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Abstract
Polarization manipulation is a key issue in electromagnetic (EM) research. Research on 90° polarization rotators and circularly-polarized wave generators has been widely conducted. In this study, a polarization conversion metasurface that can shift one linearly-polarized EM wave into multi-polarization outgoing waves at certain frequencies is demonstrated, including co-, cross-, left-hand, and right-hand circular-polarization components. The surface was made of periodically arranged chiral meta-atoms. The polarization manipulation method is based on the independent control of phase and magnitude, in which the phase control is based on the Berry-phase theory of linearly-polarized EM waves, while the magnitude control is based on the cavity mode theory of the microstrip structure. Both eigenmode analysis (EMA) and characteristic mode analysis (CMA) were utilized for magnitude control, which was further verified by the surface current distribution. Finally, the metasurface was fabricated and measured, showing good agreement between the measured and simulated results. This research proposed what we believe to be a novel polarization method, which can be potentially applied in polarization manipulation, EM radiation, filters, wireless sensors, etc., over a frequency range from optics to microwave bands.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Recently, polarization manipulation has been the focus of both microwave and optics studies. Polarization converters, which shift the polarization of electromagnetic (EM) waves to other states, are widely used in polarization manipulation [1,2], circularly polarized antenna design [3,4], and radar cross-section (RCS) reduction [5]. By employing the field transformation method [6], it can even be used to form an EM wavefront. Currently, the development of metasurfaces [7] has significantly promoted the development of 2-D polarization converters. Polarization conversion metasurfaces are widely applied in polarization manipulation to shift the incident polarization to another one.
Among studies on polarization converters, the 90° polarization rotator, which can transform the incident EM wave of linear polarization to its cross-polarization counterpart, is the most focused one. It employs anisotropic structures, whose phase response along two vertical directions has a π difference, to achieve 90° polarization rotation [8,9]. In [10,11], by utilizing Jones matrix analysis, a chiral metasurface achieves such a polarization shift in the transmissive case. By exciting the coupling between one mode and its vertical degenerate mode counterpart [12,13], the 90° polarization rotators with a substrate integrated waveguide (SIW) cavity resonator are proposed. In addition, linear-to-circular polarization conversion is another subject in polarization conversion research, which can achieve a reciprocal transformation between linearly- and circularly-polarized EM waves. Anisotropic structures, in which the phase response along two vertical directions has a π/2 difference, were used in these studies [14,15]. [16] employed a triple-twisted split-ring resonator to design a compact chiral circular polarizer. Recently, the polarization conversion from a linearly-polarized incidence to reflections in multi-polarization is developed by introducing the composite meta-atom [17,18] or by surface impedance design [19,20]. However, in these studies, the response phase between orthogonal directions should be manipulated in distinct frequency bands, so that the multi-polarization states should distribute in a wideband. In this report, we proposed an approach of polarization modulation, which can sharply shift the polarization states from linearly- to multi- in a narrow band.
This polarization control is achieved by the separate manipulation of the phase and magnitude. First, we utilized the Berry-phase [21,22] of the linear-polarization EM wave to control the phase. In EM wave research, by employing the Poincare sphere [23] or Jones Matrix [24], the Berry-phase of circularly-polarized waves has been widely applied in phase modulation, achieving some fascinating performance, such as beam forming [25], imaging [26], orbital angular momentum (OAM) generation [27], and rotational Doppler effect [28]. However, research on the Berry-phase of linearly-polarized waves has received insignificant attention. Second, we manipulate the magnitude based on the cavity mode theory [29–32] of the microstrip structure. Both the eigenmode analysis (EMA) and the characteristic mode analysis (CMA) [33,34] were introduced during magnitude control. Herein, CMAs under different boundary conditions are employed to control the magnitude of the outgoing wave. Collectively, a one-to-multi-polarization manipulation metasurface is achieved after comprehensively controlling the phase and magnitude in two orthogonal polarization.
This manuscript begins with the introduction of a polarization conversion metasurface, which can transform a linearly-polarized incident wave to reflection with co-, cross-, left-hand circular-, and right-hand circularly-polarized polarization states at different frequency bands. Then, aiming at a better understanding of the mechanism, the Berry-phase was investigated to analyze the phase responses of the metasurface. The magnitude response analysis was followed by EMA and CMA. The current distributions based on CMA and full-wave simulation show good agreement, and both meet the requirements for multi-polarization reflection. Finally, the proposed metasurface was fabricated and measured to provide experimental verification. In this research, a polarization method, which can be potentially applied in polarization manipulation, EM radiation, filters, wireless sensors, etc., over a frequency range from optics to microwave bands is proposed.
