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Abstract
The realization of cross-polarization conversion has attracted great interest in polarization conversion metasurfaces (PCMs), particularly due to polarization manipulation of electromagnetic (EM) waves with small size and low loss. An azimuth-rotation-independent (ARI) cross-polarization converter is a kind of 90° polarization rotator, which can rotate the polarization of linearly polarized incident electromagnetic (EM) waves with an arbitrary polarization direction to the orthogonally polarized transmitted EM waves. In this paper, we study the symmetry properties of chiral metasurfaces using the Jones matrix method for ARI 90° polarization rotators. The previous designs could only address C4 symmetry, but with this approach, the derived unit cell structure of the ARI PCM should possess Cn(n ≥ 3, n ∈ N+) symmetry. To confirm the design concept, two chiral structures with different symmetries are investigated by full-wave numerical simulations. The experimental results are also carried out and excellently agree with the simulated results. It could be used for polarization conversion applications and further utilized in antenna applications, polarization detection, and telecommunication applications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces, which are two-dimensional (2D) artificial materials with subwavelength thickness, have been widely studied in the past decade due to their properties that are not easily realized in natural materials [1–3]. Metasurfaces are proper platforms for electromagnetic-wave beam shaping, such as focusing, defocusing, reflection, and refraction. They have been widely applied in wavefront modulation [4,5], antenna performance enhancement [6–9], perfect absorbers [10–12], cloaking [13], scattering reduction [14–16], and energy harvesting [17]. Polarization is usually manipulated by birefringent materials, such as crystalline solids and liquid crystals, behaving as wave plates. However, they have many limitations in manipulating capacity and thickness. Recently, polarization conversion metasurfaces (PCMs) have provided more opportunities for polarization modulation in the microwave [18–22], terahertz [23,24] and optical [25,26] ranges.
For the case of linear to cross polarization conversion, most investigated PCM structures are non-${C_4}$ symmetric [14–20], corresponding to linear birefringence [27,28]. They could only realize cross-polarization conversion for certain incident azimuths (such as x- or y-polarized waves). ${C_4}$ Symmetric structures, such as gammadions [29,30] and composite gammadions [31], have been proposed for azimuth rotation-independent (ARI) cross-polarization converters. Recently, Wang et al. [32] claimed that 1) non-${C_4}$ symmetric chiral structures only display the function of the cross-polarization for the x- or y-polarized wave and 2) ${C_4}$ symmetric chiral structures can realize the cross-polarization function for both x- and y-polarized waves.
Here, we present a comprehensive study of ARI PCM derived from the Jones matrix method. The results indicate that the ${C_n}$-symmetric $(n \ge 3,n \in {N^ + })$ but not just ${C_4}$ symmetric chiral structure based on PCM could convert an arbitrarily linearly-polarized incident wave to its cross-polarized state. The operation principle for the ARI PCM can be verified by full wave simulations and experiments in different samples. These results may provide new opportunities for studying the polarization conversion properties of chiral metasurfaces.
2. Jones matrix theory of the ARI PCM
2.1 Schematic diagram
Figure 1 shows the schematic diagram of the ARI PCM. The PCM could convert the normal incidence with an arbitrary azimuth angle of $\varphi $ relative to the x axis to its cross-polarized state. The incident field ${{\mathbf E}_i}$ and the transmitted field ${{\mathbf E}_t}$ can be expressed as follows:
To better understand the dependence of the cross-polarized conversion on the chirality, the transmission Jones matrix is introduced to analyze the ARI PCM,
2.2 ARI structure
First, we deduce the Jones matrix of the structure with the same transmission characteristics for an arbitrary azimuth rotation angle of $\varphi $ with respect to the x axis. The new Jones matrix after rotation ${T_{rot}}$ remains the same as the initial matrix, namely:
where ${R_{(\varphi )}}$ is the rotation matrix,Structures with ${C_n}(n \ge 3,n \in {N^ + })$ symmetry usually have $\varphi = {{2k\pi } / n}(k \le n,k \in {N^ + })$ in the rotation matrix Eq. (7), where at least two angle $\varphi $ values can satisfy Eq. (9), and then Eqs. (10)-(12) will be valid. Therefore, the ${C_n}(n \ge 3,n \in {N^ + })$-symmetric structure is an azimuth rotation-independent (ARI) structure.
