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Abstract
In this article, a single-layer reflective anisotropic metasurface (MS) is proposed, which presents both half- and quarter-wave plate operation in different microwave frequency regimes. The unit cell of the proposed metasurface consists of a tilted rectangular plane with triangular ends accompanied by an equidistant-filled triangle on both sides. The unit cell is printed on a dielectric substrate backed by a metallic plane. The proposed meta-plate transforms horizontal polarization into vertical and vice versa in two wide frequency bands, 7.1-15.3 GHz and 19.8-21.7 GHz. Similarly, a linearly polarized (LP) wave is transformed into a circularly polarized (CP) wave and vice versa at 7.9 GHz and 21.8 GHz. The wide bandwidth is acquired through three plasmonic resonances occurring at 8.2 GHz, 12.7 GHz and 20.8 GHz, where the cross-polarization conversion ratio reaches almost 100%. Moreover, quarter and half-wave plate operations occurring at 7.9 GHz and 7.1-15.3 GHz, respectively, are robust to changes in oblique incidence angle (up to 45°) both for transverse-electric (TE) and transverse-magnetic (TM) polarizations. The physical mechanism behind polarization conversion is also explained through surface current distribution. The proposed meta-plate structure is fabricated and validated through experimental measurements. The wide bandwidth, high efficiency, angular stability, and simple structure make the proposed metastructure incredible for numerous microwave applications such as antennas, radars, and satellite communication.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials, with their exotic electromagnetic characteristics not found in natural materials, have paved the way for numerous applications and devices previously considered unreachable [1]. In recent years, a flat meta-material with sub-wavelength thickness called metasurface has been a central area of research due to its broad spectrum of applications such as negative refraction, electromagnetic cloaking [2–4], perfect lensing [5–8], holography [9,10] and polarization control [11–14], low-profile broadband antennas [15–17], polarizers [18], and super-resolution imaging [19]. The sub-wavelength unit cells or meta-atoms can be engineered to obtain a desirable, effective electromagnetic response with which the amplitude, phase and polarization of illuminated EM waves can be controlled [20–26]. The abrupt control of the phase of the EM waves gives the metasurface superiority over the conventional polarization control techniques such as the Faraday Effect, solution of sugar molecules etc., where large lengths are required for phase accumulation, especially at longer wavelengths [27]. Metasurfaces have been extensively explored for half-wave plate, a quarter-wave plate and polarization control in transmission and reflection mode in the microwave, terahertz [20,28–30], infrared, visible and optical frequency regimes [31]. Researchers have successfully manipulated the polarization state of the impinging wave using different geometrical symmetries of the meta-atoms, such as anisotropic, intrinsic or extrinsic chiral structures [32,33].
Ultrathin metasurfaces are used to convert the polarization of EM waves and are very attractive for practical applications instead of bulky wave plates [34,35]. Many examples of linear to Many examples of linear to circular [36,37], circular to linear [35,38], multifunctional [39–41], and linear to elliptical [38,42,43] polarization conversion metasurface have been presented in the literature.
Some polarization conversion metasurfaces achieve narrow bandwidth, bulky volumes and incidence angle-dependent response [44]. It is very important to improve bandwidth for practical applications, but it is a challenging issue that needs improvement. Since enhancement in bandwidth improves fabrication tolerances and permits the use of wideband signals. Moreover, the wide-angle feature is advantageous in real applications of wide-beam antennas [45]. Metasurfaces have wide applications, and their angular stability is related to the dielectric constant and thickness of the substrate used. Their performance will be stable if it is thinner relative to the incident wavelength. Angular stability and broad bandwidth will be achieved if the metallic structure is designed properly on the upper part of the dielectric so that the unit cell can get multiple resonances [46]. A highly efficient wideband (6.91-14.31 GHz) is achieved using a U-shaped polarization converter [47]. Similarly, a triangle ring resonator achieves a wideband (9.24-17.64 GHz) at three resonances [48]. A single-layer flexible metasurface is designed for half, and quarter-wave plate operation works in transmission mode in microwave frequency regimes achieving angular stability up to the incident angle [49]. Furthermore, a rectangular metasurface operates for half and quarter-wave plates in the wavelength range of 10.0-11.9 µm. Half-wave plate operation occurs in the wavelength range 10.3–10.9 µm, and quarter-wave plate operation occurs in the wavelength range 10.0-11.9 µm [50].
