Ultra-wideband linear-to-circular polarization conversion metasurface

Bao-Qin Lin; Lin-Tao Lv; Jian-Xin Guo; Zu-Liang Wang; Shi-Qi Huang; Yan-Wen Wang

doi:10.1088/1674-1056/ab9de5

1. Introduction

Polarization is one of important characteristics of electromagnetic (EM) wave, and it must be taken into consideration in most practical applications. In various wireless systems, such as mobile communication, radar tracking, satellite communication and navigation systems, circularly polarized (CP) wave has been widely used due to the advantages such as simplifying alignment, overcoming Faraday rotation effect and multi-path fading. [1] To generate a desired CP wave, in addition to the way to generate it directly using CP antenna, an alternative effective way is to first generate a linearly polarized (LP) wave and then convert the LP wave into a CP wave by using a linear-to-circular (LTC) polarization converter.

In this work, a reflective metasurface is proposed, which can realize ultra-wideband LTC polarization conversion under both x - and y -polarized incidences. Its 3-dB axial ratio (AR) bandwidth reaches up to 113%, moreover, the PCR is kept larger than 99% in most part of the 3-dB-AR-band. The high-efficiency and ultra-wideband LTC polarization conversion performance of the proposed polarization converter is verified by both simulation and experiment; moreover, the root cause of the LTC polarization conversion is analyzed in detail.

2. Design and simulation

The proposed polarization conversion metasurface consists of one layer of patterned metal film printed on a grounded dielectric substrate and covered with a dielectric layer, which is a two-dimensional (2D) square lattice periodic structure, one of its unit cells is illustrated in Fig. 1 . It is indicated that the proposed polarization conversion metasurface is an orthotropic structure with a pair of mutually perpendicular symmetric axes u and v along the directions with the tilt angles of \pm 45 with respect to the vertical y axis. In addition, the geometrical parameters of the unit cell structure are shown in Fig. 1(b) . In our design, these geometrical parameters are chosen as follows: P = 8.00 mm, w 1 = 4.2 mm, w 2 = 2.5 mm, h 1 = 3.0 mm, and h 2 = 4.2 mm; in addition, the two dielectric layers have both a dielectric constant ε r = 2.0 and a loss tangent tan δ = 0.0018; moreover, the thickness values of the metallic patterns are all t = 0.017 mm.

Figure 1.Unit cell of proposed polarization conversion metasurface: (a) three-dimensional (3D) view, and (b) top view.

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r_{y y} = E_{y}^{r} / E_{y}^{i}

Figure 2.Simulated results of proposed polarization conversion metasurface undeer y-polarized normal incidence: (a) phase difference Δ φ_yx between r_xy and r_yy and (b) magnitude of r_xy and r_yy.

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In fact, the reflected wave is still not a perfect CP one, but it can be considered as a CP one when its AR is lower than 3.0 dB. According to the relevant literature, [38] the AR of the reflected wave can be calculated from the following equation:

$$ \begin{eqnarray}{\rm{AR}}={\left(\displaystyle \frac{{|{r}_{yy}|}^{2}+{|{r}_{xy}|}^{2}+\sqrt{a}}{{|{r}_{yy}|}^{2}+{|{r}_{xy}|}^{2}-\sqrt{a}}\right)}^{1/2},\end{eqnarray}$$ (1)

where

1

Based on the simulated results in Fig. 2, the AR of the reflected wave can be calculated out, which is shown in Fig. 3, it is indicated that the AR is lower than 3.0 dB in the frequency range from 5.87 GHz to 21.13 GHz, and the anticipated LTC polarization conversion is realized in the ultra-wideband frequency band, which is corresponding to a 113% relative bandwidth.

Figure 3.Axial ratio of reflected wave under y-polarized normal incidence.

