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Abstract
Metasurfaces (MSs) offer us an efficient way to control electromagnetic wave polarization due to its capability of flexible wave manipulation and compact configurations. However, the design of dual-band polarization conversion MS with high angular stability is still a challenge, especially in transmission geometry. Here, we propose a dual-band linear-to-circular (LTC) polarization conversion MS with high angular stability by using an array of multi-resonance meta-atoms. The meta-atom consists of two outer double split-ring layers and a central bar layer with circle-slot and can realize circular polarization at two bands with high efficiency and angular stability. The MS can transform the x-polarized wave into right-hand circular polarization (RHCP) at lower band and left-hand circular polarization (LHCP) at higher band and an opposite role for the y-polarized wave. The results show that the MS operates with insertion loss less than 0.5 dB and 0.3 dB and axial ratio below 3 dB in the frequency range of 9.05-9.65 GHz and 12.55-13.1 GHz, respectively. Moreover, our MS is insensitive to the oblique incident waves and can operate at high performance with the incident angle less than 55°. The proposed MS provides a new avenue to design meta-devices with dual frequency property and also high angular stability.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Manipulating electromagnetic properties of the materials has attracted great attention of scholars for its applications in stealth technology [1,2], wireless communication [3,4] and so on. Metasurface (MS), as a planar version of metamaterial, has unprecedented ability of wave manipulation which can control the electromagnetic waves within a subwavelength scale. As a result, many fascinating phenomena can be realized by MSs, such as anomalous refraction / reflection [5–7], photonic spin Hall effects [8,9], focusing [10–12], vortex generation [13–15], asymmetric transmission [16,17]. Polarization is one of the basic and important properties of electromagnetic wave as well as frequency and phase. Conventional devices for polarization conversion are birefringence wave plates, liquid crystals, which usually suffer from bulky configurations and complex fabrication [18,19]. MS provides a feasible solution to these problems which can manipulate polarization states in an effective and convenient way, and fruitful progresses have been achieved [20–44]. Many reflective polarization conversion MSs were designed and presented [26–33]. The reflective MS based on double-head arrow structure [26], oval ring pattern [27], double V-shaped resonator [28] and H-shaped patches [29] are introduced to design wideband linear-to-linear polarization convertors. Besides, wideband [30,31]and dual-band [32,33] LTC polarization conversion MSs in reflection mode have been studied. Double split resonant square ring [30] and ellipse-shaped ring [31] are introduced to achieve reflective wideband LTC polarizer. In Ref. [32], the converter can transform a linearly polarized wave into the cross polarized wave at the lower band and a circularly polarized wave at the higher band. In Ref. [33], by using concentric rectangular patches, an ultrathin dual-band reflective MS LTC polarization convertor is proposed. Many MSs in reflection modes are studied, but they usually cause blockages in applications, thus the design of polarization conversion MS in transmission mode is of great significance [34–44]. Existing transmission type polarization convertors are usually operate on single [34,35] band and wideband [36–39] frequency range. In Ref. [35], Joyal et al design a circular polarizer based on meander lines. In Refs. [38,39], the wideband LTC polarization convertors are proposed based on multi-layered structures with bandwidth of 40% and 35.4% respectively. Besides, except for the single band and wideband polarization convertors, dual-band polarization convertors are particularly attractive in compact and dual-band communication systems and several works are reported. In Ref. [40], the transmitarray inspired dual-band transmissive cross-polarization converter is presented. In Ref. [41], an asymmetric chiral MS polarizer based on U-shaped split ring resonators is studied. But the limitation of the study is that the converter only works for x-polarized wave, making the polarization state at the lower band and higher band fixed. In Ref. [42], authors propose a dual-band polarization convertor operating at K / Ka bands with the angular stability of 30°. In Ref. [43], the dual-band convertor based on frequency selective surface is proposed. But the angular stability is only 25° and four-layered structures may lead to fabrication error. In Ref. [44], the author presented a dual-band converter with wide axial ratio band and 20° angular stability.
In this paper, the dual-band LTC polarization conversion MS with high angular stability is presented and shown in Fig. 1. This MS can make the ± 90° phase difference between two orthogonal polarizations in two transmission bands with transmission coefficients magnitudes higher than 0.95. The polarizer can generate RHCP wave in the lower band (f1) and LHCP wave in the higher band (f2) under the illumination of x-polarized wave with insertion loss of 0.5 dB and 0.3 dB, respectively. And the results are also valid for y-polarized incident wave for the orthogonal circular polarization at each band. At the same time, the MS has good angular stability. When the incident angle is large, the MS still has a good polarization conversion performance at both bands.