Although many polarization conversion metasurface works in transmission mode, as depicted in the literature, the major problem with these polarization converters is their limited efficiency, narrow bandwidth, and smaller thickness than the working wavelength [51,52]. To overcome these problems, many reflective metamaterials and metasurfaces have been proposed. However, many metasurfaces achieve cross-polarization and high polarization conversion efficiency, but their work is confined only to one incidence angle [48]. It is challenging to propose an electrically thin metasurface with high polarization conversion efficiency.
In this work, we have proposed a wideband reflective half and quarter waveplate polarization converter, which converts linearly polarized waves into orthogonal and works for oblique incidence. The presented meta plate transforms horizontal polarization into vertical and vice versa in two wide frequency bands, 7.1-15.3 GHz and 19.8-21.7 GHz. Moreover, a quarter-wave plate and half-wave plate functioning at 7.9 GHz and 7.1-15.3 GHz, respectively, are robust to changes in oblique incidence angle for transverse-electric (TE) and transverse-magnetic (TM) polarizations. Such a wideband ultrathin metasurface will help to reduce the size of optical and microwave systems, and also it can be used in a wide range of applications. Furthermore, the proposed reflective metasurface has high efficiency by comparing with previous studies.
2. Design principle
2.1 Geometrical configuration
The schematics of the proposed metasurface are shown in Fig. 1(a). It is composed of a periodic arrangement of metallic patterns on the top of a dielectric spacer, and the bottom side is covered by a metallic plane. The dielectric spacer is FR-4 with a thickness of 2.4 mm, dielectric loss tangent of 0.02, relative permeability µ = 1 and relative permittivity ε= 4.4. Figure 1(b) shows the structure of a single-unit cell. The yellow part represents the metallic part, which consists of a tilted rectangular plane with triangular ends accompanied by equidistant filled triangles on both sides. The structural geometrical parameters are as follows ${w_1}$=1.5 mm, ${w_2}$=0.375 mm, $\textrm{}{g_1}$=1 mm, ${g_2}$=5.74 mm, ${w_4}$=0.5 mm, ${w_3}$=1.5 mm, $\textrm{}{g_3}$=1.5 mm, ${g_4}$=1.5 mm as shown in Fig. 1(c). The periodicity of polarization converter is L = 7 mm. The metallic parts are made of copper which has thickness of 0.018 mm and conductivity $\sigma = $5.8${\times} {10^7}\textrm{ }S/m$. When a plane wave irradiates the metasurface, it converts the incident wave into co and cross-polarized waves.
Fig. 1. (a) Schematic diagram of y-to-x polarization conversion of proposed metasurface. (b) 3D schematic design of the unit cell. (c) Geometrical representation of the unit cell.
The impinging EM wave induces electric and magnetic dipole moments in meta-atoms rendering the surface an effective permittivity and permeability. The average effective electric and magnetic dipole moments are related to the incident fields as follows:
Subsequently, the surface currents give the scattered fields, which determine the structure's reflection and transmission coefficients. The reflection coefficients relate the reflected and incident fields through the Jones matrix:
2.2 Simulation results
2.2.1 Half-wave plate operation
Cross polarizer and half-wave plate converts linearly and circularly polarized waves upon reflection from the metasurface. The relation between incident and reflected fields can be expressed by using jones reflection matrix. The general matrix ‘R’ of reflected wave of complex magnitude is described as follows [53,54]
In above matrix co polarized reflections are ${R_{yy}} = |{{{\boldsymbol E}_{ry}}} |\textrm{ / }|{{\boldsymbol E}_{iy}}|$ and ${R_{xx}} = |{{{\boldsymbol E}_{rx}}} |\textrm{ / }|{{\boldsymbol E}_{ix}}|$ and cross polarized reflections are, ${R_{xy}} = |{{{\boldsymbol E}_{rx}}} |\textrm{ / }|{{\boldsymbol E}_{iy}}|$, ${R_{yx}} = |{{{\boldsymbol E}_{ry}}} |\textrm{ / }|{{\boldsymbol E}_{ix}}|$. Here reflection coefficient ${R_{xy}}$ represents incident electric field ${{\boldsymbol E}_i}$ is y-polarized and ${{\boldsymbol E}_r}$ is x-polarized, similarly ${R_{yx}}$ represents incident electric field ${{\boldsymbol E}_i}$ is x-polarized and reflected electric field is y-polarized. Ideally, the cross-polarization converter suppresses co-polarized components then reflection coefficients ${R_{xx}},$ ${R_{yy}}$ becomes zero and ${R_{xy}}$, ${R_{yx}}$ approaches unity.
