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Abstract
In this paper, we proposed and investigated an ultra-thin, single-layer and compact metasurface (MS) based on a meander structure that achieves linear-polarization to linear-polarization (LP-to-LP) and linear-polarization to circular-polarization (LP-to-CP) conversion for both transmission and reflection simultaneously in the microwave region. Simulation and experimental results demonstrated that the cross-polarization coefficients of both transmission and reflection are approximately 0.49 for the normal incident LP wave passing through the MS at approximately 7 GHz, indicating a near LP-to-LP conversion in both reflection and transmission modes. Furthermore, the linear-to-circular polarization coefficients for both transmission and reflection are about 0.65 at approximately 8 GHz, indicating a near LP-to-CP conversion when the incident LP wave passes through the designed MS after transmission and reflection. The simulation results are in good agreement with the experiment. This design provides a valuable reference for the practical applications of MSs in full-space multifunctional polarization conversion and wavefront manipulation.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Polarization is a crucial and fundamental property of electromagnetic (EM) waves or light, which is determined by the magnitude and phase relationship of two orthogonal electric field vectors perpendicular to the wave propagation direction [1]. In recent decades, there has been an increasing interest in controlling and manipulating the polarization state of EM waves, as it is crucial for numerous applications [2–6], such as wireless communications, displays, data storage, RCS reduction, and imaging. The conventional approach for polarization manipulation involves the utilize of the optical activity of crystal materials and the Faraday effect [7–9]. However, these methods are often unsuitable for practical applications due to their drawbacks, including bulky volume, narrow bandwidth, and low efficiency. Designing devices that can achieve various polarization conversions effectively is still a challenging task. However, metasurfaces (MSs), which are the two-dimensional planar version of metamaterials (MMs) composed of periodic artificial sub-wavelength structures, have emerged as a promising methodology for the flexible and effective control of EM waves [10]. The development of MSs/MMs has allowed us to break free from the constraints of natural materials, providing an unprecedented opportunity and an entirely new means of fully controlling EM waves. By judiciously designing the unit-cell structure of MSs, the EM field can be effectively manipulated to yield functional devices such as flat lenses [11,12], cloaks [13], antennas [14,15], vortex generators [16], absorbers [17,18], filters [19,20], and polarization converters [21–29]. Among these MS-based devices, polarization converters are particularly crucial, as they can convert one polarization state to another, offering advantages such as lower profile, thinner thickness, and lower fabrication costs compared to traditional polarization manipulation devices.
Currently, numerous polarization converters based on MSs have been proposed and investigated intensively, ranging from microwave to even visible frequencies [21–44]. These polarization converters are typically composed of bi-layer or multi-layer metal-dielectric (MD) structures, enabling them to achieve various polarization conversions [21–27,30–37], such as linear-polarization to linear-polarization (LP-to-LP), circular-polarization to circular-polarization (CP-to-CP), and linear-polarization to circular-polarization (LP-to-CP) in reflection and/or transmission modes. For instance, Mei experimentally demonstrated a reflective linear-polarization (LP) converter based on a double U-shaped MS, which could achieve orthogonal polarization transformation for the reflected EM wave with a polarization conversion ratio (PCR) exceeding 90% from 6.91 GHz to 14.31 GHz [22]. Similarly, Cheng presented a transmissive dual-band CP converter based on a bi-layered double-arrow-shaped (DAS) structure array [32], which could achieve complete CP conversion for right-circular-polarization (RCP) and left-circular-polarization (LCP) waves at 0.31 and 0.55 THz, with conversion efficiencies of 0.91 and 0.93, respectively. Moreover, Wu designed a broadband high-transmission LP-to-CP converter based on a double-layer Jerusalem cross structure MS in the terahertz (THz) region, with an average measured PCR of over 0.68 [35]. However, most of the current reported designs only achieve a single functional polarization conversion, either for cross-polarization (including LP-to-LP, CP-to-CP) or LP-to-CP conversion only operated in transmission or reflection mode. Therefore, there is a high demand for the effective design of multifunctional polarization converters capable of both LP-to-LP and LP-to-CP conversion for both transmission and reflection mode.