2. Design
A reflective one-to-multi-polarization conversion metasurface was first designed and schematically depicted in Fig. 1(a). The incidence and reflection are along the –z and + z, respectively. The working frequency band of the reflective EM wave is divided into seven parts according to the polarization states, as shown in Fig. 1(a). The polarizations at F1 and F7 are co-polarized, whereas those at F3 and F5 are cross-polarized. For an x-polarized incidence, the reflective waves at F2/F6 and F4 are left-hand and right-hand circularly-polarized, respectively, while for a y-polarized incidence, they are right-hand and left-hand circularly-polarized, respectively. This asymmetry occurs because the meta-atom is chiral. The metasurface was patterned on both layers of a substrate with a dielectric constant of 2.2 and loss tangent of 0.001. The thickness of the substrate is 0.762 mm. The meta-atom is indicated in Fig. 1(b), with the top layer in the upper and bottom layers below it. A metallic background with a cross-gap cut is printed on the top layer to function as a feed system, which ensures that the patch can be excited by the incident EM wave and the reflected wave can be transmitted back. A perturbation comprising two small metallic rectangles, which is the key structure in this design, is loaded onto the square patch across its corners. This perturbation load will cause new eigenmodes, resulting in a cross-polarized radiative component. Therefore, reflections in different polarizations can be further achieved. In the figures, G denotes the width of the gap, which is equal to 0.25 mm; D denotes the distance between adjacent cells, which is equal to 20 mm; W and the side length of the patch were 10 mm. P and O are equal to 2 mm and 2.2 mm, which represent the width and length of the perturbation rectangle, respectively.
Fig. 1. (a) Schematic of the polarization conversion metasurface. (b) Top and bottom layer of the cell. (c) and (d) show the simulation results of magnitude and phase, respectively. The information of 3-dB magnitude difference band, i.e., 3-dB axial-ratio band, is as well as shown in (c).
The simulation results of the magnitude and phase of the reflection are depicted in Figs. 1(c) and (d), respectively. The annotations denote the polarization of outgoing and incident wave, for example, “Y_X” denotes that the incident wave is x-polarized while the reflective one is y-. Considering the x-polarized wave incidence as an example, the reflective EM wave is co-/cross-polarized when the outgoing wave is x-/y-polarized. Moreover, by analyzing both the magnitude and phase, the reflection is left-hand and right-hand circularly-polarized if the phase of the y-polarized component is 90° ahead/behind that of the x-polarized component, while their magnitudes are the same. In this case, F1 and F7 correspond to the band below 9.5 GHz and above 10.7 GHz, while, F2 to F6 is around 9.77, 9.9, 10.2, 10.43, and 10.52 GHz, respectively. To consider both the phase and magnitude characters, the 90° phase difference between x- and y-polarized reflections is well kept over the investigation band, so that the axial-ratio feature at F2, F4 and F6 is determined by the magnitude difference completely. Here, we provide the band information with magnitude difference less than 3 dB in Fig. 1(c). The axial-ratio is less than 3 dB at these bands. In addition, two discussions on the proposed metasurface: (i) when the incidence is along the + z direction, the metasurface works as a low-pass frequency selective surface (FSS), which is totally-reflective in co-polarization above 0.6 GHz while transitive below (detailed in Supplement 1, S1); (ii) the performance in oblique incidence case can only been kept when the incident angle is less than 15°, owing to that, first, the meta-atom is a strong resonant structure, and second, the atom dimension is not small enough (around 0.67 λ at the working frequency).
3. Analysis
3.1 Phase manipulation based on Berry-phase of linearly-polarized EM wave
The method analysis is divided into two parts: (i) phase control based on the Berry-phase of the linearly-polarized wave and (ii) the magnitude control based on the mode analysis of the microstrip structure. For phase control, we first investigated the rotation along the equator in the Poincare sphere, which indicates the polarization rotation of the linearly-polarized EM wave. Based on the Berry-phase theory, the cross-polarization rotation will result in a ± 90° phase shift. As shown in Fig. 2(a), when an x-polarized EM radiates to an infinite PEC plane, the phases of the + y- and –y-polarized reflective components are shifted by 90° and –90°. This is verified by the simulation results in Fig. 2(b), that the phase of reflection in x-polarization advances/lags that in y-polarization by 90° when the incident polarization reaching on the PEC is in –x/+x axis. Note that, the magnitude of the cross-polarization component is very low, and such a simulation is merely exhibiting the Berry-phase of linearly-polarized waves.
