rises from 14.0 GHz to 15.0 GHz. The situations with 60° incident angle is similarity but the minimum value in the frequency band is almost unchangeable. It obviously that the TSL and BLS effect to each other because of the small distance between them and could be optimize together.
In order to obtain high PCR in wide incident angle, the balance between different angles is necessary. The slight decrease of PCR under normal incident to obtain the good performance under oblique incident is worthy. Therefore, the method to priority optimize PCR under middle oblique incident angle is proposed. And good performance can be obtained not only under normal incident wave but also under high incident wave. That because the value of PCR decrease from middle oblique incident angle to normal incident angle or high oblique incident angle is lower than the decrease value from normal incident to high oblique incident. Also, the final element is optimized by the method and the principle is shown in the section 4.3.
4. Theory analysis
4.1. Current distributions
To research the mode of these resonances, the simulations of surface current distributions are necessary. Fig 6 shows the surface current distributions of the top and bottom layer of the element. It can be observed that most currents concentration on the BLS in one direction in 0° phase state while most currents flow on TSL in 90° phase state. The currents in top and bottom layer are in opposite direction thus the magnetic resonances are generated. It can be noticed that the current can along two directions in different phase states and lend to resonances merge, which different from other converters. As shown in Fig. 2(a-b), the three resonances of the proposed element under 60° incident angle are at 13.5 GHz, 14.9 GHz and 15.3 GHz. And magnetic resonances are generated in these frequencies as shown in Fig. 7. At 15.3 GHz, the current directions on two TSL and BLS on opposite direction are antiparallel, which different with most converters. Due to the magnetic resonances, the magnetic field is increase in the dielectric substrate and the value of magnetic permeability become much larger. Thus the surface impedance of the element larger than the impedance of free space a lot. It indicate that the reflection coefficient is near to 1 and behaves as a high impedance surface at resonance frequencies. For another polarization, it has response as a perfect electric conductor so as to achieve 90° polarization convert function.
Fig. 6. The surface current distributions with 0° incident. (a) 0° phase state. (b) 90° phase state.
Fig. 7. The surface current distributions with 60° incident at (a) 13.5 GHz, (b) 14.9 GHz, and (c) 15.3 GHz.
4.2. Equivalent impedance
In order to further understand the principle of polarization conversion, the analysis of incident and reflected electric field is valuable. As shown in Fig. 8 for y-polarization incident wave, the incident electric field can be expressed as a combination of two equal u- and v-polarization components [28]:
And the reflected electric field can be expressed as
Due to the symmetry of the structure of the element along u/v-axis, the value of the cross-polarization convert components ${r_{uv}}$ and ${r_{vu}}$ is 0. And ${r_{uu}}\; $ and ${r_{vv}}$ can be expressed as ${r_u}\; $ and ${r_v}$ for simplify. Therefore, the reflected electric field $\overrightarrow {{E_r}} $ can be represented the vector sum of the co-polarization components ${r_u}\; $ and ${r_v}$, where ${r_u}$ and ${r_v}$ can be expressed as ${e^{j{\varphi _u}}}$ and ${e^{j{\varphi _v}}}$ respectively. By the anisotropy of the structure along x-/y-axis, it has phase difference between ${r_{u\; }}$ and ${r_v}$. With the condition of ${r_{u\; }} \approx {r_{v\; }}$ and $\Delta \varphi = {\varphi _u} - {\varphi _u} ={\pm} \pi $, the reflected wave has a 90° polarization change, which indicates that the polarization convert function is realized.
To verify the principle of polarization conversion, the simulation of ${r_u}$ and ${r_v}$ with the incident wave of u-/v-polarization is necessary. Fig 9 shows the reflection coefficients at 0° and 60° incident angle. The amplified of ${r_u}$ and ${r_v}$ are almost equal and the phase difference between ${r_u}$ and ${r_v}$ is about 180°, which consist with the theory.
The equivalent impedance surface is researched through the TMM [29]. And the reflection coefficients regarding the u-/v-polarized incident waves can be expressed as
According to [30], the expression of frequency dependent impedance along u-/v-directions can be defined as
Fig 10 shows the calculated imaginary and real parts of the Zu/v under 0° incident angle. The imaginary part of Zu is zero at frequencies of 13.0 GHz and 15.0 GHz while the imaginary part of Zv is zero at frequencies of 13.5 GHz and 16.0 GHz. The real parts of Zu/v are almost infinite at the these frequencies, which indicates the exist of resonances. The results are consist with ${\textrm{r}_{\textrm{xy}}}$ shown in Fig. 2. For 0° incident angle, the bandwidth is extended by the merge of resonances.
