1. Introduction

Metamaterials have been widely engineered in optical elements, such as polarizers [1], optical diodes [2], absorbers [3, 4], beam splitter [5, 6], lenses [7], wave plates [8, 9], and beam steering device [10]. Extensive researches have demonstrated that the precise arrangement of the elements enables metamaterials to exhibit desired optical properties, including polarization conversion [11, 12], amplitude and phase modulation [13–15], propagation directions adjustment [16, 17]. However, in the microwave regime most of the previous metamaterials are based on the planar structure that is manufactured by periodically arranging metal arrays in flat rigid substrates and concentrate on a single characteristic or functionality. Very few researches are carried out on the electromagnetic properties of curved metamaterial [18, 19].

So far, we have studied the metamaterials with one dimensional curved surface, which reveals that these kinds of metamaterial exhibit a very pronounced anisotropy in reflection and can integrate the bifunction of dual-band absorption and broad band polarization conversion in microwave [20]. Moreover, in recent years, the multifunction metamaterial that has the combined optical characteristics has attracted many researcher’s attention. S. Chen et al have demonstrated multifunctional metasurface of polarization conversion and perfect absorption [21]. Y. Tamayama et al have realized a half-mirror and a quarter-wave plate based on a single-layer metamaterial [22]. Y. Zhao and S. Liu have proposed multifunctional metamaterials with tunable function by coding technique [23, 24]. Substantial studies reveal that integrating various functions increases miniaturization and versatility, which provide a more promising practical application of metamaterials [25, 26].

In this paper, we design and fabricate a zigzag metamaterial (ZMM) and a planar metamaterial (PMM) with the same strip-shaped unit cell. The ZMM, with ultra-broadband, high tunability and wide incident angle, can adjust the power ratio of reflection to transmission when the incident wave is linearly polarized, which is different from PMM. At the same time, in the case of circularly polarized incidence, the ZMM achieve circular-to-linear polarization transformation with half reflection and transmission.

2 Structure design, simulation results and discussions

An anisotropic metamaterial, from which two bands of orthogonal polarized wave are totally reflected and transmitted respectively, will have the potential to act not only as the optical splitter for the linearly polarized wave, but also as a circular-to-linear polarizer for circularly polarized waves. One of the simplest ways to construct an anisotropic metamaterial is to periodically assign the metal strips on the dielectric substrate to constitute an asymmetric structure in the x and y directions. We have simulated the PMM with the strip-shaped units that is very similar to the wire grating in configuration. The results turn out that although the reflected (transmitted) strength of the transversal electric wave and transversal magnetic wave are different, the gap is far from satisfactory in size and bandwidth (shown later in this part). Therefore, we bend the substrate to be serrated to enhance the anisotropy of the metamaterial, and deposit metal strip arrays on both sides. Figure 1 exhibit the schematic diagrams of the proposed models and the unit. The metal is copper with the thickness of $0.03$mm and conductivity of $5.96\times {10}^{7}S\cdot m^{-1}$. The substrate is FR-4 circuit board with the thickness of $1.2mm$ and dielectric constant of$4(1+0.025i)$. The other optimized dimension parameters are as follows:^{$a=12mm$, $b=15mm$, $h=14mm$, $w=4mm$ $\alpha ={60}^{\circ }$.}

 

Fig. 1 (a) and (b) Schematics of the PMM and ZMM. (c) Perspective of the unit cell of the ZMM, which consists of two unit cells of the PMM.

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We use the commercial software of CST Microwave Studio to perform the full-wave simulation. The reflection and transmission properties of the PMM under normal incidence are studied first and shown in Fig. 2. Although from about 6.4 GHz to 13 GHz, the TE wave is mainly reflected and TM wave is largely transmitted. However the reflectance of TM wave reaches more than 0.4, which can’t be ignored in reflection. The transmittance of TM wave is just above 0.8, indicating the transmission is not very high. Therefore, the PMM can’t separate the TE and TM wave efficiently.

 

Fig. 2 The simulated reflection and transmission coefficients of the PMM for normal incidence.