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E^{i} = E_{y}^{i} {\hat{e}}_{y} e^{- j k z}

$$ \begin{eqnarray}\begin{array}{lll}{{\boldsymbol E}_{r}|}_{{\boldsymbol E}_{i}={E}_{y}^{i}{\hat{e}}_{y}} & = & {E}_{y}^{i}({r}_{xy}{\hat{e}}_{x}+{r}_{yy}{\hat{e}}_{y})\\ & = & \displaystyle \frac{{E}_{y}^{i}\sqrt{2}({r}_{xy}+{\rm{i}}{r}_{yy})}{2}\displaystyle \frac{\sqrt{2}({\hat{e}}_{x}-{\rm{i}}{\hat{e}}_{y})}{2}\\ & & +\displaystyle \frac{{E}_{y}^{i}\sqrt{2}({r}_{xy}-{\rm{i}}{r}_{yy})}{2}\displaystyle \frac{\sqrt{2}({\hat{e}}_{x}+{\rm{i}}{\hat{e}}_{y})}{2}.\end{array}\end{eqnarray}$$ (2)

Now, if two LTC polarization conversion reflection coefficients are defined as

r_{RHCP - y} = E_{RHCP}^{r} / E_{y}^{i}

and

r_{LHCP - y} = E_{LHCP}^{r} / E_{y}^{i}

respectively, equation (2) shows that the two reflection coefficients can be obtained from the following equation:

$$ \begin{eqnarray}\begin{array}{lll} & & {r}_{{\rm{RHCP}}-y}=\sqrt{2}({r}_{xy}+{\rm{i}}{r}_{yy})/2,\\ & & {r}_{{\rm{LHCP}}-y}=\sqrt{2}({r}_{xy}-{\rm{i}}{r}_{yy})/2.\end{array}\end{eqnarray}$$ (3)

According to the above simulated results, the two LTC polarization conversion reflection coefficients of the proposed polarization conversion metasurface are obtained from Eq. (3), and the magnitudes of the two reflection coefficients are shown in Fig. 4(a), it is implied that the magnitude of the LHCP component is much larger than that of the RHCP component in the reflected wave. In addition, in order to show the LTC polarization conversion performance of the polarization conversion metasurface in detail, the polarization conversion rate (PCR) is calculated from the following equation:

$$ \begin{eqnarray}{\rm{PCR}}=\displaystyle \frac{{|{r}_{{\rm{LHCP}}-y}|}^{2}}{{|{r}_{{\rm{RHCP}}-y}|}^{2}+{|{r}_{{\rm{LHCP}}-y}|}^{2}}.\end{eqnarray}$$ (4)

The calculated results, shown in Fig. 4(b), indicates that the PCR is kept larger than 97.14% in the whole 3-dB-AR-band. Why is that so? In fact, by using the two LTC polarization conversion reflection coefficients: r_RHCP – y and r_{LHCP – y}, the AR of the reflected wave can be expressed as

$$ \begin{eqnarray}{\rm{AR}}=\displaystyle \frac{|{r}_{{\rm{LHCP}}-y}|+|{r}_{{\rm{RHCP}}-y}|}{||{r}_{{\rm{LHCP}}-y}|-|{r}_{{\rm{RHCP}}-y}||}.\end{eqnarray}$$ (5)

In this way, through the following derivation, it can be well known that the PCR will be kept larger than 97.14% and the magnitude of r_RHCP – y or r_{LHCP – y} will be less than – 15.43 dB in the 3-dB-AR-band of any LTC polarization converter.

$$ \begin{eqnarray}\begin{array}{lll} & & {\rm{AR}}=\displaystyle \frac{|{r}_{{\rm{LHCP}}-y}|+|{r}_{{\rm{RHCP}}-y}|}{||{r}_{{\rm{LHCP}}-y}|-|{r}_{{\rm{RHCP}}-y}||}\le \sqrt{2}\Rightarrow \displaystyle \frac{|{r}_{{\rm{LHCP}}-y}|}{|{r}_{{\rm{RHCP}}-y}|}\,\,{\rm{or}}\,\,\displaystyle \frac{|{r}_{{\rm{CHCP}}-y}|}{|{r}_{{\rm{LHCP}}-y}|}\le 0.1716,\end{array}\end{eqnarray}$$ (6)

$$ \begin{eqnarray}\begin{array}{lll} & & {\rm{PCR}}=\displaystyle \frac{{|{r}_{{\rm{LHCP}}-y}|}^{2}}{{|{r}_{{\rm{RHCP}}-y}|}^{2}+{|{r}_{{\rm{LHCP}}-y}|}^{2}}\ge \displaystyle \frac{1}{{1}^{2}+{0.1716}^{2}}\ge 97.14 \%,\end{array}\end{eqnarray}$$ (7)

$$ \begin{eqnarray}\begin{array}{lll} & & {|{r}_{{\rm{RHCP}}-y}|}^{2}{\rm{or}}\,\,{\begin{array}{c}|{r}_{{\rm{LHCP}}-y}|\end{array}}^{2}\le \sqrt{100 \% -97.14 \% }\Rightarrow \begin{array}{c}|{r}_{{\rm{RHCP}}-y}|\end{array}\,{\rm{or}}\,|{r}_{{\rm{LHCP}}-y}|\le -15.43\,{\rm{dB}}.\end{array}\end{eqnarray}$$ (8)

