## Abstract

An ultra-wideband and efficient single layer polarization converting metasurface based on an L-shaped resonator is presented. The metasurface is based on an F4B dielectric substrate with relative permittivity of 2.65 and a loss tangent of 0.002. The size of the unit cell is 0.132*λ*_{o} × 0.132*λ*_{o} and the thickness of the metasurface is 0.05*λ*_{o}, where *λ*_{o} is the largest wavelength (corresponding to the lower frequency) in the operation band of interest. The proposed structure effectively transforms the linearly or circularly polarized incident wave to its orthogonal equivalent, which is justified by both simulated and measured results where the polarization conversion ratio (PCR) is greater than 90% in the frequency range from 8.6 GHz to 22 GHz with a fractional bandwidth of 88%. The polarization transformation process is illustrated in depth by the surface current distribution. Simulation results reveal that ultra-wideband is achieved because of strong electric and magnetic dipole resonances on the upper and the lower layer of the metasurface. Furthermore, the bandwidth and central frequency can be efficiently adjusted over a wide spectrum by changing the geometric aspects of the unit cell, thereby retaining high transformation proficiency. The designed converter can be used in applications such as antenna design, radar invisibility, imaging, microwave communications, and remote sensing.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Metamaterials have many unnatural electromagnetic properties including but not limited to negative refractive index [1], invisibility [2], perfect lensing [3], perfect absorbing [4], and backward propagation [5], and as a result, they have been extensively used in a wide range of applications such as antenna systems and polarization conversion [6–9], [10]. Among the different types of metamaterials, the so-called metasurfaces, a planar version of metamaterials, have drawn particular interest due to their great potential for use in control and manipulation of electromagnetic waves. One flourishing branch of applications of metasurfaces is polarization conversion. Many such metasurfaces have been reported [11–18]. However, those reported polarization conversion metasurfaces (PCMS’s) generally suffer from one important limitation, i.e., narrow bandwidth. Many methods can be used to expand polarization conversion bandwidth, and the popular ones include the multiple-resonator/layer method and the unit cell optimization method. The former combines two or more resonators with different sizes to form a super unitcell [19], or stacks multiple resonator layers with different geometric extents isolated by dielectric layers of suitable thicknesses [20], [21] or superstrate layers [22], [23], or uses via connection [24], [25]. Although it extends the bandwidth, this method leads to complicated PCMS structures with multiple metal-dielectric layers. As a result, the fabrication process is challenging and time-consuming and the resulting thickness of PCMS is often unacceptable. The latter increases the bandwidth by properly designing the unit cell structure to resonate at wide plasmon resonances [26], [27], [28]. Nevertheless, how to design ultra-wideband and efficient PCMS is still a challenging problem and further efforts in this perspective is indispensable.

This paper is concerned with expansion of polarization bandwidth. It presents an ultra-wideband single layer PCMS, which rotates a linearly or circularly polarized wave into its orthogonal counterpart with a high efficiency. The ultra-wideband performance is the result of multiple resonances created by electric and magnetic reflex of the surface current distributions, which generate four plasmon resonances, leading to expansion of polarization bandwidth. For linearly or circularly polarized incident waves, the polarization conversion ratio (PCR) is greater than $90\%$ with a fractional bandwidth of $88\%$ in the frequency band from $8.6$ GHz to $22$ GHz.

## 2. Design and unit cell configuration

MS structures with symmetric resonators have been used as effective absorbers with low co- and cross-polarization reflection. It is found that breaking the symmetry of the resonators decreases co-polarization reflection while increases cross-polarization reflection. This principle has been employed to design polarization converters with anisotropic MS structures, which consists of periodic asymmetrical metallic patterns [29]. Following a similar line of ideas, we propose an ultra-wideband and highly efficient cross-polarization converter based on asymmetric L-shaped resonator. This ultra-wideband MS unit cell is made up of three layers as illustrated in Fig. 1(a): upper layer, which is a metallic L-shaped structure, central layer, which is a dielectric substrate, and base layer, which is a metallic ground. The unit cell structure consists of two copper layers (L-shaped resonator and ground) with thickness of $0.035$ mm for each, separated by $3$-mm ($=0.05\lambda _{\textrm {o}}$) thick F4B substrate. So, the metasurface is ultra-thin as the thickness is much smaller than the wavelength. The electrical properties of the metal and dielectric layer are: $\sigma =5.8\times 10^7$ S/m, $\epsilon _r = 2.65$, tan$\delta = 0.002$. The physical dimensions of the cross polarization converter (CPC) are $w = 8$, $l = 5.6$, $g = 0.8$, and $h_{\mathrm {s}} = 3$ (all in mm). The proposed design is obtained through four major steps. In step 1, a square patch of size $l\times l$ is used, which is shown in Fig. 2(a). This step does not show any polarization conversion. In step 2, a square ring as shown in Fig. 2(b) is employed, which again shows no sign of polarization conversion. In step 3, the upper center part of the square ring is removed and again there is no polarization conversion achieved as seen in Fig. 2(c). In step 4, the right-hand side of the square ring is removed, which results in an asymmetric L-shaped resonator structure as shown in Fig. 2(d). This now leads to four plasmon resonances, resulting in efficient polarization conversion in an ultra wideband from $8.6$ GHz to $22$ GHz. These properly designed steps correlate the surface at four plasmon resonances, which result in an ultra wideband and a highly efficient polarization converter.