In this study, we proposed a straightforward design of an ultra-thin, single-layer and compact MS based on a meander structure for multifunctional polarization conversion in both transmission and reflection mode in microwave region. Initially, we demonstrated the operating principle for multifunctional polarization conversion and the design of the MS. Subsequently, we performed numerical simulations and experiments to validate the performance and functionality of the design, with the experimental results closely matching those of the simulations. Finally, we illustrated the multifunctional polarization characteristics of the design through the transmission and reflection coefficients, polarization conversion parameters, and the distributions of the surface current and electric field of the unit-cell structure. The simulation and experimental results demonstrate cross-polarization coefficients of approximately 0.49 in both transmission and reflection modes at approximately 7 GHz. Furthermore, the LP-to-CP conversion coefficients for both transmission and reflection are approximately 0.65 at approximately 8 GHz. These results validate the efficacy of our design for multifunctional polarization conversion based on a single-layer compact MS with a meander structure in the microwave region. Our findings will serve as a significant reference for practical applications utilizing MSs for complete polarization and wavefront control.
2. Fundamental theory
To better illustrate the multifunctional polarization conversion of our designed MS for both transmission and reflection modes simultaneously, we will first briefly review some fundamental theories. In the x-y-z coordinate system, let us consider an incident planar LP wave propagating in the z-axis direction with an electric field vector Ei. The expressions of the electric field vectors of the incident, reflected, and transmitted LP waves with x-polarization and y-polarization can be written as follows:
The transmission coefficient $t_{ij}^{}\textrm{ = }E_i^t\textrm{/}E_j^i$ and reflection coefficient $r_{ij}^{}\textrm{ = }E_i^r\textrm{/}E_j^i$ are defined in terms of the complex amplitude of the electric field of the transmitted and reflected respect to the incident waves. The first and second subscripts “i” and “j” correspond to the polarization states of the transmitted or reflected wave and the components of the incident wave, respectively. For LP, the subscripts “x” and “y” represent the polarization direction along the x- and y-axis direction, respectively, while “+ “ and “ -” indicating RCP and LCP.
To clearly demonstrate the polarization conversion properties and polarization state of the transmitted and reflected waves, we define the polarization azimuth rotation angle θ and ellipticity η for an incident x(y)-polarization wave along the z-axis direction, expressed by the following formulas [38]:
To describe the LP-to-CP conversion for both transmission and reflection mode, two orthogonal CP eigenstates (RCP, +; and LCP, -) are associated with the incident two orthogonal LP states and the dependence relation between them can be expressed as follows [38]:
Therefore, to achieve efficient LP-to-CP conversion in both transmission and reflection modes, it is imperative to maximize the transmission amplitudes and PER values for the designed MS.
3. Structure design, simulation and experiment
The objective of this study is to achieve efficient multifunctional polarization conversion for both transmission and reflection modes using a compact MS structure in the microwave region. In recent years, the meander line and its various structures have been proposed and investigated extensively due to their distinctive EM response [45–49]. These structures have been utilized to design various compact devices such as polarizers and absorbers. Therefore, it is suggested that using the meander structure to build a compact and miniaturized single-layer MS for multifunctional polarization conversion would be a promising approach. Figure 1 illustrates the design of the proposed single-layer MS, which comprises a metal meander structure affixed to an ultra-thin dielectric substrate. Geometrical anisotropy of the MS unit-cell structure is critical for achieving effective polarization conversion [28–44]. Therefore, the unit-cell symmetry axis of the proposed single-layer MS with respect to the x(y)-axis direction is set at a certain angle α. Furthermore, asymmetry is incorporated into the unit-cell structure to eliminate mirror symmetry, allowing for polarization conversion in both transmission and reflection modes. The optimized geometry parameters of the designed MS unit-cell are as follows: px=py = 5 mm, l = 3 mm, g = w = 0.2 mm, t = 0.5 mm, and α = 45°. Thus, the total size of the designed MS unit-cell is only about 0.116λ0 × 0.116λ0 × 0.012λ0, where the λ0 is the wavelength at 7 GHz. Obviously, our designed MS is much compact and ultra-thin compared to the operation wavelength.