Fig. 1. Schematic and working principle of dual-band LTC polarization conversion MS. The x-polarized wave will be transformed into RHCP at lower frequency and LHCP into higher frequency. The y-polarized wave will be transformed into LHCP at lower frequency and RHCP at higher frequency.
2. Linear-to-circular polarizer design
To design the dual-band polarization conversion MS with high angular stability, the key point is to find out the element which has dual-band performance at two frequencies and maintains stable performance in case of oblique incidence. Based on these, double-layered structure is considered as the basic meta-atom, and the period of the element should be small for the less sensitivity to oblique incidence. In this paper, we propose a meta-atom as the structure shown in Fig. 2. The meta-atom is symmetric along u and v axis (uvw is the local coordinate system of the meta-atom, 45° around the z axis with respect to the main xyz coordinate system). It can be seen that the meta-atom is composed of three metallic layers and two thin dielectric layers. The first and the third layers are identical which are composed of double split rings as shown in Fig. 2(c), and the middle layer is composed of a rectangular patch and a circular slot as shown in Fig. 2(d). The metallic layers are separated by dielectric layer with height h = 1 mm, ${\varepsilon _r}$ = 2.65 and loss tangent of 0.001.
Fig. 2. Structure of the meta-atom. (a) Perspective, (b) side view, (c) first and third metallic layer and (d) second metallic layer of the meta-atom. The geometrical parameters are listed as: r1 = 4.1 mm, r2 = 3.1 mm, d1 = 0.6 mm, d2 = 0.5 mm, g1 = 2.9 mm, g2 = 3 mm, l = 4.3, w = 2.7 mm, p = 9 mm.
Taking the y-polarized incident wave as an example. Considering a y-polarized wave is propagating along the + z direction, and the incident wave can be decomposed into two components $\vec{E}_u^i$ and $\vec{E}_v^i$:
Where ${t_{uu}} = |{{t_{uu}}} |{e^{j{\varphi _{uu}}}}$ and ${t_{vv}} = |{{t_{vv}}} |{e^{j{\varphi _{vv}}}}$ present the co-polarization transmission coefficients, respectively. Since the structure is symmetric of u- and v-axis, the magnitudes of the cross-polarization transmission coefficients .. and ${t_{vu}}$ can be ignored for the weak mutual coupling between the two orthogonal components. If the magnitudes and phase of the co-polarization transmission coefficients satisfy the condition:
To investigate the electromagnetic response, the meta-atom is simulated under the illumination of two plane wave propagating along + z axis with electric field in u and v directions as depicted in Fig. 3(a). The simulation is carried out in CST Microwave Studio by using frequency domain solver based on finite element method. As contrasted with the meta-atom, a meta-atom without circular slot in the second metallic layer is simulated with the same condition. The meta-atom proposed in this paper is denoted by meta-atom I, the meta-atom without circular slot is denoted by meta-atom II, and the top view of the meta-atom I and II are shown in Fig. 3(b). From the transmission coefficients of the meta-atom I shown in Figs. 3(c)–(d), the meta-atom I can transmit u-polarized and v-polarized wave with + 90° phase difference at 9.4-9.7 GHz and -90°at 12.6-12.9 GHz, and magnitudes $|{{t_{uu}}} |$ and $|{{t_{vv}}} |$ are equal and close to 1. From the transmission coefficients of the meta-atom II shown in Figs. 3(e)–(f), the meta-atom II can transmit u-polarized and v-polarized wave with + 90° phase difference at 9.6-9.8 GHz and -90° at 12.8-13 GHz, and magnitudes are almost equal but $|{{t_{vv}}} |$ are slightly smaller than $|{{t_{uu}}} |$. By comparing two meta-atoms, it can be found that both of meta-atoms at two bands satisfy Eq. (3), but the introduction of circular slot increases the resonances of u-polarized and v-polarized wave, which makes the meta-atom I have higher magnitude $|{{t_{vv}}} |$ and $|{{t_{uu}}} |$ and possess wider phase difference simultaneously. In addition, the dimension of the meta-atom I (meta-atom II) at lower frequency is 0.285λ1 × 0.285λ1 (0.291λ1 × 0.291λ1), and 0.384λ2 × 0.384λ2 (0.387λ2 × 0.387λ2) at higher band (λ1 and λ2 are the wavelengths of the center of the lower band and higher band in free space).
Fig. 3. Electromagnetic response of the meta-atom I and II to normal incident wave in u-polarized and v-polarized. (a) The element is illuminated by the plane wave with the electric field in u and v directions. (b) top view of the meta-atom I and meta-atom II. (c) Amplitude and (d) phase of the transmission coefficient of the meta-atom I to u-polarized and v-polarized incident wave. (e) Amplitude and (f) phase of the transmission coefficient of the meta-atom II to u-polarized and v-polarized incident wave.