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Figure 3 represents the reflected and transmitted coefficients of the ZMM when $\theta \text{=}{0}^{\circ }$. In the broad bands from 5.26 to 14.46 GHz, $r_{yy}>0.9$ and $r_{xx}<0.3$, which implies that the TE wave is fully reflected while the TM wave is poorly reflected. On the contrary, the transmission is weak for TE and strong for TM wave from 5.16 to 14.51 GHz ($t_{yy}<0.3$ and $t_{xx}>0.9$). The ratio of cross-polarization conversion can be neglected because of the rotational symmetric structure of the ZMM. According to the formulas of $A=1-{\left|r_{xx}\right|}^2-{\left|t_{xx}\right|}^2$ and $A=1-{\left|r_{yy}\right|}^2-{\left|t_{yy}\right|}^2$, the losses of TE and TM waves are both less than 0.1 in the range of 5.33 - 13.68 GHz and could be ignored. Profiles of the spectra imply that the ZMM behaves as a metal mirror to transverse electric wave and a dielectric slab to transverse magnetic wave.

 

Fig. 3 The simulated reflection and transmission coefficients of the ZMM when $\theta \text{=}{0}^{\circ }$.

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That is to say TE wave can be almost completely reflected while the TM wave can be nearly totally transmitted through the ZMM, the electromagnetic property of which is very similar to the wire grating in ultra-broad band

The reflected and transmitted spectra indicate that the electromagnetic wave can be fully reflected or transmitted through the ZMM selectively in broadband, depending on its polarization direction. For the incident wave with an arbitrary polarization angle of $\phi$ (the angle between the electric vector and the x axis), the reflectance (transmittance) can be decomposed into x and y components with the normalized amplitude of $r_{xx}\cos \phi$ and $r_{yy}\sin \phi$ ($t_{xx}\cos \phi$ and $t_{yy}\sin \phi$) respectively. Accordingly, the reflection (transmission) energy can be expressed by $I_r=r_{xx}^2{\cos }^2\phi +r_{yy}^2{\sin }^2\phi$ ($I_t=t_{xx}^2{\cos }^2\phi +t_{yy}^2{\sin }^2\phi$). When the reflectance and transmittance remain constant, the magnitude of the reflected and transmitted energy is only related to the polarization angle, and the different value of $\phi$ correspond to different energy allocations between the reflection and transmission. Figure 4(a) and (b) display the energy spectra of the reflection and transmission (denoted by $I_r$ and $I_t$) at various polarization angles. As $\phi$ grows, $I_r$ increases and $I_t$ decreases. This is because the component along the y direction gradually takes up a growing proportion and $r_{yy}$ is much larger than $r_{xx}$. These two factors lead to enhanced reflection and reduced transmission. Moreover, the magnitudes of $I_r$ and $I_t$ remain unchanged across a wide frequency range at every definite polarization angle of incidence, consequently the energy ratio of the reflection to the transmission is also fixed and just relates to the value of $\phi$ in working frequency band. The relationship among the energy ratio of the reflection and transmission, the frequency and the polarization are illustrated in Fig. 4(c). The color scale is actually logarithmic scale. Overall, the value of $I_r/I_t$ increases gradually as $\phi$ rises. However, for each value of $\phi$ from about ${20}^{\circ }$ to ${80}^{\circ }$, the energy ratio nearly keeps constant from 5.24 to 14.52 GHz, which suggest that the intensity of reflected or transmitted wave can be tuned conveniently by turning the polarization of incidence or adjusting the position of the ZMM.In the case of circularly polarized incident wave, which can be decomposed into TE and TM waves with the same amplitude and phase difference of ${90}^{\circ }$, the reflected TE wave constitutes the main component of the reflection, and the transmitted TM wave is the major part in the transmission. In order to specifically describe the polarization state of reflected (transmitted) wave, we introduce the azimuth angle $\eta$ and ellipticity $\chi$, which together can embody the characteristics of the polarization ellipse [20,27]. $\eta =\frac{1}{2}{\tan }^{-1}\left(\frac{2\tau \cos \Delta {\psi }_{yx}}{1-{\tau }^2}\right)$, $\chi =\frac{1}{2}si{n}^{-1}\left(\frac{2\tau \sin \Delta {\psi }_{yx}}{1+{\tau }^2}\right)$, in which $\tau =r_{yy}/r_{xx}$, (or $\tau =t_{yy}/t_{xx}$), $\Delta {\psi }_{yx}$ is the phase difference between the x and y components of the reflection (transmission). Figure 5 present the azimuth angles and ellipticities of the polarization ellipse for the reflected (transmitted) waves under the situation of the left-handed circularly polarized (LCP) or right-handed circularly polarized (RCP) incidence, the inset is the polarization states. Due to the small absolute value of $\chi$, less than $9^{\circ }$, each ellipse is extremely flat and could be approximated as a line along the major axis close to the y-axis (x-axis) for reflection (transmission) from 5.24 to 14.52 GHz. Accordingly, the reflected (transmitted) wave is considered as the y-axis polarized wave, and the chirality of the incident wave only generates perturbation on the polarization direction. These features of the ZMM make it possible to simultaneously act as a half-mirror and a circular-to-linear polarization converter.