## 3. Simulation results and discussion

Simulations of the ultra-wideband PCMS are performed by the finite element method (FEM) in ANSYS HFSS. Floquent port in $z$ and link boundary condition are applied in the $x$-$y$ plane. To understand the polarization transformation of the PCMS, let us consider to decompose a linearly polarized incident EM wave, ${E_{\mathrm {i}}}$, into two components, ${E_{\mathrm {i}u}}$ and ${E_{\mathrm {i}v}}$ in the $u$- and $v$-directions as illustrated in Fig. 1(b). Then, the incident field can be written as $\overrightarrow {E_{\mathrm {i}}} = {{\overrightarrow {u}} {E_{\mathrm {i}u}} +{\overrightarrow {v}} {E_{\mathrm {i}v}} }$, and the reflected field is written as $\overrightarrow {E_{\textrm {r}}} = {{\overrightarrow {u}} {\stackrel {\sim }{r_u}}{E_{\mathrm {i}u}} } + {{\overrightarrow {v}} {\stackrel {\sim }{r_v}}{E_{\mathrm {i}v}} }$, where the $u$- and $v$-axis are orthogonal to each other and inclined ${45}^{\circ }$ with respect to the $y$-axis, the ${\stackrel {\sim }{r_u}}$ and ${\stackrel {\sim }{r_v}}$ represents, respectively, the reflection ratios along the $u$- and $v$-axis. There is a phase difference between ${\stackrel {\sim }{r_u}}$ and ${\stackrel {\sim }{r_v}}$, which is denoted as $\Delta \varphi$. If ${r_u}$ ${\approx }$ ${r_v}$ and $\Delta \varphi$ approaches ${180}^{\circ }$, polarization conversion occurs. The simulated amplitudes of the reflection coefficients, their corresponding phases, and the phase difference for $u$- and $v$-polarized waves are plotted in Fig. 3(a), which validates that the amplitudes are close to each other (i.e., ${r_u}$ ${\approx }$ ${r_v}$) and the phase difference $\Delta \varphi$ is close to ${180}^{\circ }$ in the frequency range of $8.6$ GHz to $22$ GHz. As a result, the polarization transformation is achieved. To comprehend the wide bandwidth and high efficiency of the proposed PCMS, the plasmon resonances of the unit cell are investigated. The reflectance for arbitrarily polarized incident EM wave along the $u$- and $v$-axis are shown in Fig. 3(b). The results show that four plasmon resonances are excited in the MS unit structure. Two plasmon resonances (ii) and (iv) are excited in the $u$-polarized state, and two plasmon resonances (i) and (iii) are excited in the $v$-polarized state. Ultra-wideband polarization conversion is achieved because of multiple resonances in the operating frequency band.

The reflection amplitudes in the $x$- and $y$-directions are defined as $r_{xy}$ = $|E_{\mathrm {r}x}|/|E_{\mathrm {i}y}|$, $r_{yy}$ = $|E_{\mathrm {r}y}|/|E_{\mathrm {i}y}|$, $r_{yx}$ = $|E_{ry}|/|E_{\mathrm {i}x}|$, $r_{xx}$ = $|E_{\mathrm {r}x}|/|E_{\mathrm {i}x}|$, where $x$ and $y$ represents the paths of EM waves. The reflection amplitudes of (${r_{xy}}$, ${r_{yy}}$) and (${r_{yx}}$, ${r_{xx}}$) are similar because of geometrical symmetry of the PCMS, creating identical responses for polarization transformation of the $y$- and $x$-polarized incident EM waves. Therefore, the surface is illuminated with $y$-polarized incident waves and the corresponding reflection amplitudes of ${r_{xy}}$ and ${r_{yy}}$ are plotted in Fig. 4(a). The level of ${r_{xy}}$ is close to 0 dB (greater than $-0.05$ dB) and the level of ${r_{yy}}$ is smaller than $-13$ dB in the studied band, i.e., $8.6-22$ GHz, which indicates that highly effective $y$- to $x$-polarization transformation is achieved with the proposed PCMS.