Reflection coefficients under normal x- and y-polarized states are presented in Fig. 2. It can be described from Fig. 2(a) that magnitude of the co-polarized reflection coefficient, ${R_{xx}},$ reaches minimum value at three resonance frequencies 8.2 GHz, 12.7 GHz and 20.8 GHz. The dips occurring at three resonances reach to -20.77 dB, -16.33 dB and -25.13 dB respectively and hence co-polarized reflection vanishes. On the other hand, the cross-polarized reflection coefficient reaches to 0 dB at 8.2 GHz, 12.7 GHz and 20.8 GHz and thus an x-polarized incident wave is fully reflected as a y-polarized wave at these three resonances. The response to the y-polarized state can be determined from the symmetries of the unit cell. Moreover, the structure appears same for both x and y-polarized waves and hence gives same response to both TE and TM polarizations. This can be seen from the results shown in Fig. 2(b) for y-polarized state where resonances occur at the same three frequencies 8.2 GHz, 12.7 GHz and 20.8 GHz. Moreover, at two resonance frequencies 8.2 GHz and 12.7 GHz the cross-polarized reflection coefficient ${R_{xy}}$ approaches to 0 dB.
Fig. 2. Co and cross polarized reflection coefficients for normal incidence under (a). x-polarized illumination and (b). y-polarized illumination.
Due to the structural feature of proposed polarization conversion metasurface, it is realized that only x-and-y polarization states converted into their respective orthogonal polarization y-and-x that exhibits polarization selective conversion. As polarization conversion metasurface is backed by copper, so all EM waves reflect. Thus, there will be no transmission and in other words transmission coefficient appraised to be zero. A good measure of the polarization transformation capability of a metasurface is the ratio of the power reflected in cross polarized waves to the metasurface is called polarization conversion ratio (PCR). Under x-polarized illumination, PCR is given by:
It is obvious from Fig. 3 that PCR approaches 100% at three plasmonic resonances occurring at 8.2 GHz, 12.7 GHz and 20.8 GHz. Moreover, PCR exceeds 80% in two frequency bands 7.1-15.3 GHz and 19.8-21.7 GHz which qualify as the operating bands for cross-polarization conversion under 80% efficiency criteria. The wide frequency range (8.2 GHz) in the first band is caused by the overlapping of the first two nearby resonances.
2.1.2 Quarter-wave plate operation
When incident waves reflect from metasurface then the proposed quarter-wave plate converts linearly polarized waves into circularly polarized waves, and vice versa. We can express electric field of the incident wave into left-handed and right-handed circularly polarized components. ${E_{ + r}}$ and ${E_{ - r}}$ represents right and left-handed circularly polarized components of electric field
On the Cartesian basis, the matrix elements of ${R_{\textrm{c}l}}$ can be written as follows.
The above equation represents that the structure has ability to convert linearly polarized waves into circularly polarized waves. Scaling factor $\frac{1}{{\sqrt 2 }}$ normalizes the electric field vector that is reflected between 0 and 1 while simultaneously satisfying the passivity criterion. The magnitude of co and cross polarized reflection coefficients must be equal to 0.7, such as $|{{R_{xx}}} |= |{{R_{yx}}} |\approx 0.7.$ The amplitude ratio lies within the range 0.85-1.15. The amplitude ratio is in between 0.85≤$|{{{\boldsymbol R}_{xx}}} |\textrm{ / }|{{\boldsymbol R}_{yx}}|$≤1. The phase difference satisfies the condition($n{90^\circ } - {5^\circ }$)≤$\Delta {\varphi _{yx}}\; \le (n{90^\circ } + {5^\circ }$) here n is odd integer.
Reflection components ${R_{yy}}$ and ${R_{xy}}$ have nearly same magnitude ($|{{R_{xx}}} |/|{{R_{yx}}} |\approx 1$) at 7.9 GHz and 21.8 GHz, as shown in Fig. 4(a). It is worth mentioning that at the two frequency bands 7.9 GHz and 21.8 GHz offer near ideal circular polarization conversion. It can be seen from Fig. 4(b) that phase is -90° at frequency 7.3 and 7.4 GHz representing a pure left handed circularly polarized (LHCP) wave and phase difference (∠${R_{yx}}$ − ∠${R_{xx}}$ ≈ + 270°) is 270° in the frequency range of 19.4 -20.4 GHz for normal incidence).These ideal characteristics are attributed to negligible loss in the substrate, equal power distribution and ±90° phase difference between the two orthogonal reflection components. It is clear from the equations 6,7 that the condition for quarter wave plate is fulfilled.
