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Abstract
In this work, an ultrawideband and high-efficient polarization conversion metasurface (PCM) is proposed, which can efficiently convert linearly polarized waves into cross-polarized waves in an ultra-wide frequency range. The unit cell of the proposed PCM is composed of two pairs of L-shaped metallic patches covered by a dielectric superstrate and an air-based substrate attached with a metallic ground. The PCM has an operating band from 3.37 to 22.07 GHz with the polarization conversion ratio (PCR) over 90% under the normal incidence, which the ratio bandwidth (fH/fL) is 6.5:1. The PCR can achieve 100% at seven resonant frequencies. The equivalent circuit model is analyzed to explain the fundamental cause of the PCM’s multi-resonance and polarization conversion behaviors. In addition, all possible near-field interactions among the resonator, the superstrate, and the ground sheet can be accurately calculated using interference theory, which reveals the underlying physical mechanisms of the multi-resonance metasurface. The theoretical calculated, numerically simulated, and measured results are in good agreement. Compared to other PCMs, the proposed PCM has a simple geometry structure but an ultrawideband and high PCR property.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurface is a kind of two-dimensional metamaterials that have been widely used in various fields such as polarization converter [1], ultrathin lens [2], invisible cloak [3], phase shifter [4,5], absorber [6], and low scattering [7], because of its low profile characteristics and potential ability to manipulate electromagnetic (EM) waves. The polarization conversion metasurface (PCM) is an important EM structure, which can be widely applied to radar cross section (RCS) reduction [8], polarization controlled devices [9], and so on. Generally, PCMs can be classified into transmission [10,11] and reflection types [12–14].
In recent years, many studies [15–21] have been made on reflective PCMs. In terms of wideband PCMs, an L-shaped structure is proposed in [15], whose polarization conversion ratio (PCR) is higher than 90% from 7.8 to 34.7 GHz under the normal incidence. In [16], a linear-to-linear 2.5-dimensional PCM with a high PCR is presented. Its PCR is higher than 0.96 within a ratio bandwidth (fH/fL) of 3.1:1. A butterfly-shaped reconfigurable and wideband reflective PCM is designed, whose functionalities can be dynamically switched among linear-to-linear, linear-to-elliptical, and linear-to-circular polarization conversions in a wideband [17]. In [21], a single-layer PCM with five resonances is introduced to realize a 4.1:1 ratio bandwidth with the PCR above 90%. Due to their resonant characteristics, it is challenging to control the polarization state of EM waves with a high polarization conversion efficiency over an ultrawide frequency range, which limits their practical applications.
In this paper, a novel ultrawideband and high-efficient PCM composed of two pairs of L-shaped patches is designed. The aim of this work is to expand the bandwidth of the PCM while guaranteeing a high conversion rate and lessening the size of the unit cell. Following this, this PCM can convert linearly polarized waves to their orthogonal direction in an ultra-wideband from 3.37 to 22.07 GHz with a ratio bandwidth of 6.5:1 under the normal incidence. To the best of our knowledge, the proposed PCM is beyond state-of-the-art of the performance in terms of bandwidth. Besides, the dimensions and thickness of the unit cell in terms of the wavelength at 3.37 GHz is only 0.112 λ0×0.112 λ0×0.095 λ0. The equivalent circuit concept and interference theory are employed to analyze the root cause of the polarization conversion and prove that adding superstrate can widen the bandwidth.
2. Design, simulation, and measurement
The proposed PCM’s unit cell is composed of two pairs of L-shaped metallic patches covered by a single-layer F4B-2 dielectric superstrate (εr=2.65, tanδ = 0.001). The metallic ground is placed at the height of h_air away from L-shaped metallic patches. Figure 1 presents the structure of the unit cell of the proposed PCM. In order to avoid strong magnetic coupling, we set h_air to 5 mm, which is one quarter of the wavelength at 15 GHz. The reason why we choose two pairs of L-shaped patterns is that the length of the L-shaped patch determines the frequency band of resonance. The larger length can achieve the lower frequency band. Therefore, the L-shaped patches with different lengths can obtain the polarization conversion in different frequency bands. From this, two pairs of L-shaped patches with different lengths are combined to expand the bandwidth of the PCM. The unit cell of the PCM was simulated and optimized using the CST Microwave Studio. The optimized parameters of unit cell are as follows: p = 10 mm, l1 = 9.57 mm, l2 = 4.76 mm, w1 = 1 mm, w2 = 0.7 mm, d = 1.1 mm, h = 3.5 mm, and h_air = 5 mm.