The reflection amplitudes of right-hand circular polarized waves are ${r_{++}}$ = $|E_{\mathrm {r}+}|/|E_{\mathrm {i}+}|$ and ${r_{-+}}$ = $|E_{\mathrm {r}-}|/|E_{\mathrm {i}+}|$. They are plotted in Fig. 4(b), which reveals that the proposed PCMS effectively rotates the circular polarized wave to its orthogonal equivalent in the studied band. Polarization azimuth angle ($\theta$) tells the effect of polarization rotation, which is defined as $\theta = {a \tan } (r_{xy}/r_{yy})$. The result is plotted in Fig. 4(c), which is larger than ${75}^{\circ }$ in the studied frequency band. Moreover, at the resonance frequencies of $9.3$, $13.1$, $19.0$, and $21.7$ GHz, the value of $\theta$ approaches ${90}^{\circ }$, which conforms a highly efficient polarization transformation.

PCR is a measure used to quantify the effectiveness of polarization converters. It is computed as PCR$_{\mathrm {YPOL}}$ = ${|r^2_{xy}|}/{|r^2_{xy}|+|r^2_{yy}|}$, PCR$_{\mathrm {RHCP}}$ = ${|r^2_{++}|}/{|r^2_{++}|+|r^2_{-+}|}$. Figure 4(d) plots the PCR, which is more than $90\%$ in the frequency range from $8.6$ GHz to $22$ GHz with a fractional bandwidth of $88\%$ for both linear and circular polarized waves. The polarization converter is also studied for oblique incidence, and the corresponding simulated reflection coefficients (${r_{xy}},{r_{yy}}$) and PCR are plotted in Fig. 5. It is seen that the incidence angle has a great influence on polarization transformation efficiency, i.e., polarization efficiency decreases as the incidence angle increases. The proposed structure is quite stable against variation in angle up to ${20}^{\circ }$. As the incidence angle shifts to ${40}^{\circ }$, the reflection coefficient (${r_{yy}}$) continuously increases and the polarization conversion bandwidth decreases; but the PCR is still more than $80\%$ for the band of $8.53$-$18.18$ GHz for incidence angle of ${40}^{\circ }$, as seen in Fig. 5(b).

## 4. Working mechanism

To comprehend the basic working principle, the surface current distribution for the $u$- and $v$-polarized cases on the upper and lower metallic part of the metasurface at four eigen-modes are shown in Fig. 6. As seen in Fig. 3(b), two eigen-modes (i) and (iii) occur under $v$-polarization and two eigen-modes (ii) and (iv) occur under $u$-polarization. The orientation of the induce current indicates the type of resonance. Figure 6(a) and (d) show that the orientations of the current on the L-shape resonator and metal ground are same at eigen-modes (i) and (iv); therefore, the resonances at $9.3$ GHz and $21.7$ GHz are deemed to be electrical resonance. Figure 6(b) and (c) shows that the orientations of the current on the L-shape resonator and metal ground are opposite at eigen-mode (ii) and (iii); so the resonances at $13.1$ GHz and $19.0$ GHz are deemed to be magnetic resonance. The increase in magnetic permeability (i.e., $\mu$) results in higher surface impedance ($Z$= $\sqrt {{ \mu }/{\epsilon }}$), which enables the reflection to be in phase. The electric and magnetic reflex of the designed PCMS produces four plasmon resonances, leading to the expansion of bandwidth.