Fig. 4. (a). Magnitude ratio of cross and co-polarized reflections. Inset shows the frequency region where metasurface exhibits ideal characteristics i.e., $|{{R_{xx}}} |/|{{R_{yx}}} |= 1$ necessary for circular polarization. (b) Phase difference between cross and co-polarized reflections for y- polarized incident wave. (c) Axial ratio (AR).
It is worth mentioning that Axial ratio is an important factor for measuring circularly polarized waves, and the axial ratio reflects the degree of circular polarization. In this paper, the frequency band with the axial ratio less than 3 dB is defined at two frequency bands 7.9 GHz and 21.8 GHz as shown in Fig. 4(c). The calculation formula of the axial ratio is described in equation
The proposed design has same response for both x and y polarization such as ${R_{xy}} = {R_{yx}}$ . It is due to the reciprocal nature of metasurface and due to reversal symmetry, that it converts Linear x polarization to linear y polarization and also linear to circular polarization in two frequency bands.
2.1.3 Angular stability
In practical scenarios, the metasurface is often hit by an impinging EM wave obliquely. Under such circumstances, the metasurface must be able to maintain its polarization conversion efficiency to qualify for integration with optical and microwave applications. To investigate this, the metasurface is simulated under oblique incidence. It is obvious from Fig. 5 the cross-polarized reflection coefficients are robust to changes in incidence angle in the first operating band 7.1-15.3 GHz for both cases when the electric field is in the yz and xz plane.
Fig. 5. (a) cross polarization reflectance for x-polarized wave. (b) cross polarization reflectance for y-polarized wave for different angles of elevation.
On the other hand, the structure loses its robustness to changes in incidence angles in the second operating band 19.8-21.7 GHz. The lack of angular stability in the second frequency band is caused by the relatively large size when compared to the wavelength. In the first band, the wavelength is larger and hence the relative size of the unit cell is smaller due to which diffraction effects are negligible.
Thus, the relationship between polarization conversion and incidence angle performance have need of investigation [55]. Their angular stability is related to dielectric constant and thickness of the substrate used. The performance of polarization conversion metasurface will be stable if it is thinner relative to the incident wavelength. Angular stability and broad bandwidth will be achieved if metallic structure is designed properly on the upper part of dielectric so that unit cell can get multiple resonances [44]. In this section, polarization conversion metasurface shows incident angle independent response up to $\theta = {45^\circ }\; $. Where $\theta $ is angle between incident wave and reflected wave. The simulated reflection coefficients co and cross for different incidence angle up to $\theta = {45^\circ }\; $ are shown in Fig. 5(a) and (b).
Such insensitive behavior of angles is quite stable with in the required frequency band 7.1-15.3 GHz and higher polarization reflection coefficient within 3 dB bandwidth. In case of angle independent polarization, EM waves propagate back and forth in a dielectric substrate. By increasing the propagation phase the bandwidth decreases drastically. It is clear from the Fig. 5(a) and (b) that linearly polarized waves converted completely into cross polarized waves within the required frequency range from 7.1-15.3 GHz up to ${45^\circ }\; \; $ incident angle.
2.1.4 Theoretical Analysis
To analyze the principle of metasurface theoretically u and v coordinate system is used the principle of polarization converter for u and v polarized waves is described in Fig. 6(a). It is obvious from the structure of the unit cell that it has conservation of parity along ${45^\circ }\; $ to x-axis, along u-axis as shown in Fig. 6(a), therefore the structure appears same for both x and y-polarized waves and hence gives same response to both TE and TM polarizations.
Fig. 6. (a) Working principle for u and v polarized incidence for normal incidence of the designed polarization conversion metasurface. (b, c) magnitude of co-polarization reflection coefficient and phase.
We can decompose x polarized incident wave into u-and v- polarized components.