To assess the LTC transmission coefficients of meta-atoms, the meta-atom I and II are illuminated by x-polarized incident wave perpendicularly. Once, a x-polarized wave illuminates the meta-atom which makes ± 45° angle in relation to the u- and v- directions, and the meta-atom can decompose the incident wave into two orthogonal components along u- and v- axes. The meta-atom transmits the two orthogonal components with almost equal amplitude and ± 90° at lower and higher band respectively, and the circular polarizations are generated. As the LTC transmission coefficients plotted in Fig. 4, it is clearly that both of the meta-atoms can transform the x-polarized wave into RHCP at lower band and LHCP at higher band. The insertion loss of meta-atom I is 0.12 dB at 9.5 GHz and is 0.3 dB at 12.8 GHz, and is 1 dB at 9.7 GHz and is 0.8 dB at 12.9 GHz for meta-atom II. At the same time, the polarization extinction ratio [45] between linear-to-LHCP and linear-to-RHCP transmission coefficients of meta-atom I is over 50 dB at lower ban and over 40 dB at higher band, but that of meta-atom II does not reach 25 dB at two band.
Fig. 4. Linear-to-circular transmission coefficient of (a) meta-atom I and (b) meta-atom II to normal incident wave in x-polarized.
Next, to investigate performances of meta-atoms under oblique incidence, the LTC transmission coefficients and axial ratios of the transmitted circular polarized wave with incident angle θ changing from 0 to 55° (θ is the angle between the incident wave and yoz plane, see Fig. 2(a)) are simulated and plotted in Fig. 5. As depicted in Figs. 5(a) and (b), it illustrates that at the lower band of the meta-atom I, the insertion loss is less than 1 dB when incident angle θ is below 50°. At the higher band of meta-atom I, the insertion loss is less than 1 dB when θ is below 45° and it increases to 1.3 dB when incident angle θ up to 55°. As depicted in Figs. 5(e) and (f), at the lower band of meta-atom II, the insertion loss is 1.1 dB when θ = 15°, and it increase to 2.6 dB when θ up to 55°. At the higher band, the insertion loss is 1 dB when θ = 30° and it increases to 2.5 dB when θ up to 55°. Moreover, axial ratios of the transmitted wave on the variation of incident angle θ at lower band and higher band are presented in Figs. 5(c), (d), (g) and (h). For meta-atom I, at lower band the axial ratio is below 3 dB when incident angle in the range of 0 - 55°, and at higher band the axial ratio is less than 3.2 dB when incident angle θ = 55°. For meta-atom II, at lower band the axial ratio is below 3 dB and insertion loss less than 2.86 dB when incident angle is less than 50°, and at higher band the axial ratio is below 3 dB and insertion loss less than 1.3 dB when incident angle θ in the range of 0 - 30°. Based on the results above, it is evident that meta-atom I not only has greater angular stability than that of meta-atom II, but also has higher LTC transmission coefficients. It may due to the multi-resonances of the meta-atom I. The multi-resonances make high transmission coefficient amplitude and broad phase difference in a wide bandwidth, and guarantee the meta-atom can transmit the orthogonal eigen modes with ± 90° phase delay and equally amplitude even case of oblique incidence. Moreover, performances of meta-atoms at lower band is slightly better than that at higher band. It can be explained that the meta-atom has smaller dimension at lower band which is of less sensitivity to the incident angle. In the next section, we’d like to fabricate the MS based on meta-atom I and verify the performance of the MS.
Fig. 5. The performance of the meta-atom I (a)-(d) and meta-atom II (e)-(h) at different incident angles. (a)-(d) are the results of meta-atom I : x-polarized wave to RCHP transmission coefficients at (a) lower band and x-polarized wave to LCHP transmission coefficients at (b) higher band, axial ratio at (c) lower band and (d) higher band of the meta-atom I. (e)-(h) are the results of meta-atom II : x-polarized wave to RCHP transmission coefficients at (e) lower band and y-polarized wave to LCHP transmission coefficients at (f) higher band, axial ratio at (c) lower band and (d) higher band of the meta-atom II.