However, for the proposed polarization conversion metasurface, figures 4(a) and 4(b) show that the PCR is larger than 99% and the magnitude of r_{RHCP – y} is less than –20 dB in the wide frequency range from 8.08 GHz to 20.92 GHz, which shows that the proposed polarization conversion metasurface has not only wider bandwidth but also higher efficiency.

Figure 4.(a) LTC reflection coefficients and (b) polarization conversion rate (PCR) of proposed polarization conversion metasurface under y-polarized normal incidence.

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3. Theoretical analysis

Why can the proposed polarization conversion metasurface perform such an ultra-wideband and high-efficiency LTC polarization conversion? To obtain a physical insight into the root cause, we carry out a detailed theoretical analysis in the following. As the proposed polarization conversion metasurface is an orthotropic anisotropic structure with a pair of mutually perpendicular symmetric axes u and v, no cross-polarized reflection components will exist under u - and v -polarized incidences, the magnitudes of r uu and r vv will both be very close to 1.0 because of the little dielectric loss. Therefore, in the case of neglecting the little dielectric loss, the following equation can be established:

$$ \begin{eqnarray}{r}_{vv}={r}_{uu}{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}},\end{eqnarray}$$ (9)

where Δφ_uv represents the phase difference between r_uu and r_vv, which can be limited between r_uu and r_vv. In addition, as the symmetric axes u and v are along the directions with the tilt angles of ± 45° with respect to the y axis, the y- and x-polarized unit waves can be expressed as

{\hat{e}}_{y} = (\sqrt{2} / 2) ({\hat{e}}_{u} + {\hat{e}}_{v})

and

{\hat{e}}_{x} = (\sqrt{2} / 2) ({\hat{e}}_{u} - {\hat{e}}_{v})

, respectively. In this way, when the incident wave is supposed to be a y-polarized one

E^{i} = E_{0} {\hat{e}}_{y} = E_{0} (\sqrt{2} / 2) ({\hat{e}}_{u} + {\hat{e}}_{v})

, the total reflected wave can be expressed as

$$ \begin{eqnarray}\begin{array}{lll}{\boldsymbol E}^{{\rm{r}}} & = & {E}_{u}^{{\rm{r}}}{\hat{e}}_{u}+{E}_{v}^{{\rm{r}}}{\hat{e}}_{v}\\ & = & \displaystyle \frac{\sqrt{2}}{2}{E}_{0}({r}_{uu}{\hat{e}}_{u}+{r}_{vv}{\hat{e}}_{v})\\ & = & \displaystyle \frac{\sqrt{2}}{4}{E}_{0}[({r}_{uu}+{r}_{vv})({\hat{e}}_{u}+{\hat{e}}_{v})+({r}_{uu}-{r}_{vv})({\hat{e}}_{u}-{\hat{e}}_{v})]\\ & = & {E}_{0}\displaystyle \frac{1}{2}({r}_{uu}+{r}_{vv}){\hat{e}}_{y}+{E}_{0}\displaystyle \frac{1}{2}({r}_{uu}-{r}_{vv}){\hat{e}}_{x},\end{array}\end{eqnarray}$$ (10)

which implies that the co- and cross-polarization reflection coefficient under the y-polarized incidence can be expressed, respectively, as

$$ \begin{eqnarray}\begin{array}{lll} & & {r}_{yy}=\displaystyle \frac{1}{2}({r}_{uu}+{r}_{vv})=\displaystyle \frac{1}{2}{r}_{uu}(1+{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}}),\\ & & {r}_{xy}=\displaystyle \frac{1}{2}({r}_{uu}-{r}_{vv})=\displaystyle \frac{1}{2}{r}_{uu}(1-{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}}).\end{array}\end{eqnarray}$$ (11)