Because of the same polarization conversion characteristics for x- and y- polarized waves, we supposed that the incident wave is y-polarized. The cross- and co-polarization reflection coefficients can be defined as rxy=|Exr/Eyi| and ryy=|Eyr/Eyi|, in which Eyi presents the electric field of y-polarized incident waves, Exr and Eyr indicate the electric field of x- and y-polarized reflected waves, respectively. To measure the efficiency of the polarization conversion, we introduce the polarization conversion ratio (PCR), which can be written as PCR = $\textrm{r}_{\textrm{xy}}^{\textrm{2}}$/($\textrm{r}_{\textrm{xy}}^{\textrm{2}}$+$\textrm{r}_{\textrm{yy}}^{\textrm{2}}$). The simulated results of co- and cross-polarization reflection coefficients under y-polarized normal incidence are presented in Fig. 2(a). It can be seen that the reflection coefficient of co-polarization has a wide frequency range from 3.37 to 22.07 GHz below −10 dB, and the cross-polarization reflection coefficient almost reaches 0 dB in this frequency band. There are seven resonant frequencies at 3.65, 5.6, 9.78, 13.69, 16.78, 20.53 and 21.9 GHz, respectively. The PCR at these resonant frequencies can be up to 100%, which indicates the completely polarization conversion. The fractional bandwidth of the PCM is 147% (fH/fL = 6.5:1) with the PCR higher than 90%.
Fig. 2. The ultrawideband PCM (a) Simulated and measured results of co- and cross-polarization reflection coefficients under the normal incidence. (b) The fabricated photograph.
To validate the above-mentioned simulations, a prototype of the PCM with 24×24 unit cells is fabricated, as shown in Fig. 2(b). The sample is fabricated by printed circuit board (PCB) technologies. The metallic bottom ground and the superstructure are connected by nylon columns. High-precision test is performed using the compact antenna test range (CATR) system at Science and Technology on Electromagnetic Scattering Laboratory in Beijing, China. The measured result of co-polarization reflection coefficients is shown in Fig. 2(a), which matches well with the simulated one.
Table 1 presents a comparison between the proposed PCM and other reported wideband polarization converters. Obviously, the proposed PCM works in a lower frequency band and has better broadband characteristics while ensuring a smaller electrical size. The proposed PCM is far beyond state-of-the-art of the performance in terms of bandwidth.
Table 1. Comparison with other wideband PCMs
3. Analysis and discussion
3.1 Analysis of surface impedance concept
To understand the principle of polarization conversion, we take the direction of electric field along the y-axis under the normal incidence as an example. We rotate the original coordinate axis by 45° to obtain a u-v coordinate system, as shown in Fig. 3(a). The direction of the electric field can be decomposed into the u- and v-axes, thus the incident waves and the reflected waves can be expressed as
Fig. 3. (a) Electric field vector image of y-polarized incident waves rotated to x-polarized reflection waves. (b) Simulated reflectance and phase difference with the incident electric field along u- and v-axes.
In order to further investigate the cause of the phase difference between ${\tilde{r}_u}$ and ${\tilde{r}_v}$, the transmission line theory and equivalent circuits are applied and discussed. Due to the anisotropy of the structure, the L-shaped metallic patches have different equivalent circuit models along the u- and v-directions. The inductor (L) is related to the current distribution in the metallic patches and the capacitor (C) results from the electric field distribution in the gaps between metallic patches [20]. Using the above principles, Fig. 4 shows the analysis diagram by the geometrical parameters and simplified circuit model. The detailed circuit parameters are evaluated by fitting the S-parameters according to the data returned from the full-wave simulation. The parameters are obtained as follows: L1 = 2.8 nH, L2 = 4.405 nH, C1 = 0.21 pF, C2 = 0.018 pF, L3 = 0.04 nH, L4 = 3.0 nH, C3 = 0.038 pF, C4 = 0.056 pF, and C5 = 0.12 pF. The surface impedances of the metallic patches are different in these two directions, which results in different input impedances ${Z_u}$ and ${Z_v}$. According to the transmission line theory, the input impedance of u- and v-polarized incident waves under the normal incidence can be expressed as
where Z0 is the wave impendence of the free space. It is confirmed that ${r_u} \simeq {r_v} \simeq 1$, and Zu is different from Zv. Therefore, the reflection phases ${\varphi _u}$ and ${\varphi _v}$ are different, resulting in a certain phase difference. According to the above theoretical analysis, if the phase difference is kept at around 180° within a frequency range, the y- or x-polarized EM wave will rotate to its cross-polarization in this frequency band.Fig. 4. Analysis diagram of equivalent circuit model for (a) the u-direction and (b) the v-direction and simplified circuit model for (c) the u-direction and (d) the v-direction.