2.3 Linear-to-cross ARI PCM
In general, chiral metasurfaces have three important parameters that affect the performance, i.e., polarization rotation angle, ellipticity angle and polarization conversion ratio. The polarization rotation angle $\theta $ characterizes the optical activity:
and ellipticity angle $\eta $ characterizes the difference of the circular dichroism:For linear to cross polarization conversion, based on Eqs. (13) and (14), $\theta $ is supposed to be 90° and $\eta $ is 0°. According to Eq. (12), we have the following property:
and B is related to the chiral structure and cannot be 0. Furthermore, to obtain efficient transmittance, the magnitude of B should be close to 1.In summary, to obtain a high-efficiency linear-to-cross ARI PCM, the element pattern should be ${C_n}(n \ge 3,n \in {N^ + })$-symmetric, and A = 0, |B|≈1 in the Jones matrix.
3. ARI PCM samples with ${C_{n,z}}$ structures
For 2D periodic structures, only square and regular hexagonal lattices could cover the plane under the condition of ${C_n}(n \ge 3,n \in {N^ + })$ symmetry. Consequently, the metal pattern structure is confined by the lattice. The pattern should be ${C_{4m,z}}$-symmetric with a square lattice or ${C_{3m,z}}$-symmetric with a regular hexagonal lattice ($m \in {N^ + }$). To validate the proposed theory above, we employ ${C_{3,z}}$- and ${C_{4,z}}$-symmetric structures as two examples (120° and 90° clockwise rotations about the z axis, respectively). The models are simulated by CST Microwave Studio Suite software, where periodic boundary conditions are applied around the unit cells.
As shown in Figs. 2(a) and (b), the regular hexagonal lattice and the square lattice have the same period. The L-shaped metal strips in the two cases are identical. The dimensions are as follows: period p = 7.6 mm, long strip length a = 3.4 mm, short strip length b = 2.1 mm, and strip width w = 0.4 mm. The substrates are the F4B substrate (${\varepsilon _r}$=2.65 and $\tan \delta $=0.001) with 1 mm thickness. The thickness tm of the copper layers on both sides is 70 µm.
Figure 3(a) shows the magnitude of the transmission under the LCP/RCP incident wave for the ${C_{3,z}}$- and ${C_{4,z}}$-symmetric structures. The magnitudes of ${t_{ +{+} }}$ and ${t_{ -{-} }}$ are almost the same for both cases. The maximal ${t_{ +{+} }}$/${t_{ -{-} }}$ are 0.94/0.91 at 9.28 GHz for the ${C_{3,z}}$ case, and 0.95/0.94 at 9.87 GHz for the ${C_{4,z}}$ case, respectively. There are six adjacent elements for a regular hexagonal lattice and four adjacent elements for a square lattice. The regular hexagonal lattice with the same period and dimension has a larger interelement capacitance due to more adjacent elements, leading to a decrease in the resonant frequency. The simulated results in Fig. 3(a) also indicate it. The simulated polarization rotation angles of the chiral metasurfaces are plotted in Fig. 3(b), which can be calculated by the phase difference of ${t_{ +{+} }}$ and ${t_{ -{-} }}$ through Eq. (13). The $\theta $ is 88.0° at 9.28 GHz for the ${C_{3,z}}$ case and 90.8° at 9.87 GHz for the ${C_{4,z}}$ case, respectively. In terms of rotation per material thickness of one wavelength, the optical activity is about $2495{^\circ{/} \lambda }$ for the ${C_{3,z}}$ case and $2378{^\circ{/} \lambda }$ for the ${C_{4,z}}$ case. Giant optical activities are observed for the chiral structures. The polarization rotation angles are both close to 90° for the two cases, indicating an ARI linear-to-cross polarization conversion characteristic. The simulated ellipticity $\eta $ is shown in Fig. 3(c), which can be calculated by the magnitudes of ${t_{ +{+} }}$ and ${t_{ -{-} }}$ through Eq. (14). The $\eta $ is -1.1° at 9.28 GHz for the ${C_{3,z}}$ case and -0.17° at 9.87 GHz for the ${C_{4,z}}$ case, respectively. Therefore, the transmitted EM wave is linearly polarized. These results validate the theory in section 2.2.
Fig. 3. The simulated (a) transmission coefficients for circularly polarized incident waves, (b) polarization rotation angle and (c) ellipticity of the chiral metasurfaces.
Figure 4 plots the simulated cross- and co-polarization transmissions of the two cases for linearly polarized incidence with three typical azimuth angles (i.e., $\varphi $=0°, 30°, and 60°). The transmission coefficients are independent of azimuths in the whole band, which manifests the proposed theory. The cross-polarization maxima are 0.92 at 9.28 GHz for the ${C_{3,z}}$ case and 0.94 at 9.87 GHz for the ${C_{4,z}}$ case, indicating an efficient linear-to-cross polarization conversion. In contrast, the co-polarization transmission coefficients are 0.03 and 0.01 at the maximal cross polarization transmission frequencies for the two cases. Moreover, the maximal cross-polarization transmission frequencies are the same as the resonant frequencies shown in Fig. 3(a) for the two cases.