After a similar derivation under x-polarized incidence, the total reflection matrix R_lin in the X–Y coordinate system is obtained as follows:

$$ \begin{eqnarray}\begin{array}{lll}{\boldsymbol R}_{{\rm{lin}}} & = & \left(\begin{array}{cc}{r}_{xx} & {r}_{xy}\\ {r}_{yx} & {r}_{yy}\end{array}\right)=\displaystyle \frac{1}{2}\left(\begin{array}{cc}{r}_{uu}+{r}_{vv} & {r}_{uu}-{r}_{vv}\\ {r}_{uu}-{r}_{vv} & {r}_{uu}+{r}_{vv}\end{array}\right)\\ & = & \displaystyle \frac{1}{2}{r}_{uu}\left(\begin{array}{cc}1+{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}} & 1-{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}}\\ 1-{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}} & 1+{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}}\end{array}\right).\end{array}\end{eqnarray}$$ (12)

According to Eq. (12), the following equation can be established

$$ \begin{eqnarray}\displaystyle \frac{{r}_{yy}}{{r}_{xy}}=\displaystyle \frac{{r}_{xx}}{{r}_{yx}}=\displaystyle \frac{1+{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}}}{1-{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}}}=\displaystyle \frac{{{\rm{e}}}^{{\rm{j}}\Delta {\varphi }_{uv}/2}+{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}/2}}{{{\rm{e}}}^{{\rm{j}}\Delta {\varphi }_{uv}/2}-{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}/2}}.\end{eqnarray}$$ (13)

Due to –180° < Δφ_uv < + 180°, Δφ_uv/2 will be between –90° and +90°. When 0° < Δφ_uv/2 < 90°, it is indicated in Fig. 5(a) that the phase difference between the co- and cross-polarization reflection coefficient under x- and y-polarized incidences will be –90°; however, when –90° < Δφ_uv/2 < 0°, figure 5(b) indicates that the phase difference will be +90°. From the above analyses, one can well know why the phase difference between r_xy and (r_yy) is always equal to in the band 5.0 GHz–21.5 GHz. Furthermore, the relation r_yy/r_xy = r_xx/r_yx appears in Eq. (13), and it is shown that the ratio of y- to x-polarized reflected component under the y-polarized incidence is always equal to that of x- to y-polarized reflected component under the x-polarized incidence, which implies that when an anisotropic metasurface can convert a y-polarized incident wave into an RHCP/LHCP reflected one, the LTC polarization conversion under x-polarized incidence can be realized at the same time, however, the x-polarized incident wave will be converted into an LHCP/RHCP reflected one.

Figure 5.Intuitive schematic diagram of phase difference between co- and cross-polarization reflection coefficients under x- and y-polarized incidences.

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In addition, based on Eq. (12), the magnitudes of r yy, r xx and r xy, r yx can be expressed as

$$ \begin{eqnarray}\begin{array}{lll}|{r}_{yy}| & = & |{r}_{xx}|=\displaystyle \frac{1}{2}|{r}_{uu}|\left|1+{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}}\right|\\ & = & \displaystyle \frac{1}{2}|1+\cos (\Delta {\varphi }_{uv})-{\rm{j}}\sin (\Delta {\varphi }_{uv})|\\ & = & \sqrt{(1+\cos \Delta {\varphi }_{uv})/2},\\ |{r}_{xy}| & = & |{r}_{yx}|=\displaystyle \frac{1}{2}|{r}_{uu}|\left|1-{{\rm{e}}}^{-{\rm{j}}\Delta {\varphi }_{uv}}\right|\\ & = & \displaystyle \frac{1}{2}|1-\cos (\Delta {\varphi }_{uv})+{\rm{j}}\sin (\Delta {\varphi }_{uv})|\\ & = & \sqrt{(1-\cos \Delta {\varphi }_{uv})/2}.\end{array}\end{eqnarray}$$ (14)

Because +90° phase difference will always exist between the co- and cross-polarization reflection coefficients under x- and y-polarized incidences, now equation (14) implies that the magnitude of the co- and cross-polarization reflection coefficients will be equal to each other when Δφ_uv = ± 90°, so that a perfect LTC polarization conversion will be realized in the reflected wave at this time. However, the magnitude of the co- and cross-polarization reflection coefficients will not be equal to each other in common cases, thus the reflected wave will be an elliptically polarized one, whose AR can be expressed as

$$ \begin{eqnarray}{\rm{AR}}=\sqrt{(1\pm \cos \Delta {\varphi }_{uv})/(1\pm \cos \Delta {\varphi }_{uv})},\end{eqnarray}$$ (15)