The imaginary parts of the input impedance for the u- and v-polarized EM components are shown as the solid lines in Fig. 5(a), which are calculated from (3), respectively. Since the metasurface uses a lossless dielectric, the real part of the equivalent impedance is very small and can be ignored. Additionally, in order to accurately describe the input impedance using the equivalent circuit models in Fig. 4, we optimized these two circuit models in the frequency range of 2 to 23 GHz using a commercial software. The air and F4B superstrate were modeled by transmission lines with the characteristic Z0 and ${\textrm{Z}_\textrm{0}}\textrm{/}\sqrt {{{\varepsilon}_\textrm{r}}} $, respectively. The imaginary parts of the input impedance calculated by the equivalent circuit model in these two directions are shown as the dashed curves in Fig. 5(a). Obviously, the calculation results from (3) are consistent with the results calculated by the equivalent circuit models. It is observed that the imaginary parts of Zu are infinite at frequencies of 3.2, 9.4, 16.6, and 22 GHz, and are almost zero at 5.1, 13.67 and 20.7 GHz; which is opposite to the equivalent impedance in the v-direction. It is consistent with the simulated results when the resonant frequencies are 3.65, 5.6, 9.78, 13.69, 16.78, 20.53, and 21.9 GHz.
Fig. 5. (a) Imaginary parts of input impedance for an incident field along u- and v-axes. (b) Reflection phase under u- and v-polarized normal incidence.
At 9.5 GHz, the imaginary part of Zu is infinite, and the reflection phase of u-polarization under the normal incidence is close to 0°, as shown in Fig. 5(b). In this case, in-phase reflection occurs, and the PCM is analogous to a high-impedance surface. Meanwhile, the imaginary part of Zv is close to 0°, and the reflection phase under v-polarized normal incidence is about 180°, so the metasurface is equivalent to a perfect electric conductor. Thus, the phase difference between φu and φv is about 180°. It is the same as the differences at 3.4 and 16.6 GHz. In addition, the imaginary part of Zv is infinite at about 13.67 GHz and φu is about 0°. At the same time, the imaginary part of Zu is close to 0, and φv is about 180°. It is the same at 5.1 and 20.7 GHz. Thus, the phase difference between φu and φv is about −180°. Due to the anisotropy of the input impedance, there will be a ${\pm}$180° phase difference between φu and φv, which makes the y-polarized incident waves transformed into x-polarized reflected waves.
3.2 Method of interference theory
In order to study the polarization conversion characteristics of the PCM, multiple interference theory [22,23] is applied to model multilayered metasurface. In Fig. 6, the equivalent model of PCM with multilayered media is presented. First, to facilitate the analysis, we regard the part excluding the superstrate (the metal patches and everything to the right) as a reflection surface, then the superstrate and the reflection surface form a three-layer model.
Fig. 6. Schematic of y-polarized incident waves propagating in the PCM described by the reflection and transmission coefficients.