Fig. 2. (a) Reflection of a PEC plane. (b) shows the phase responding of x- and y-polarized reflection in the case of x-polarized incidence. (c) One symmetrical and one unsymmetrical structures for comparison of Berry-phase of linearly-polarized wave. (d) Simulation results of these two models.
If we replace the PEC plane with a metasurface, its element should be symmetrical such that this phase difference can be maintained. Here, we employ the proposed rotator metasurface to act as a symmetrical structure example, of which the element is delineated in Fig. 2(c) as Model 1. In contrast, an unsymmetrical structure achieved by loading only one perturbation to the square patch was simulated as Model 2. Figure 2(d) compares the phase performance of the symmetrical and unsymmetrical structures. For Model 1, the phase difference is approximately 90°, −90°, or −270°, whereas for Model 2, the phase cannot be maintained in the resonant frequency band. Therefore, we load two perturbations across the corner, which can maintain a phase difference of ±90° at all frequencies.
3.2 Magnitude manipulation based on EMA and CMA
The analysis of the magnitude manipulation of the reflection starts from eigenmode analysis, followed by characteristic mode analysis. According to the cavity mode theory of the microstrip structure eigenmode analysis [25,26], which is analyzed by solving the source-free Helmholtz equation in the case of different boundary conditions, can characterize the electric/magnetic field and surface current performance with quantitative results. A square patch antenna with its side w is shown in the first subgraph of Fig. 3(a), in which its two fundamental eigenfunctions of the electric infield can be normalized as:
In the equations, Δs and s are the areas of perturbations and patches, respectively. ka and kb have different values, implying that these two modes have different resonant frequencies. ψa and ψb are the new fundamental eigenfunctions in the form of subtraction and addition of ψ10 and ψ01, respectively. This signifies the perturbation loading results in coupling between ψ10 and ψ01, which may lead to polarization conversion. Because a feeding system formed by a cross-gap-loaded PEC plane on the top layer of the substrate is further added, the derivation process would be too laborious to obtain an accurate calculation.
Fig. 3. CMA of three different structures. (a) patch, (b) patch with perturbation, and (c) patch with both perturbations and feeding system. The first columns are schematics of the structures. The second one shows the Model Significances of the two fundamental Characteristic modes. The last two columns demonstrate the normalized current distribution of mode 1 and mode 2, respectively.
Currently, the use of multilayer (ML) solver powered by Computer Simulation Technology (CST) Microwave Studio (MWS) plays a powerful role in the design and analysis of microstrip structures. By calculating the scattering properties based on the method of moments (MoM), CMA was performed to replace the complicated EMA. Herein, we employed the ML solver to investigate magnitude manipulation. The CMA process comprises three steps: (i) simulation for a patch, (ii) simulation for a patch with perturbation, and (iii) simulation for a patch with both perturbations and feed system, which are shown in Figs. 3(a) to (c), respectively. The dimensions of the structure employed for the CMA are same as those in the proposed metasurface design. In Fig. 3, the first columns show the simulation structures, the second ones show the Model Significances (MS) of the two fundamental characteristic modes, and the last two columns demonstrate the normalized current distribution in vector of mode 1 and mode 2, respectively, at their own resonant frequencies. One note: MS is a key parameter of CMA theory, which demonstrates the coupling performance between resonance mode and the hypothetical source. The structure is resonant when MS = 1, i.e., the frequency with MS = 1 is the resonance frequency.
The CMA for the patch, as shown in Fig. 3(a), corresponds to Eq. (1), of which the resonant frequencies of modes 1 and 2 are both at 9.5 GHz. Meanwhile, the surface currents in vector of mode 1 and 2 are along the x- and y-axis, respectively, with the same distribution. In (b), the CMA for the patch with perturbations loaded indicates that the resonant frequencies are 7.8 GHz and 9.5 GHz for mode 1 and 2, respectively. For mode 1, the frequency is 7.8 GHz, at which the surface current distributions are in accordance with the calculation results of the first formula in Eq. (2). For mode 2, the frequency is 9.5 GHz, at which the surface current distributions are in accordance with the calculation results of the second formula in Eq. (2). The distribution in x- or y-polarization is similar to that of the proposed patch.