Fig. 10. Equivalent impedance of the element with 0° incident angle. (a) Imaginary-part. (b) Real-part.
It can be observed that at the frequency of 15.0 GHz which Zu approaches to infinity, the reflection phase of u-polarized incident wave is about 2nπ(where n = 0, 1, 2, . . .), as shown in Fig. 9. The property imply that the functionality of the metasurface is equivalent to high impedance surface which leads to the amplified of ${r_u}$ near to 1. And the reflection phase of ${r_u}$ is nearly mπ(where m = 1, 2, 3, . . .) which has the character as perfect electrical conductor with ${\textrm{r}_\textrm{u}}$ near to -1. The phase difference between ${\textrm{r}_\textrm{u}}$ and ${\textrm{r}_\textrm{v}}$ is approximately π. Therefore, the reflected wave is along the x-axis and the polarization convert function is achieved. The situations of other resonances for both u- and v-axis are similarity although accurate consist with the theory is difficult. As shown in Fig. 11, the imaginary part of Zu is zero at 11.9 GHz and 16.0 GHz and the frequencies is 12.4 GHz and 14.2 GHz for Zv under 60° incident angle. It can be noticed that there are more resonances compared with 0° incident angle so that the bandwidth is wider, which consist with the reflection coefficient results in Fig. 2. Although the small peaks lead to the phase change more irregularity, the phase difference between ${\textrm{r}_\textrm{u}}$ and ${\textrm{r}_\textrm{v}}$ is near to π. Similarity, the element represents as high impedance character along u(v)-axis and has character of perfect electrical conductor along v(u)-axis. Compared with 0° incident angle, the PCR is higher and relative bandwidth(PCR > 0.85) is larger because of more resonances.
Fig. 11. Equivalent impedance of the element with 60° incident angle. (a) Imaginary-part. (b) Real-part.
4.3. Impedance convert model
To better analysis the reason of high angle stability of the proposed element, the comparison between normal element and polarization convert element with TE/TM incident waves is necessary. As shown in Fig. 12(a-b), the incident and reflected wave is both TE/TM mode. The TE/TM mode of incident and reflected wave is different for the orthometric polarization convert element as shown in Fig. 12(c).
Fig. 12. Schematic diagram of element with different incident and reflected wave. (a) Normal element with TE incident wave and (b) TM incident wave. (c) Polarization convert element.
Based on the distinguish of TE/TM mode, the equivalent circuit model of the three situations are shown in Fig. 13, where ${Z_{in}}$ and ${Z_{re}}$ is the incident and reflected impedance respectively. The impedance of dielectric substrate ${Z_{substrate}}$ is determined by the propagation constant and the thickness of element. The equivalent circuit with one resonance can be simplified to a efficient inductance ${L_{eff}}$ and capacitance ${C_{eff}}$ [31]. It clearly that the normal element with TE/TM incident wave is network with one port while orthometric polarization convert element is described by two ports equivalent circuit model because one port can only represent one polarization.
Fig. 13. Equivalent circuit model of element. (a) Normal element with TE incident wave (b) And TM incident wave. (c) Polarization convert element.
It can be noticed that the impedance of free space is ${Z_0} = 377\Omega $ with normal incident wave. For TE and TM cases, the impedance can be expressed as
where $\mathrm{\theta }$ is the incident angle. It indicates that the impedance of free space is different at oblique incident angle and the difference increases rapidly with the rise of $\mathrm{\theta }$, as shown in Fig. 14. The difference between $Z_0^{TE}$ and $Z_0^{TM}$ is 267$\mathrm{\Omega }$ and 566$\mathrm{\Omega }$ at 45° and 60° incident angle respectively. Although the element which has symmetry along u-/v-axis has consist impedance in TM and TE mode under normal incident, the response is different under oblique incident and the difference is larger with higher incident angle. Thus the angle ability for TE and TM mode is different and the realization of high angle stability element for both TE and TM mode incident wave becomes more difficult.Fig. 14. The value of $\textrm{Z}_0^{\textrm{TE}}$ and $\textrm{Z}_0^{\textrm{TE}}$ at different incident angles.