## 5. Theoretical analysis

To unveil the dynamics of polarization transformation of the proposed PCMS, we analyze the $y$-polarized wave, which can be broken down into two perpendicular symmetry elements along the $u$- and $v$-axis as illustrated in Fig. 1(b). The incident and reflected EM waves are described by the following equations:

The reflected wave fulfils the following equation [30]:

Now, using the fact that ${E_y}=\frac {\sqrt 2}{2}\begin {pmatrix}{\hat {e}_u}+{\hat {e} _v}\end {pmatrix}$ and ${E_x}=\frac {\sqrt 2}{2}\begin {pmatrix}{\hat {e}_u}-{\hat {e} _v}\end {pmatrix}$, we can write (5) as

So, the $x$- and $y$-polarized elements are

Furthermore, the cross- and co-polarization reflections are computed as follows:

Figure 7(a) plots the magnitude of the reflection coefficients computed according to (8a). The results of Fig. 7(a) are subsequently used to compute the PCR, which is plotted in Fig. 7(b). As seen, the calculated results of $y$-polarized incident wave are in strong agreement with the simulation results in Fig. 4(a) and (d), which corroborates that the designed PCMS achieves efficient polarization transformation in an ultra wideband from $8.6$ GHz to $22$ GHz.

## 6. Unit cell scaling

Any electromagnetic system used in one frequency band can be tuned to other operating frequency bands by adjusting the geometrical extents of the system. Up and down scaling of the length and width of the proposed metasurface unit cell are done through scale transformation in ANSYS HFSS. Simulation boundary conditions are kept the same for both original and scaled version of the unit cell. The frequency sweep for the scaled variants of the unit cells was chosen relying on the indirect correlation among size of the metasurface unit cell and the frequency. A higher dimension of the structure performs polarization transformation for a lower frequency band while a smaller dimension results in such phenomenon for a higher frequency band. The proposed PCMS is examined for different unit cell sizes. The simulated results are plotted in Fig. 8. Proportional shift in the frequency response is noted by increasing or decreasing the unit cell size. Figure 8(a) shows that by doubling the length of the unit cell the frequency response is shifted towards the lower side ($2$-$12$ GHz), and the plasmon frequencies are nearly halved, i.e., $4.6$, $6.5$, $9.4$, and $10.8$ GHz. Figure 8(b) shows that, by decreasing the length of the unit cell by half, the resonance frequencies are nearly doubled to $18.5$, $25.9$, $39$, and $43.3$ GHz, and the frequency response is shifted to the higher band ($10$-$50$ GHz). This analysis shows that the proposed metasurface is flexible in terms of achieving ultra-wideband cross-polarization within any frequency range by carefully scaling the dimensions of the unit cell.

## 7. Experimental results

The proposed metasurface is fabricated on F4B substrate of $160\times 160$ mm$^2$, which contain $20\times 20$ unit cells. A photo of the manufactured sample is displayed in Fig. 9(a). A KEYSIGHT N5224A vector network analyzer and wideband horn antennas were connected to test the prototype, as illustrated in Fig. 9(b). The fabricated prototype was placed below the horn antennas surrounded by absorbers. The metal back side of the prototype was used for the system calibration. We performed the polarization reflection performance test of the fabricated prototype by using one horn antenna for transmitting horizontally polarized waves, and the second horn antenna for receiving vertically polarized waves. Comparison of simulated and experimental results are shown in Fig. 10. As seen, the simulated and measured results are in close agreement, except for the minor fluctuations, which is primarily due to fabrication and measurement errors. Comparison between the designed and already reported PCMS’s is presented in Table 1. It is seen from the table that the designed PCMS exhibits wide operating bandwidth (except for [31]). Moreover the proposed PCMS has higher fractional bandwidth, smaller size, and thinner thickness as compared to the references listed in Table 1.

## 8. Conclusion

An ultra-wideband and efficient polarization converter was presented. The metasurface structure was made of L-shaped resonator, which transform linearly or circularly polarized incident waves into their orthogonal equivalent in the frequency band from $8.6$ GHz to $22$ GHz. As a result, the converter can be used in the $X$, $K_u$, and $K$-bands of microwave spectrum. The PCR is more then $90\%$ in the frequency band of $8.6$-$22$ GHz with a fractional bandwidth of $88\%$. The PCR reaches approximately $100\%$ at $9.1$-$9.4$, $12.6$-$13.5$, and $18.7$-$19.4$ GHz.

## Funding

National Key Research and Development Program of China (2018AAA0102200); Key Program of National Natural Science Foundation of China (NFSC) (61831019).

## Acknowledgments

This work was supported in parts by the National Key Research and Development Program of China under Grant No. 2018AAA0102200 and in part by the Key Program of National Science Foundation of China (NSFC) under Grant No. 61831019.

## Disclosures

The authors declare no conflicts of interest.

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