After loading the feeding system, the resonant frequencies move to 9.5 GHz and 10.4 GHz for mode 1 and mode 2, respectively. Meanwhile, these two modes maintain the surface current distributions as in the case of a structure without a feeding system in Fig. 3(b), indicating that they have similar characteristic functions as the expressions in Eq. (2).
A full-wave EM simulation is performed to verify the proposed CMA and further analyze the mechanism of the metasurface. The surface currents at frequencies with different reflective polarization states are shown in Figs. 4(a)–(g). The phase difference between the current along the y- and x-axis is marked in the top-right corner. The current intensity is schematically indicated with the arrow patterns, where the intensity signified by two arrows is approximately double that represented with one. There is limited current on the patch in Figs. 4(a) and (g), implying that the incident EM wave is totally reflected by the top layer, that is, no current is induced on the patch. Therefore, their performance is the same as reflection by a PEC plane, with total reflection in co-polarization at these two frequency bands. In Figs. 4(b) and (c), the magnitudes along the x- and y-axis are equal, while the phase has a difference of 180°. In Figs. 4(e) and (f), the magnitude/phase in the x- and y-directions are similar. In Fig. 4(d), the current along the x-axis seems too light owing to the phase difference of 90° between the x- and y-polarized currents. In fact, the magnitude of the y-polarization is approximately twice that of the x-polarization. Therefore, to consider both phase and magnitude, although the current performance is similar in Figs. 4(b) and (c), as well as in Figs. 4(e) and (f), their essential working modes are completely different.
Fig. 4. Full wave simulation results at different frequencies with different reflective polarization states in the x-polarized incidence. The current distribution at 9.0 GHz, 9.77 GHz, 9.90 GHz, 10.2 GHz, 10.43 GHz, 10.52 GHz, and 11 GHz are shown in (a) to (g), respectively.
Based on the current performance in the CMA and full-wave EM simulation, we then represent the reflective performance with the corresponding formulas. The modes in Eq. (2) are the basis modes; therefore, every working mode can be indicated by the linear combinations of the two. Meanwhile, because the currents of both basis modes focus at the edge of the patch, the analysis can be achieved by surveying only the current on the edges. The total surface current comprises two components: one is induced by incidence and the other is to generate reflection. In the case of x-polarized incidence, we assume the excitation current as J whose direction is along the x-axis here, denoted as normalized Jex. Meanwhile, its response current is formulated as Jaexp(jθ)ex + Jbexp(jφ)ey, where a and b represent the magnitude of the response current along the x- and y-axis, respectively, and θ and φ denote their phases. So that, the total current in x- and y-polarization can be formulated as J + Jaexp(jθ) and Jbexp(jφ), respectively. To calculate the expression of the surface current, i.e., to solve the values of a, b, θ and φ requires four constraint conditions. Herein, we utilize the conditions including: (i) a2 + b2 = 1 achieved by the energy conservation, (ii) the value of a/b achieved by the working polarization, (iii) the value of θ–φ achieved by the working polarization, and (iv) the phase difference of the total current between the x- and y-direction achieved by the full-wave simulation. Based on such four conditions, we can first obtain the expressions at different frequencies, and second validate our method by comparing the current intensity of calculation results and the full-wave simulation results. The results at 9.77 GHz and 10.52 GHz, which are shown in Figs. 4(b) and (f), are both left-hand circularly-polarized reflection, can be formulated as respectively:
The magnitudes of the x- and y-oriented total-current are both equal to $J\sqrt 2 /2$, while the phase difference is 180° and 0°, respectively, which coincide with the simulation results.
At 9.9 GHz and 10.43 GHz, the polarization conversion metasurface transforming the incident EM wave to be cross-polarized, as shown in Figs. 4(c) and (e), are denoted as:
The magnitude of the total-current along the x- and y-axis is equal to J, while the phase has a 180° and 0° difference, respectively. The intensity and direction also coincide with the simulation results. The case of right-hand circularly-polarized reflection at 10.20 GHz, as shown in Fig. 4(d), is represented by the following equation:
From the results, the magnitude of the current along the x-direction (0.3J) is around the half of that along the y- (0.7J), which coincides with the full-wave simulation results. The detailed derivations of the magnitude and phase calculation in Eqs. (3)–(5) are shown in Supplement 1, S2.