3. Experimental results
To realize an experimental validation for our design, the proposed LTC polarization MS is fabricated by using PCB technology which consists of 25×25 meta-atoms with size of 225×225 mm2. The top (bottom) metallic layer and middle metallic layer of the fabricated MS are shown in Figs. 6(a) and (b). The frequency response of the MS is measured based on free-space measurement. As the measurement setup drawn in Figs. 6(c) and (d), two ridged horns operating at 8-18 GHz are used as transmitting and receiving antennas with MS placing at the center of them, and the pair of ridged horns are connected to the vector network analyzer with coaxial cables. For the oblique incidence measurement, the sample can rotate along its vertically central line. As the structure details inset in Figs. 6(a) and (b), the local coordinate system of the meta-atom is 45° angle in relation to the global coordinate system, and the transmitting antenna emits x-polarized wave which will be transformed into the circularly polarized wave. The measurement is carried out as follows. Firstly, we measured the transmission coefficients without the sample to calibrate the system. Secondly, we measured the transmission coefficients with the sample placing at the center of transmitting and receiving antennas. Thirdly, to test the angle stability, we rotate the sample along y axis to realize oblique incidence and measure the transmission coefficients. Next, we rotate the receiving antenna 90° for orthogonal polarization measurement. Finally, repeat step three to get transmission coefficients for oblique incidence of the orthogonal polarization. Considering the symmetries of the MS, we just carry out the measurement under the illumination of x-polarized wave.
Fig. 6. Photograph of the sample and the experimental setup. Pictures of the (a) top and bottom metallic layers, and (b) middle metallic layer of the MS with the inset of structure details. (c) Diagram and (d) picture of the experimental setup.
The amplitudes and phase of the transmission coefficients will be measured by the vector network analyzer, and the axial ratio can be calculated by [46]:
The measured transmission response, axial ratio and transmission efficiency for the x-polarization for the incident angle from 0 to 55° are shown in Fig. 7. For normal incidence, polarizer converts the x-polarized wave with insertion loss less than 1 dB in the range of 8.8 - 9.95 GHz and 11.9 - 14 GHz. The lowest insertion loss at two bands appears in 9.35 GHz and 12.65 GHz with value of 0.26 dB and 0.2 dB. The operation band of the measurement results move to the lower frequency slightly compared with the simulation one. The axial ratio of the transmitted wave is less than 3 dB in the frequency range of 9.05-9.65GHz and 12.55-13.1 GHz. At the same time, the insertion loss is less than 0.5 dB and 0.3 dB. For oblique incidence, although performances of the polarizer are gradually changed as incident angle increases, the insertions loss still less than 1.2 dB in the range of 8.95-9.85 GHz and 12.4-13.4 GHz when incident angle up to 55°. The axial ratio remains stable in the lower band and a little deteriorates in the higher band with the increase of incident angle. It is consistent with simulation results because meta-atom dimension at lower band is smaller which is less sensitivity to the incident angle. At the lower band, the polarizer operate with axial ratio remains blow 3 dB at 9.25-9.5 GHz and insertion loss less than 1.2 dB when the incident angle ranged from 0 to 55°. At the higher band, the operation band of the axial ratio move to the lower frequency slightly but still lower than 3 dB at 12.6-12.8 GHz with incident angle in the range of 0-50°, and the insertion loss is less than 1 dB. The measurement results verify that the dual-band LTC polarization conversion MS possesses dual-band performance and high incident angle stability. Table 1 lists the comparisons of the reported dual-band LTC polarization conversion MSs and our work. It is obvious that the proposed convertor shows lower insertion loss and higher incident angle stability simultaneously.
Fig. 7. Measured transmission response and axial ratio of the proposed MS at different incident angle. (a) Transmission response and (c) axial ratio and at lower band, (b) transmission response and (d) axial ratio at higher band.
Table 1. Performance comparisons between our work and reported literature.
4. Conclusion
In this paper, we propose a high efficiency dual-band wide-angle LTC polarization conversion MS which can transform the linearly polarized wave into circularly polarized wave at two bands. A meta-atom with multi-resonance is proposed which can realize + 90° / -90° phase shift at lower / higher band and almost equal amplitudes for two orthogonal polarizations, and maintains stable performance under oblique incidence. The MS can transform the x-polarized wave into RHCP at lower band and LHCP at higher band, and the results are also valid for y-polarized incident wave with opposite circular polarizations at each band. The MS is fabricated and measured, and the results show that the axial ratio of the transmitted wave is less than 3 dB with incident angle below 55° at lower band, and with incident angle up to 50° at higher band. The measurement verifies the good performance of the MS, and the dual-band wide-angle LTC polarization conversion MS has promising potential in applications of satellite communication and so on.
Funding
National Natural Science Foundation of China (61871394, 61901512); Postdoctoral Innovation Talents Support Program of China (BX20190293); Natural Science Foundation of Shaanxi Province (2019JQ-013).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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