Fig. 15. Measurement. (a) Photo of the metasurface sample. (b) Amplification view. (c) Measurement environment.
Fig. 16. Measurement results of the metasurface at different incident angles. (a) Cross-polarization reflection coefficients. (b) Co-polarization reflection coefficients.
However, the situation of polarization convert element is better. For the TE/TM mode incident wave, the reflected wave is TM/TE mode due to the polarization convert function. According to the reciprocity principle, the reflected character of TE and TM incident wave is consist. Thus the following discuss only consider TE incident wave for polarization convert element. By the analysis above, the incident impedance and reflected impedance is different and the difference is much larger with high incident angle. The design of polarization convert element for high angle stability is to match the incident and reflected impedance according to two ports network theory. The proper impedance of polarization convert element can improve the PCR. However, it can be noticed that the TE/TM mode impedance of polarization convert element is different under oblique incident. But the independence adjust of TE and TM mode independence is difficult for polarization element because of the symmetry along u-/v-axis. Also, the multi-solutions of TE and TM mode independence with specific oblique incident angle may all satisfy the reflection coefficients of element. Although giving and adjusting the TE and TM mode independence is difficult, the method of optimize the PCR in middle incident angle first is still effective because the response of TE/TM mode for polarization convert element is the same. It can be observed that the element with impedance of ${\textrm{Z}_0}$ has good performance under normal incident. But it reflected character decreases rapidly with the increase of the incident angle. However, the design has good match in middle incident angle can obtain good performance not only under normal incident but also under high incident angle because the character decrease is lower than the decrease from normal incident angle to high incident angle. It can be noticed that the value of ${L_{eff}}$ and ${C_{eff}}$ changes with the variation of incident angle, which have effect on element impedance. But it not impact the design method of optimize reflected property at middle incident angle first. The design principle is consist with the proposed element which has best polarization convert character at 45° incident angle while the performance at 0° and 60° incident angle is also high quality.
5. Measurement
In order to confirm 90° polarization convert function of the proposed polarization convert element, a 35 × 35cm metasurface is fabricated with 39 × 39 elements, as shown in Fig. 15. The polarization of the two horn antennas are parallel and perpendicular for measurement of co- and cross-polarization reflection coefficients respectively. To confirm the incident and reflected angle is consist, the location and orientation of the horn antennas should be adjust. As shown in Fig. 16(a), the measured cross-polarization reflection coefficients are better than -2 dB within the frequency of 13.5-14.7 GHz from 0° to 60° incident angle, which shows high angle stability. Also, reflection coefficient at 45° incident angle is highest which consist the simulation. As shown in Fig. 16(b), the co-polarization reflection coefficients of the metasurface are low and in good agreement with simulated results. Although the loss is a little larger in measurement which may caused by the loss of horn antennas and propagate paths, the measurement results are in good agreement with simulated results.
Performance compared is given in Table 1. It can be seen that some elements is broadband but the angle stability is not given. Although some elements [25,26,32] have angle stability of 40-45°, the performance of 60° incident angle is not given. Only few researches [25,33] show the element performance at 60° incident angle. But their relative bandwidths are low and have sharp decrease under high oblique incident. In this work, the relative bandwidth with 60° incident angle is the best and even larger than the relative bandwidth under normal incident. Also, the height of proposed metasurface element is the lowest with one layer and none via holes. It obviously that the proposed polarization convert element has great performance on angle stability.
Table 1. Performance compare with other polarization convert elementsa
6. Summary
In this paper, a high angle stability polarization convert metasurface element is proposed. The element is composed of bending metallic lines on the top layer and ground on the bottom with one dielectric substrate. By the proposed method of priority optimize PCR under oblique incident angle based on impedance convert model, higher angle stability can be obtained. Different from traditional element, the PCR and bandwidth increases with the rise of incident angle from 0° to 45° and also has high performance at 60° incident angle. The design process, current distributions, equivalent impedance and impedance convert model of the element is introduced. The angle stability of the polarization convert element can achieve 60° with 17.8% relative bandwidth at Ku band which rarely other elements can achieve.
Funding
National Key Research and Development Program of China (2020YFB180- 7400); National Program on Key Basic Research Project of China (2019-JCJQ-ZD-067-00).
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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