Hence, the total reflection coefficient can be calculated by a consequence of multiple reflections within region 2. Suppose the y-polarized EM waves are incident on from the left, the reflection and transmission will occur on the surface of the superstrate. Due to the isotropy of the superstrate, the reflected and transmitted waves have the same polarization. The Fresnel reflection and transmission coefficients are ${\tilde{r}_{yy12}}\textrm{ = }{r_{yy12}}{e^{j{\varphi _{yy12}}}}$ and ${\tilde{t}_{yy12}}\textrm{ = }{t_{yy12}}{e^{j{\phi _{yy12}}}}$, respectively. The transmitted waves continue to propagate with the propagation phase ${\beta _1}$ in the superstrate until they reach the interface of superstrate and metallic patches, after which they are reflected to the superstrate with the reflection coefficients ${\tilde{r}_{xy23}}\textrm{ = }{r_{xy23}}{e^{j{\varphi _{xy23}}}}$ and ${\tilde{r}_{yy23}}\textrm{ = }{r_{yy23}}{e^{j{\varphi _{yy23}}}}$. These waves are partially reflected back to the superstrate with the reflection coefficients ${\tilde{r}_{yy21}}\textrm{ = }{r_{yy21}}{e^{j{\varphi _{yy21}}}}$ and ${\tilde{r}_{xx21}}\textrm{ = }{r_{xx21}}{e^{j{\varphi _{xx21}}}}$, and partially transmitted into the free space with the transmission coefficients ${\tilde{t}_{yy21}}\textrm{ = }{t_{yy21}}{e^{j{\varphi _{yy21}}}}$ and ${\tilde{t}_{xx21}}\textrm{ = }{t_{xx21}}{e^{j{\varphi _{xx21}}}}$. The overall reflections for y-to-y and y-to-x polarizations are consisted of superposition of multiple reflections. The propagation process between the EM waves ‘touching’ the air-superstrate interface two times is defined as a roundtrip. The overall reflection coefficient [23] at the interface between region 1 and region 2 can be written as
In closed form, let
Second, the polarization conversion characteristic between the metallic L-shaped patches and the ground was analyzed. Similar to Eq. (4), the total reflection coefficients from region 3 to region 2 can be written as
Plugging Eq. (9) into Eq. (8), the total reflection matrix can be simplified as
Reflection and transmission coefficients at the metallic patches interface obtained by simulations are shown in Fig. 7. Bring those parameters into the above formula (11)–(14), the overall co- and cross-polarized reflectance at the different interfaces obtained by simulations and theory calculations are shown in Fig. 8. It can be seen that the minimum operating frequency without substrate is higher than that with substrate. Besides, the introduction of the substrate with an optimized thickness h generates more resonances and improves the polarization conversion efficiency. Since the operational wavelength is much larger than the dimensions of the unit cell at low-frequency region, a good approximation is to keep only zero-order Bragg modes [24] when analyzing the interference process, as inter-order couplings are expected to be weak. The neglect of near-field interactions is the reason for the difference at high-frequency region between theoretical calculation and simulation. In general, the calculated and simulated results are similar to each other, which provides a theoretical basis for the performance of the double-layer PCM better than the single layer one.
Fig. 7. Reflection and transmission coefficients at the metallic patches interface obtained by the full-wave simulations. (a) Magnitudes and (b) phases of the reflection coefficient. (c) Magnitudes and (d) phases of the transmission coefficient.
Fig. 8. Reflection coefficients at the different interfaces obtained by the simulations and the theory calculations: (a) ${r}_{{yy23}}^{ - }$, (b) ${r}_{{yy12}}^{ - }$, (c) ${r}_{{xy23}}^{ - }$, and (d) ${r}_{{xy12}}^{ - }$.
3.4 Surface current distributions
In order to get a better physical insight, Fig. 9 illustrates the surface current distributions at resonant frequencies of 3.65, 5.6, 9.78, 13.69, 16.78, 20.53, and 21.9 GHz. It is quite helpful to show the features of both resonances at the seven frequencies, and then, to determine the contributions of electric and magnetic modes. Magnetic resonances are generated by anti-parallel currents coupling between the metallic patches and the ground plane due to the circulating current flow. Electric resonances are generated by parallel currents between them [1,21]. At the lowest resonant frequency of 3.65 GHz [see Fig. 9(a)], it can be observed that surface currents flow along the outer L-shaped patches without changing direction, which makes the outer patches equivalent to a cut-wire resonator in the fundamental resonant mode [25]. The currents on the ground plane are antiparallel to the induced currents on the patches layer generating magnetic resonance. For Fig. 9(b), the currents on the patches layer are perpendicular to the induced currents on the ground plane. According to the principle of vector decomposition, the black arrows can be decomposed into two components including the green and blue arrows. For the currents indicated by blue arrows, they indicate electric resonance due to the parallel direction; while for the currents represented by green arrows, they form magnetic resonance duo to the directions are antiparallel. Therefore, the mode pattern of 5.6 GHz is the combination of both electric and magnetic resonances.