In summary, all the calculation results show good agreement with the simulation results, which can verify the calculation sufficiently. The calculations in the x-polarized incidence are performed, whereas the analysis for the y-polarized incidence is based on the same method. Another important result of the calculation is that the two modes at 9.9 GHz and 10.43 GHz which can be represented as respectively J–J and J + J correspond to the two fundamental modes in Eq. (2). Both the working frequencies and current distribution agree with the CMA and full-wave simulation results. So that, the lower frequency for mode 1 will red-shift with an increase in the perturbation size, while the higher frequency for mode 2 will remain unchanged. We simulated the reflective performance with different perturbation sizes, as shown in Fig. 5. The higher frequency maintains around 10.4 GHz, while the lower frequency is shifted from 10.1 GHz to 8.7 GHz when P changes from 0.5 mm to 4 mm with a step of 0.5 mm. This performance verified the proposed method as well.
Fig. 5. Simulation results of reflective EM wave when we shift the length of perturbation from 0.5 mm to 4 mm with a step of 0.5 mm. The higher frequency maintains around 10.4 GHz while the lower frequency step down from 10.1 GHz to 8.7 GHz.
3.3 Discussion on one-to-multi-polarization conversion metasurface
As analysis above, we presented a method of polarization manipulation, in which the phase and magnitude are controlled separately. The phase difference between the orthogonal polarizations is manipulated based on the Berry-phase of linearly-polarized wave, while, the magnitude is manipulated by introducing the EMA and CMA based on the cavity mode theory of microstrip. The CMA results, full-wave simulation results and the calculation expressions are coincident. The proposed metasurface demonstrated a one-to-multi-polarization conversion. Furthermore, there exists no PEC background in the previous reflective polarization-conversion metasurfaces, so that the metasurface can work as an FSS, i.e., provide an EM transmission window, in the case of inverted incidence.
The proposed metasurface has various applications. First, the metasurface can generate a far-field radiation with multi-polarization states, so that it can be applied in the communication research such as the satellite communication which demands uplink/downlink channels. Second, the polarization convertor can achieve multi-polarization waves by a single metasurface, which may benefit the experimental EM studies which need investigation in different polarization cases. Third, it can be utilized in wireless sensor, such as, the strain-sensor of which the deformation can be evaluated by the polarization transformation. At last, such a multi-polarization feature can be utilized in information encoding through introducing polarizers, of which the different polarizations represent different codes.
Herein, we also provide a comparison between Ref. [17–20] and this research, as shown in Table 1. From the perspective of design method, Ref. [17–20] focused on the phase manipulation of anisotropic structures, of which the one-to-multi-polarization conversion is achieved by introducing composite meta-atom or by modulating the imaginary part of surface impedance. In this work, the polarization manipulation is achieved by controlling both the phase and magnitude characters. From the perspective of performance, Ref. [17–20] demonstrate a polarization conversion, of which the reflective multi-polarization states should distribute in a wideband, since the response phase between orthogonal directions should be manipulated in distinct frequency bands. Whereas in this work, the proposed metasurface obtains a sharp polarization variation in a narrowband. From the perspective of structure, our metasurface introduced no metallic background, which can provide an EM transmission window at the lower frequency.