 

Fig. 4 (a) and (b) The energy spectra of reflection and transmission. (c) The energy ratio of reflection to the transmission.

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Fig. 5 The azimuth angle, ellipticity and polarization states of the reflected and transmitted wave under circularly polarized incidence.

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In many cases, the operating wave contains a wide range of incident angle. In order to further demonstrate the performance of the proposed ZMM, we display the reflected and transmitted coefficients under oblique incidence in Fig. 6(a) and (b). The band with the frequency selectivity turns narrower and redshifts as the incident angle increases. However, on a whole, the shapes of the lines keep essentially unchanged when $\theta$ is limited to within ${60}^{\circ }$ and the frequency is less than 8 GHz, which indicates that the properties of the ZMM remain stable at a wide incident angle. All the results suggest a great convenience in the practical application of the ZMM, either as a power divider or as a circular-to-linear polarization converter.

 

Fig. 6 The reflected and transmitted coefficients of the ZMM under oblique incidence.

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3 Experimental results

Figure 7 shows the photographs of the samples of the PMM and ZMM. The printed circuit board process is employed to fabricate the PMM. Then we incise another PMM sample into narrow strips, fix them on a jagged plastic base and glue the adjacent strips together to make the ZMM. Both the PMM and ZMM samples consist of $24\times 15$ unit cells. Two standard gain broadband linearly polarized antennas are connected to a vector network analyzer (Agilent E8362B) to produce and detect the electromagnetic wave in the experiments. The measured reflection and transmission coefficients of the PMM are presented in Fig. 8, which are basically coincide with the simulations (seeing in Fig. 2). The test results of the ZMM are illustrated in Fig. 9, which are qualitatively in good agreement with the simulated results (shown in Fig. 3).The discrepancy between the simulated and experimental results is mainly owing to the following two reasons: First, we manually cut the printed circuit boards into strips and made them into the ZMM. Therefore, the shape of the experimental samples was not as regular as the simulation models. In the second point, we set a periodic boundary condition during simulation, indicating that the size of the model is infinite. However, the actual sizes of the PMM and ZMM are approximately $28.80cm\times 22.50cm$ and $33.78cm\times 22.5cm$, so the edge diffraction can’t be ignored and will also result in discrepancy.

 

Fig. 7 (a) Part of the scan image of the PMM. (b) and (c) The photographs of the ZMM and its local enlarged drawing.

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Fig. 8 The measured reflection and transmission coefficients of the PMM.

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Fig. 9 The measured reflection and transmission coefficients of the ZMM when $\theta \text{=}{0}^{\circ }$.

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4. Conclusion

In conclusion, we have proposed and studied the electromagnetic properties of a ZMM. Numerical simulated and experimental results exhibit that the ZMM with TE-metal-like and TM-dielectric-like property has the advantage of high efficiency and broad bandwidth compared to the traditional PMM, which allow the ZMM to achieve multiple functions depending on the polarization state of the incident wave. It is able to manipulate the power ratio of reflection to transmission flexibly from 5.24 to 14.52 GHz, equivalent to 93.93% relative bandwidth by adjusting the polarization angle of the incident wave. In the case of the circularly-polarized incidence, it almost transforms the wave into linearly polarized wave, with half of the energy reflected and half transmitted. Besides worked as a power splitter, half mirror and polarization converter, the ZMM also has positive significance to develop the metamaterials in the direction of integration and versatility.