Electric field component for incident wave is as follows:
And the reflected wave is as follows:
At resonant frequency of 8.2 GHz, we can decompose the electric field ${E_i}$ into two components such as ${E_{iv}}$ and ${E_{iu}}$ as shown in Fig. 6(a). Meanwhile, the reflection phase difference along u and v direction is ${180^\circ }$, the reflected electric field component ${E_{rv}}$= - ${E_{iv}}$ and ${E_{ru}}$= ${E_{iu}}$. Thus ${E_r}$ the total reflected field can be acquired and parallel to y-axis, now the reflected electric field component of the incident wave can be seen as rotated by ${90^\circ }$ with respect to incident component of electric field which leads to cross polarization conversion. Similarly, the same process of polarization conversion can be applied for the other two resonant frequencies of 12.7 GHz and 20.8 GHz. So, the surface behaves as pure electric conductor at 8.2 GHz, 12.7 GHz and 20.8 GHz for the u and v polarized components of electric field.
2.1.5 Surface current distribution
We further consider surface current distribution for both u and v polarized incidence. The surface current distribution on top and bottom of dielectric is shown in Fig. 7. Current on top and bottom metallic surface are only due to normal incidence. Surface currents are large on these frequencies 8.2 GHz, 12.7 GHz, 20.8 GHz due to electromagnetic resonance produced by u and v polarized incidence. The flow direction of arrows on top and bottom surface shows the type of resonance. Current on the upper surface also produce current on the lower surface. Since the distribution of current along the upper layer at three resonance frequencies 8.2 GHz, 12.7 GHz and 20.8 GHz are anti parallel to those produce on the lower metallic layer so it will produce magnetic resonance. These three resonance frequencies play important role in achieving wide-band and high polarization conversion efficiency.
Fig. 7. Surface current distributions on the metallic parts of proposed metasurface (a, b) shows current distribution on upper and lower parts of metasurface at resonance frequency 8.2 GHz. (c, d) shows current distribution at 12.7 GHz. (e, f) shows current distribution at resonance frequency 20.8 GHz.
2.1.6 Experimental verification
To validate experimentally the proposed metasurface was fabricated by using substrate FR4 as shown in Fig. 8(a). Fabricated sample consist of 43 ${\times} $ 43-unit cells. In experimental setup two horn antennas are used one act as transmitter and other as a receiver. To measure co and cross polarization reflection coefficients the receiving horn antenna is rotated by ${0^\circ }$ or ${90^\circ }$, respectively. The (EM) electromagnetic waves from transmitting antenna reflects from sample and then received by receiving horn antenna. Center of fabricated sample and antennas were fixed at same height as shown in Fig. 8(b). The measured co and cross polarization results and PCR are shown in Fig. 8(c) and (d). The experimental results are nearly in agreement with the simulated results. Some discrepancies are due to imperfections which causes diffraction effects.
Fig. 8. (a). Fabricated photograph of sample (b). measurement setup. (c). simulated and measured results for cross polarized reflection coefficient. (d). Simulated and measured results for PCR.
2.1.7 Performance analysis
Performance of our designed metasurface against previously reported designs is also compared and is presented in Table 1. Performance has been compared against electrical size (Size), bandwidth (BW), incident angle variation and its polarization type. It can be seen that already presented work has large bandwidth comparison to proposed work but they all achieving only one functionality that is linear to linear (LP-LP) polarization conversion. It is important to note that proposed metasurface achieve both linear to linear (LP-LP) and linear to circular (LP-CP) polarization conversion. Although, the proposed metasurface has less thickness compared to the Ref. [57,58,59] also the design is very simple compared to reported designs and is easy to fabricate.
Table 1. Performance of proposed design with some previous reported designs
3 Conclusions
In summary, we have realized a thin polarization converting metasurface work as a high-efficiency cross-polarizer and circular polarizer for a wide range of frequencies under normal incidence in the microwave frequency regime. The proposed design transforms horizontal polarization into vertical and vice versa in two wide frequency bands, 7.1-15.3 GHz and 19.8-21.7 GHz. Similarly, a linearly polarized wave is transformed into a circularly polarized wave and vice versa at 7.9 GHz and 21.8 GHz. Moreover, it is shown that PCR approaches 100% at three plasmonic resonances occurring at 8.2 GHz, 12.7 GHz, and 20.8 GHz. Moreover, the polarization transformation capabilities remain stable for obliquely incident waves up to 45°.
Funding
Beijing Municipal Science and Technology Commission (Z211100004821012); National Natural Science Foundation of China (61975014, 62035003, U22A2079); National Key Research and Development Program of China (2021YFB3600500).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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 requests.
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