Fig. 4. Simulated transmission coefficient magnitude of the (a) Case 1 (${C_{3,z}}$-symmetric) and (b) Case 2 (${C_{4,z}}$-symmetric) PCMs with different linearly polarized azimuths $\varphi $=0°, 30°, and 60° under normal incidence.
The simulated PCR results of the ${C_{3,z}}$- and ${C_{4,z}}$- symmetric structures are depicted in Fig. 5. For the ${C_{3,z}}$ case, there are two bands with PCR > 90%, namely, 9.14-9.5 GHz and 10.86-11.43 GHz. For the ${C_{4,z}}$ case, the bandwidth PCR > 90% is 9.37-10.7 GHz. The maximal PCR values reached 99.96% and 99.99% for the ${C_{3,z}}$ and ${C_{4,z}}$ chiral structures, respectively, where a high cross polarization conversion was obtained.
Figure 6 shows the electric field distributions of the ${C_{3,z}}$ case at 9.28 GHz and the ${C_{4,z}}$ case at 9.87 GHz under y-polarized (i.e. $\varphi $=90°) incident EM wave. The EM wave propagates along the -z direction. The transmitted wave is converted into x-polarization, indicating strong polarization conversion. The electric field varies more drastically near the PCM, and a higher electric field intensity is observed between the adjacent elements.
Fig. 6. The E-field distributions of the (a) ${C_{3,z}}$ case at 9.28 GHz and (b) ${C_{4,z}}$ case at 9.87 GHz under y-polarized EM wave incidence.
As an experimental verification, the prototype of ${C_{4,z}}$-symmetric PCM is fabricated and measured in an anechoic chamber. The measurement schematic is shown in Fig. 7(a). Two horn antennas, the transmitter and receiver, are placed coaxially with the PCM sample. Absorbing materials are fixed around the PCM so that the receiver can only receive the EM waves passing through the PCM. When the transmitter and the receiver are kept in parallel, the co-polarized transmission coefficients are measured. In contrast, when the receiver is rotated 90° along the z axis, the cross-polarized transmission coefficients are measured. The transmission coefficients with different linearly polarized azimuths can be obtained by rotating the sample. The fabricated sample is shown in Fig. 7(b).
Figure 8 plots the simulated and measured cross- and co-polarization transmissions for linearly polarized incidence with three typical azimuth angles. The measured cross-polarized transmission coefficients reach 0.94 at 9.85 GHz with all the three polarization azimuths. The corresponding co-polarized transmission coefficients are 0.09, 0.1, and 0.14 with 0°, 30°, 60° polarization azimuth angles, respectively. The measured co-polarized transmission coefficients are slightly higher than the simulated values, since the PCM is placed at the far-field of the horn antenna and some electromagnetic waves diffract from the absorbing materials. The measured results agree well with the simulated results.
Fig. 8. Simulated and measured transmission coefficient magnitude of the ${C_{4,z}}$-symmetric ARI PCM with different linearly polarized azimuths under normal incidence: (a) $\varphi $=0°, (b) $\varphi $=30°, and (c) $\varphi $=60°.
4. Conclusion
In this work, we analyze the properties of a PCM with a ${C_n}(n \ge 3,n \in {N^ + })$-symmetry structure for an ARI 90° polarization rotator, in contrast to what was predicted in previous studies in [32]. In addition, we presented a detailed analysis of PCM for an effective linear-to-cross polarization conversion with A = 0 and |B|≈1 in the Jones matrix. To verify the proposed theory, the PCMs with ${C_{3,z}}$- and ${C_{4,z}}$-symmetry in geometry are designed. High transmission coefficients and exceeding 99.9% PCR are both observed at the operating frequency for the two proposed PCM samples. Our work can broaden the understanding of the ARI polarization conversion of chiral metasurfaces; subsequently, it may have applications in many real physical systems, such as polarization detection, chiral radar imaging, and chiral molecular sensing.
Funding
National Program on Key Basic Research Project (173 Program) (2019-JCJQ-349); National Key Research and Development Program of China (2018YFF0212103); National Natural Science Foundation of China (61527805); 111 Project (B14010); International Cooperation Research Base Foundation of Beijing Institute of Technology (BITBLR2020014).
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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