Fig. 1. The schematic diagram and the fabricated sample of the designed meander structure MS: (a,b) the front and perspective view of the unit-cell structure, (c) the corresponding portion photograph of the tested sample.
To investigate the functional behavior and underlying physical mechanism of the proposed MS structure, numerical simulations were conducted using the finite integration technique (FIT) based frequency domain solver of the CST Microwave Studio. The unit-cell structure was subjected to periodic boundary conditions along the x/y-axis directions, while open boundary conditions were set along the z-axis direction. A broadband plane EM wave with LP is used as the wave source. The meander structure, adhered to an ultra-thin Rogers RO4350 dielectric substrate, was modeled as copper with an electric conductivity of σ = 5.8 × 107 S/m and a thickness of 0.017 mm. The dielectric substrate had a relative permittivity of εr = 4.2*(1 + 0.0037i).
To experimentally demonstrate its function and efficiency, a 36 × 36 unit-cell sample of the designed single-layer MS was fabricated using conventional printed circuit board (PCB) process, following the simulation optimization. The final total dimensions of the fabricated single-layer MS slab are 180 mm × 180 mm × 0.517 mm. The measurements of the fabricated single-layer MS sample were conducted in an EM anechoic chamber, using two broadband horn antennae connected to a vector network analyzer (Agilent PNA-X N5244A) by coaxial cable. The measurement process for both transmission and reflection coefficients of the proposed single-layer MS can be found in Refs. [24,50]. Finally, the four transmission and reflection components (the complex Jones matrix, rxy, ryy, ryx, rxx, and txy, tyy, tyx, txx) can be obtained.
4. Results and discussions
Figure 2 presents the simulated and measured transmission coefficients (txy, tyy, tyx, txx) and reflection coefficients (rxy, ryy, ryx, rxx) of the designed single-layer MS for the normal incident planar LP wave with both x-polarization and y-polarization propagation along the z-axis direction. The measured results are in good agreement with the simulated data over the entire frequency range of interest, from 4 GHz to 10 GHz. As depicted in Figs. 2(a,b), both simulated and measured transmission coefficients (tyx and txy) for cross-polarization exhibit a maximum value of approximately 0.49 at 7.1 GHz. Meanwhile, the simulated and measured transmission coefficients (txx and tyy) for co-polarization are equivalent and reach a minimum value of about 0.47 at 7 GHz. This indicates that the normal incident LP with both x-polarization and y-polarization, undergo partial conversion into their orthogonal components after transmitting through the proposed single-layer MS.
Fig. 2. The (a,c) simulated and (b,d) measured (a.b) transmission coefficients (txy, tyy, tyx, txx) and (c,d) reflection coefficients (rxy, ryy, ryx, rxx) of the designed single-layer MS for the normal incident both both x-polarization and y-polarization waves propagation along the z-axis direction.
Based on Figs. 2(c) and (d), it is evident that both the simulated and measured reflection coefficients (ryy and rxx) of the co-polarization are equivalent and reach a maximum value of about 0.57 at 6.6 GHz. Similarly, the reflection coefficients (ryx and rxy) of the cross-polarization are also equivalent and reach a maximum value of about 0.49 at 7.1 GHz. This implies that the incident x(y)-polarization wave can be partially converted into the reflected y(x)-polarization wave through the designed single-layer MS. These findings demonstrate that the proposed single-layer MS can achieve partial polarization conversion for both transmission and reflection modes at around 7 GHz, converting the incident x(y)-polarization wave to its orthogonal components simultaneously. That is, near half the power of the incident LP (both x-polarization and y-polarization) wave is transmitted and the other half one is reflected through the designed single-layer MS. The absolute values of the transmission and reflection coefficients of the cross-polarization satisfy the necessary conditions (|txy|=|tyx| and |rxy|=|ryx|) for an LP-to-CP converter. Notably, the single-layer MS based on a meander structure is compact and ultra-thin, with dimensions of approximately 0.116 λ0 × 0.116 λ0 × 0.012 λ0, where λ0 is the operational wavelength of 7 GHz. Therefore, the designed single-layer MS slab has the potential to function as an LP-to-LP and LP-to-CP converter in both transmission and reflection modes.