Fig. 9. Surface current distributions of metallic parts and ground plane of the proposed PCM for normal y-direction incident wave at the seven resonant frequencies: (a) 3.65 GHz, (b) 5.6 GHz, (c) 9.78 GHz, (d) 13.69 GHz, (e) 16.78 GHz, (f) 20.53 GHz, and (g) 21.9 GHz.
Parallel surface currents are induced by the metallic resonator and the ground plane, forming electric dipole resonance in 9.78 GHz, as shown in Fig. 9(c). From Fig. 9(d), it can be observed that surface current currents flow along the outer L-shaped patches and change direction in the half section, which is the characteristic of the second-order resonant mode. Similar to Fig. 9(b), due to the combination of both electric and magnetic resonances, the currents on the patches layer are perpendicular to the induced currents on the ground plane. Additionally, the resonance patterns of Figs. 9(e) and (f) are similar to Figs. 9(a) and (b), respectively. The difference is the surface currents are transferred from the outer L-shaped patches to the inner L-shaped patches. The third-order mode resonant mode of outer L-shaped patches and the fundamental resonant mode of the inner L-shaped patches are excited in Fig. 9(g). According to the vector synthesis principle, all arrows can be combined into a black arrow, the resultant currents on the metallic patches and ground plane are parallel to each other generating electric resonance. In summary, the types of resonance modes in Figs. 9(a) and (e) are magnetic modes; the resonant frequencies of Figs. 9(c) and (g) are electric resonance; the resonance modes of Figs. 9(b), (d), and (f) are induced by the combination of both electric and magnetic resonances. Consequently, the proposed PCM works in an ultrawideband frequency domain due to the resonances mentioned above.
3.5 Oblique incidence performance and parametric analysis
It is important to investigate the polarization conversion of the proposed PCM for oblique incidence. Figure 10 shows simulated PCRs of the proposed PCM for different oblique incident angles. It is clearly shown that the incident angles have a great influence on the bandwidth of polarization conversion. The main reason is the propagation phase changes between normal and oblique incidence, which create a destructive interference condition at some frequencies [1,20]. Due to the additional propagation phase changes more drastically at the higher frequencies, PCR rapidly decreases at an increment of incident angle. In addition, the notches around 8.5 and 13 GHz of PCR for oblique incidence are mainly the wave absorption due to dielectric loss [19].
In order to investigate the influence of the height (h_air) of the air layer on the polarization conversion characteristics, we simulated the reflection coefficients of co- and cross-polarization with different thicknesses, as displayed in Figs. 11(a) and (b), respectively. It can be seen that increasing the height of air can generate more resonant frequencies, i.e., when the thicknesses of air space are 3 and 6 mm, the proposed PCM has four and seven resonant frequencies, respectively; and shifts the operating frequency band to lower frequency. The near-equal ripple reflection coefficients with an optimized thickness of 5 mm are selected to balance the bandwidth and polarization conversion efficiency.
Fig. 11. Simulated coefficients of the proposed PCM for different thickness (h_air) of the air layer: (a) $\textrm{r}_{\textrm{yy12}}^\textrm{ - }$, and (b) $\textrm{r}_{\textrm{xy12}}^\textrm{ - }$.
4. Conclusion
In this paper, an ultrawideband and high-efficient L-shaped PCM was designed, simulated, and fabricated. The bandwidth of the PCM was broadened to 6.5:1 with PCR more than 0.9, which is wider than other PCMs. Besides, The PCR can achieve 100% at seven resonant frequencies. The root cause of multi-resonance and polarization conversion behaviors was analyzed through the transmission line theory and equivalent circuit model. We showed that the fundamental reason for the polarization conversion is a certain reflection phase difference in u- and v-directions, which is caused by the anisotropy of the equivalent impedance. Besides, we proved that adding dielectric superstrate can widen the bandwidth using simulations and the interference theory. Simulation, theoretical calculation and measurement results validate the capability of the proposed PCM to convert linearly polarized waves to its orthogonal direction in an ultra-wide frequency range.
Funding
National Natural Science Foundation of China (61701448, 62071436).
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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