4. Fabrication and measurement
The metasurface was fabricated by employing a printed circuit board of Taconic TLY-5 with a dielectric constant of 2.2, and a loss tangent of 0.001. The fabrication is shown in Fig. 6(a) with a magnification of the top and bottom layers on the right. The entire surface is formed by periodically ranging 11 × 11 proposed cells of size 220 mm × 220 mm. As introduced above, the reflection contains four different polarization states at different frequencies by synthetically analyzing the magnitude and phase performance. Nevertheless, the measurement of the phase may be inaccurate, which will result in incorrect measurement results. Aiming at an effective test, the four reflective polarization states are measured directly; the measurement setup is shown in Fig. 6(b). The transmitter is a linearly-polarized horn antenna, working with four different receivers: co- and cross-polarized antennas for co- and cross-polarized reflective EM wave measurements, respectively, and left-hand and right-hand circularly-polarized antennas for right-hand and left-hand circularly-polarized reflection measurements, respectively. According to the reflection law, the angle between the transmitter and the normal direction of the metasurface under test is 5°, which is equal to the angle between the receiver and the normal direction. For co- and cross-polarized measurements, the test system is calibrated to 0 dB in the case that: (i) a PEC plane with same dimension as the metasurface under test is introduced as the reflection plane; (ii) the transmitter and receiver are in same linearly-polarization. For the circularly-polarized measurements, the test system is calibrated to −3 dB in the case that: (i) a PEC plane with same dimension as the metasurface under test is introduced as the reflection plane; (ii) the transmitter is linearly-polarized while the receiver is in circular-polarization with corresponding hand-state. The measured results for all reflective polarization states are shown in Figs. 6(c), in which the subscript have the same meaning as what is mentioned above; furthermore, “R” and “L” denote that the polarization state is right-hand and left-hand circularly-polarized, respectively. The first letter of the legend in the figure denotes the polarization of reflection, while the second denotes the polarization of incidence. Take the “R_X” for example, it represents that the incident wave is x-polarized while the reflection is right-hand circularly-polarized. From the results, there exists four reflective polarizations in the x-/y-polarized incidence, including: (i) co-polarized at the band below 9.5 GHz and above 10.7 GHz, (ii) cross-polarization around 9.9 GHz and 10.4 GHz, (iii) right/left hand circular-polarization around 10.2 Ghz, and (iv) left/right hand circular-polarization around 9.8 GHz and 10.5 GHz. These results are in accordance with expectations based on theoretical analysis. Detailed results: in the x-polarized incidence case, the peak values of cross-, right-hand circularly-, and left-hand circularly-polarized reflections are respectively −0.42 dB (9.95 GHz) / −0.62 dB (10.39 GHz), −0.66 dB (10.19 GHz), −0.67 dB (9.78 GHz) / −1.34 dB (10.52 GHz); in the y-polarized incidence case, they are respectively −0.44 dB (9.95 GHz) / −0.51 dB (10.40 GHz), −0.84 dB (9.76 GHz) / −0.64 dB (10.5 GHz), −0.59 dB (10.16 GHz). The axial-ratio performance can also be evaluated by the magnitude difference between co- and cross-polarized reflections that: in the x-polarized incidence case, the 3 dB axial-ratio bands are 9.78-9.85 GHz (left-hand), 10.09-10.27 GHz (right-hand), and 10.48-10.56 GHz (left-hand); in the y-polarized incidence case, they are 9.77-9.84 GHz (right-hand), 10.08-10.28 GHz (left-hand), and 10.49-10.56 GHz (right-hand). To compare the simulation and measurement results in detail, we depicted the co- and cross-polarized reflections in Fig. 6(d). They coincide with each other in terms of both operation frequencies and reflective performance at these frequencies.
Fig. 6. (a) Fabrication of proposed polarization conversion metasurface. (b) shows the test setup for the metasurface’s measurement, which comprises a linearly-polarized transmitter and four different polarization antennas for different polarization states measurement. (c) denotes the test results of reflection in different outgoing polarization. (d) compares the simulation and measurement results of co- and cross-polarized reflection.
5. Conclusion
In this study, a one-to-multi-polarization conversion was achieved by a metasurface comprising a periodically arranged chiral meta-atom. In the linearly-polarized wave incidence, the outgoing wave is transformed into multi-polarization states at different frequencies. The conversion method is based on the independent control of the phase and magnitude, in which the phase control utilizes the Berry-phase of linearly-polarized waves, while the magnitude control is based on the cavity mode theory of the microstrip. Both EMA and CMA were employed during the magnitude analysis, which was verified by a full-wave simulation. The work mechanism was then represented by the corresponding formulas, meeting a coincident relationship between the calculation and simulated results in the CMA and full-wave simulation. Finally, the metasurface was fabricated and measured, achieving an evident one-to-multi-polarization conversion. This work shows a novel polarization behavior, which may be potentially used in engineering applications and polarization manipulation over microwave and optical bands.
Funding
National Natural Science Foundation of China (62001068, 62101262); Fundamental Research Funds for the Central Universities (2022CDJXY-019).
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.
Supplemental document
See Supplement 1 for supporting content.
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