To elucidate the physical mechanism underlying the observed polarization conversion, the distribution of the z-component of the electric field (Ez) and the induced surface current on the meander structure were monitored at the resonance frequency of 7 GHz. The inset of Fig. 3(a) reveals that the electric field component ($E_y^i$) of the normally incident LP wave can be decomposed into two orthogonal components ($E_u^i$ and $E_v^i$) along the u- and v-axes, respectively. Notably, the two orthogonal components are mutually oriented at an angle of 45° with respect to the positive y-axis direction. Upon illuminating the metallic meander structure with an incident LP wave with x(y)-polarization, the electric field components of the transmitted and reflected waves are generated by in-phase and out-of-phase coupling for both transmission and reflection, respectively, at the resonance frequency. The periodic metallic meander structure array can be considered a homogeneous anisotropic MS layer, as demonstrated in Figs. 1(a,d). This indicates that the resonant response of eigen-mode for the meander structure can be efficiently excited by the u- and v-components of the incident electric fields. In this case, the electric fields (Ei, Et and Er) of the incident, transmitted and reflected waves can be described as ${{\boldsymbol E}^i} = (E_u^i\hat{u} + E_u^i\hat{v}){e^i}^{( - \kappa z + \omega t)}$, ${{\boldsymbol E}^t} = ({\hat{t}_u}E_u^i + {\hat{t}_v}E_u^i){e^i}^{( - \kappa z + \omega t)}$ and ${{\boldsymbol E}^r} = ({\hat{r}_u}E_u^i + {\hat{r}_v}E_v^i){e^i}^{(\kappa z + \omega t)}$, respectively, where ${\hat{t}_u} = \hat{u}{e^\varphi }^{_u}$ and ${\hat{t}_v} = \hat{v}{e^\varphi }^{_v}$, ${\hat{r}_u} = \hat{u}{e^\varphi }^{_u}$ and ${\hat{r}_v} = \hat{v}{e^\varphi }^{_v}$ are the transmission and reflection coefficients along the u- and v-axis, $\hat{u}$ and $\hat{v}$ are the unit vectors along the u- and v-axis directions, respectively.
Fig. 3. The simulated (a) electric field (z-component, Ez) and (b) surface current distributions of the proposed meander structure at 7 GHz for the normal incident y-polarization wave passing through the single layer MS along z-axis direction.
Based on the results presented in Fig. 3(a), it can be observed that for the normal incident y-polarization, the meander structure exhibits mainly induced negative and positive electric charges distributed along the v-axis direction. This implies that the meander structure responds predominantly to the v-component of the incident y-polarization wave, forming a fundamental electrical dipole mode along the v-axis direction at resonance. It can be postulated that the meander structure only responds to the v-component of the electric field for the normal incident x-polarization wave at resonance. Figure 3(b) shows that the induced surface current on the meander structure flows along the v-axis direction, consistent with the distribution of the electric field. Therefore, the observed partial polarization conversion in the proposed MS for both transmission and reflection simultaneously is primarily attributed to the electrical dipolar resonance response and the anisotropic structure.