where the choice of addition or subtraction symbol depends on wheteher the AR is ensured to be never less than 1.0. In addition, when Δφ_uv = ± 180°, the magnitude of r_yy and r_xx will be equal to zero, so that a cross polarization conversion will be realized. Why can a perfect LTC polarization conversion be realized when Δφ_uv = ± 90°? In fact, under x- and y-polarized incidences, in the case of neglecting the little dielectric loss, the incident wave and reflected wave both can be regarded as a composite wave composed of u- and v-polarized components with equal amplitude, the two orthogonal components in the incident wave are in phase with each other, however, in the reflected wave, the phase difference between the two orthogonal components will be changed: when Δφ_uv = ± 90°, the phase difference will be changed to ± 90°, so the perfect LTC polarization conversion will be realized.

Figure 6.Simulated results of proposed polarization conversion metasurface under u- and v-polarized normal incidences: (a) phase difference between r_uu and r_vv, (b) magnitudes and (c) phases of r_uu and r_vv, (d) axial ratio (AR) of the reflected wave.

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Through the above analysis, it is well understood why the polarization conversion metasurface can perform such a high-efficiency and ultra-wideband LTC polarization conversion, which, apart from the two first resonant modes under u - and v -polarized incidences, can be attributed mainly to the two second resonant modes. The appropriate difference between the two first resonant modes causes the phase difference Δ φ uv to be close to -90° in the band of 6.0 GHz-11.0 GHz, but the similarity, together with the small Q values, of the two second resonant modes leads to Δ φ uv to stay close to -90° in the wide subsequent band of 11.0 GHz-21.0 GHz. In this way, the anticipanted LTC polarization conversion is realized in the ultra-wide frequency band of 6.0 GHz-21.0 GHz.

4. Experimental validation

Finally, we fabricated an experimental sample and carried out an experimental validation for our design. The fabricated sample is shown in Fig. 7(a), where the inset is a zoom view of one unit cell. Firstly, its co- and cross-polarization reflection coefficients under y -polarized normal incidence have been measured, which was measured in a microwave anechoic chamber by using an Agilent E8363B network analyzer together with a pair of identical standard-gain horn antennas. The schematic illustration of the measurement setup is shown in Fig. 7(b), in which the pair of horn antennas was used to transmit and receive a y -polarized incident wave and its reflected wave, respectively, the sample was irradiated; to carry out the measurement under normal incidence, the separation angle between the orientations of the pair of antennas should ideally be close to 0°, it was set to be 6° for the finite sizes of the fabricated sample. The co- and cross-polarization reflection coefficients under y -polarized normal incidence were measured (R yy and R xy) when the receiving horn antenna was rotated 0° and 90°, respectively. Then, based on the measured R yy and R xy, the AR of the reflected wave was obtained from Eq. (1). Finally, when the transmitting antenna was set to be x -polarized, the AR of the reflected wave under x -polarized incidence was measured through the same experimental steps. In this experiment, the measured results are shown in Fig. 7(c), showing that the measured results under y -polarized incidences are in good agreement with the simulated ones in Fig. 3 . In addition, under x - and y -polarized incidences, these measured results are basically the same, which agree well with the theoretical predications.

Figure 7.(a) Photographs of experimental sample, (b) schematic diagram of measurement setup, and (c) measured results: axial ratio (AR) of reflected wave under x- and y-polarized incidences.

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5. Conclusions

In this paper, an LTC polarization conversion metasurface is proposed, which can realize high-efficiency and ultra-wideband LTC polarization conversion in the frequency band from 5.87 GHz to 21.13 GHz with a relative bandwidth of 113% under x - and y -polarized incidences, the effective LTC polarization conversion performance is verified through simulations and experiment. In addition, to obtain an insight into the root cause of the LTC polarization conversion, a detailed theoretical analysis is presented, it is indicated that the proposed metasurface can perform an ultra-wideband and high-efficiency LTC polarization conversion, apart from its two first resonant modes under u - and v -polarized incidences, it can be attributed mainly to the two second resonant modes, these resonant modes cause Δ φ uv to stay close to -90° in an ultra-wide frequency band of 6.0 GHz-21.0 GHz, thus the anticipated LTC polarization conversion is realized in the ultra-wide frequency band. Compared with the previous designs, the proposed LTC polarization conversion metasurface has not only ultra-wide bandwidth but also much high efficiency, so it is of great application values for realizing polarization controlled devices, stealth surfaces, antennas, etc.