To further elucidate the polarization conversion characteristics of the proposed MS, we calculated the polarization azimuth rotation angles (θ) for both transmission and reflection modes. As depicted in Figs. 4 (a,b), it is observed that the $\theta _x^t$ for the normal incident x-polarization wave is minimized to -45°, while the $\theta _y^t$ for the normal incident y-polarization wave is maximized to 45° around the resonance frequency of 7 GHz. This indicates that the transmitted wave undergoes a rotation of -45° (+45°) with respect to the x(y)-axis direction at resonance for the normal incident LP wave with x(y)-polarization propagating through the MS slab along the z-axis direction. Similarly, comparable outcomes can be observed for the reflection modes, as illustrated in Figs. 4(c,d). Moreover, it is revealed that the normal incident x(y)-polarization wave propagating through the MS slab along the z-axis direction will experience a -(+)45° polarization rotation angle with respect to the x(y)-axis direction upon reflection. Note that there is a large difference between the experimental data and simulation data as shown in Figs. 4(c,d) due to the finite sizes of the MS slab in measurements but not accounted for in the simulation, and the imperfections and tolerances in the test environment also should be considered.
Fig. 4. The (a,c) simulated and (b,d) measured (a,b) transmission and (c,d) reflection polarization azimuth rotation angles (θ) for the normal incident x-polarization and y-polarization wave propagation along the z-axis direction.
In order to verify the polarization state of the outgoing wave resulting from the incident LP wave with x(y)-polarization propagating along the z-axis direction on a designed MS slab, we performed calculations to determine the polarization ellipticity angles (η) for both the transmission and reflection modes. As shown in Figs. 5 (a,b), it can be observed that the $\eta _x^t$ for normal incident x-polarization wave is close to 0° around 7 GHz and decreased to the minimum of about -30° around 7.7 GHz, while the one ($\eta _y^t$) for normal incident y-polarization wave is also close to 0° and up to maximum of about 30° at the same frequencies. This indicates that for a LP wave with x(y)-polarization propagating normally through the designed MS slab along the z-axis direction, the transmitted wave exhibits pure LP at approximately 7 GHz and elliptical polarization (close to CP) at approximately 7.7 GHz. The similar results of the $\eta _x^r$ and $\eta _y^r$ also can be observed for the reflection mode as shown in Figs. 5(c,d). The value of the $\eta _x^r$($\eta _y^r$) is about –(+)18.8°around 7 GHz, and –(+)27.7° around 8 GHz for the normal incident x(y)-polarization wave. The analysis further demonstrates that when a LP wave with x(y)-polarization propagates normally through a MS slab along the z-axis direction, the reflected wave exhibits elliptical polarization (close to LP at around 7 GHz and close to CP at around 8 GHz).
Fig. 5. The (a,c) simulated and (b,d) measured (a,b) transmission and (c,d) reflection polarization ellipticity angles (η) for the normal incident x-polarization and y-polarization wave propagation along the z-axis direction through the designed MS slab.
The above simulated and measured results of the θ and η indicate that the incident LP wave through the designed MS slab will be converted to LP with polarization direction of about –(+)45° angle respect to the x(y)-axis direction around 7 GHz, and to near CP around 8 GHz for both transmission and reflection modes.
In the following section, we have presented an analysis of the LP-to-CP conversion for both transmission and reflection modes. Specifically, we have presented the simulated and measured LP-to-CP conversion coefficients for a LP wave with x-polarization and y-polarization propagating normally through a designed MS slab along the z-axis direction. As depicted in Figs. 6 (a,b), the transmission coefficient (t-x/t + y) for the conversion of LP to LCP/RCP reaches a maximum of approximately 0.65 at around 8 GHz, while the transmission coefficient (t + x/t-y) for the conversion of LP to RCP/LCP is only about 0.25. This implies that when a planar EM wave with x/y-polarization propagates through the designed MS slab, it will be converted to a near LCP/RCP wave after transmission at around 8 GHz.
Fig. 6. The (a,c) simulated and (b,d) measured (a,b) transmission and (c,d) reflection LCP and RCP coefficients from LP-to-CP conversion for the normal incident x-polarization and y-polarization wave propagation along the z-axis direction.
The findings shown in Figs. 6(c,d) indicate that at around 8 GHz, the reflected coefficient (r + x/r-y) for the conversion of LP to RCP/LCP is approximately 0.51, while the coefficient (r-x/r + y) for the conversion of LP to LCP/RCP is only about 0.18. These results suggest that when a LP wave with x/y-polarization propagates through the designed MS slab, it will be converted to a near RCP/LCP wave after reflection at the same frequency. Taken together with the previous analysis of the transmission coefficients, these simulated and measured results of the LCP and RCP coefficients from LP-to-CP conversion demonstrate that the designed MS slab can efficiently convert a normal incident LP wave to a near CP wave after both transmission and reflection at around 8 GHz.
To provide additional evidence of the LP-to-CP conversion for both transmission and reflection modes of the proposed single-layer MS, we have presented the simulated and measured polarization extinction ratio (PER, γ) for a LP wave with x-polarization and y-polarization propagating normally through the MS slab along the z-axis direction. As depicted in Figs. 7(a,b), the $\gamma _x^t$ for a normal incident x-polarization wave is observed to decrease to a minimum value of approximately -11.2 dB at around 8 GHz. Conversely, the $\gamma _y^t$ for a normal incident y-polarization wave exhibits an increase up to 0° and a maximum value of approximately 11.2 dB at the same frequency. These findings provide further confirmation that the transmitted wave through the MS slab is a near CP wave around 8 GHz for a LP wave with x(y)-polarization propagating normally through the MS slab along the z-axis direction. The measured results of the $\gamma _x^r$ and $\gamma _y^r$ for the reflection mode are similar to those of the transmission mode, as depicted in Figs. 7(c,d). The values of $\gamma _x^r$($\gamma _y^r$) for normal incident x(y)-polarization waves are about +(–)10.2 dB around 8 GHz. This confirms that the reflected wave is a near CP wave around the same frequency of 8 GHz. These outcomes further support the conclusion that the designed MS slab can convert the normal incident LP wave to the near CP wave after transmission and reflection simultaneously around 8 GHz, and that the conversion efficiency is much comparable to that of previous chiral or anisotropic structures [50–56].
Fig. 7. The (a,c) simulated and (b,d) measured (a,b) transmission and (c,d) reflection polarization extinction ratio (PER,γ) for the normal incident x-polarization and y-polarization wave propagation along the z-axis direction.
Furthermore, Table 1 presents the functional comparison of the proposed MS with previous works. Our design for a multi-functional polarization conversion for both transmission and reflection mode boasts several advantages over previously reported designs. It is noteworthy that the proposed MS has achieved successful realization of a LP-to-LP and LP-to-CP conversion for both transmission and reflection mode simultaneously. This accomplishment demonstrates a multi-function of comparability with previous studies in the microwave region. The proposed MS design scheme has been compared to recently reported designs based on various parameters such as structure configuration, polarization conversion function, mode of operation, and unit-cell size. According to the comparison presented in Table 1, a clear improvement can be observed, indicating that the proposed MS design outperforms the previously reported designs in one or more of the mentioned parameters. Note that the angular stability of the proposed single layer MS and its performance will be deteriorated significantly when the angles is over 30° (not shown).
Table 1. Function comparison of the proposed MS with previous worksa
5. Conclusion
In summary, we have presented a numerical and experimental demonstration of an ultra-thin, single-layer and compact MS based on a metal meander structure. This structure is capable of converting an incident LP wave into both LP and near CP waves simultaneously for both transmission and reflection modes at the same frequency. Our simulation and experimental results exhibit a high level of consistency. Analysis of the simulated electric field and surface current on the unit-cell structure shows that the polarization conversion of the proposed MS structure for both transmission and reflection is mainly due to its electrical dipolar resonance response and structural anisotropy. Additionally, this meander structure is ultra-thin and compact in size, measuring only about 0.116λ0 × 0.116λ0 × 0.012λ0 (λ0 is the operation wavelength of 7 GHz). Given its multifunctional polarization conversion properties for both transmission and reflection mode, we anticipate that our proposed MS structure will have practical implications for designing full-space polarization converters or wavefront modulators.
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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