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We propose a metasurface which consists of three conductive layers separated by two dielectric layers. Each conductive layer consists of a square array of square loop apertures, however, a pair of corners of each square metal patch surrounded by the square loop apertures have been truncated, so it becomes an orthotropic structure with a pair of mutually perpendicular symmetric axes u and v. The simulated results show that the metasurface can be used as a wideband transmission-type polarization converter to realize linear-to-circular polarization conversion in the frequency range from 12.21 GHz to 18.39 GHz, which is corresponding to a 40.4% fractional bandwidth. Moreover, its transmission coefficients at x- and y-polarized incidences are completely equal. We have analyzed the cause of the polarization conversion, and derived several formulas which can be used to calculate the magnitudes of cross- and co-polarization transmission coefficients at y-polarized incidence, together with the phase difference between them, based on the two independent transmission coefficients at u- and v-polarized incidences. Finally, one experiment was carried out, and the experiment and simulated results are in good agreement with each other.
Polarization is an important characteristic of an electromagnetic (EM) wave and it must be taken into consideration in the practical application of the EM wave. In various wireless systems, such as mobile communications, radar tracking, satellite communications, and navigation systems, circularly polarized (CP) waves are preferred due to the advantages such as simplifying alignment and overcoming Faraday rotation.[1] To generate a desired CP wave, in addition to the way to generate it directly by using CP antennas, an alternative effective way is to generate a linearly polarized (LP) wave and pass it through an LP-to-CP polarization converter. This way is particularly attractive in situations where the radiating system is a planar antenna array and generating CP waves at each element is not convenient. Moreover, one already designed LP antenna can be modified as a CP one by using a proper LP-to-CP polarization converter.
The polarization converter is a kind of polarization control device, which can convert an incident wave with a given polarization to a reflected or transmitted wave with a different polarization, it can be realized in different ways. Conventional polarization converters were usually designed by using the birefringence effect and optical activity of natural materials, which often suffer from bulky volumes, high losses, and narrow bandwidths in practical applications.[2,3] Over the past decade, it has been found that metamaterials (MMs) can provide a convenient way to control the polarization state of an EM wave. Based on various MMs, many different polarization converters have been proposed.[4–48] They were usually realized in one of the following two ways: one is to divide a wave into two orthogonal components and generate a phase difference between them (the fundamental of birefringence effect) by using anisotropic MMs, and the other one is to mimic the molecule chirality (the fundamental of optical activity) by using chiral MMs. The existing literatures indicate that the two methods can both be used to design various polarization converters, we can choose a proper design method according to the different work patterns of various polarization converters. Anisotropic two-dimensional MMs (also called metasurfaces) are more suitable for the design of reflective polarization converters, especially by using multiple plasmon resonances, high-efficiency and ultra-wideband polarization converters can be achieved in this way.[4–15] For example, in Ref. [5], the authors presented a reflective polarization converter based on a double-V-shaped anisotropic metasurface, which can realize an ultra-wide band LP conversion due to four plasmon resonances, and another ultra-wideband polarization converter was proposed in Ref. [14], which is composed of three resonators. The chiral MM is convenient for designing transmissive polarization converters, and now most transmissive polarization converters are proposed based on various planar[16–42] or 3D[43–48] chiral MMs, which can realize linear[16–29] or circular[30–48] polarization conversion. In addition, due to the asymmetry of these chiral MM structures, in most cases, the asymmetric transmission effects, which means that the transmission coefficients are different for the incident waves with different polarizations (x/y- or RHCP/LHCP-polarizations), can also be observed at the same time.[16–29,32–48] The asymmetric transmission effect can be used for polarization selection, it is very useful, however it should be avoided sometimes.
In this work, we propose an anisotropic metasurface, which is an orthotropic structure with a pair of mutually perpendicular symmetric axes u and v along
The unit cell of the proposed metasurface consists of three conductive layers separated by two dielectric layers, as shown in Fig.
![]() | Fig. 1. (color online) Unit cell of the proposed metasurface: (a) 3D view, (b) the top and bottom conductive layers, and (c) the middle conductive layer. |
Owing to the orthotropy of the metasurface structure, when a common plane wave is incident on it, the transmitted wave would consist of both x- and y-polarized components, we invoke the transmission matrix
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![](cpb_27_5_054204/cpb_27_5_054204_ieqn4.gif)
To numerically analyze the polarization conversion performance of our design, we suppose that the metasurface is located in the x–y plane, and a y-polarized wave with the magnitude of one unit
If the incident wave is assumed as a y-polarized one
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![](cpb_27_5_054204/cpb_27_5_054204_ieqn13.gif)
![](cpb_27_5_054204/cpb_27_5_054204_ieqn14.gif)
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Based on the simulated results in Fig.
![]() | Fig. 3. (color online) Y-to-CP transmission coefficients of the proposed metasurface at normal y-polarized incidence. |
In fact, the transmitted wave is an elliptically polarized wave, we have calculated its axial ratio (AR) by using the following formula:
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![](cpb_27_5_054204/cpb_27_5_054204_ieqn15.gif)
![](cpb_27_5_054204/cpb_27_5_054204_ieqn16.gif)
![]() | Fig. 4. (color online) The total transmittance ![]() |
The above-mentioned results are all obtained at the y-polarized incidence. In fact, as the simulated results using Ansoft HFSS, we have obtained the transmission coefficients at x-polarized incidence at the same time. It is shown that the metasurface does not have an asymmetric transmission effect, its reflection and transmission coefficients at the x- and y-polarized incidences are completely equal. It is just because the metasurface is a symmetric structure with a pair of mutually perpendicular symmetric axes u and v along
In order to gain physical insight into the cause of the polarization conversion in the proposed metasurface, we present a detailed analysis.
The metasurface is symmetric with respect to both u and v axes, so no cross-polarized components will exist at u- and v-polarized incidences, and the two transmission coefficients can be expressed as tu and tv. The above-assumed y-polarized incident wave can be considered as a composite wave consisting of both u- and v-polarized components, moreover, the magnitudes of the two polarized components are exactly equal, thus the incident and transmitted waves can be respectively expressed as
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Due to the orthotropy of the metasurface structure, tu and tv are mutually independent. In order to facilitate the derivation of the formula, we define the magnitude ratio between tu and
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![](cpb_27_5_054204/cpb_27_5_054204_ieqn26.gif)
In the x–y coordinate system, by using the relationships
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![](cpb_27_5_054204/cpb_27_5_054204_ieqn29.gif)
![](cpb_27_5_054204/cpb_27_5_054204_ieqn30.gif)
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![](cpb_27_5_054204/cpb_27_5_054204_ieqn31.gif)
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Formulas (
To validate the polarization conversion performance of the proposed metasurface by using formula (
Moreover, to validate formulas (
![]() | Fig. 6. (color online) The comparison between the calculated and simulated results at y-polarized incidences: (a) the magnitudes of tyy and txy; (b) the phase difference ![]() |
From the above analysis, we can conclude that the orthotropy of the metasurface structure has resulted in two independent transmission coefficients tu and tv; according to the two independent transmission coefficients tu and tv, the total transmission properties of the metasurface can be determined completely; however, to determine the polarization state of the transmitted wave, only the difference between tu and tv (the magnitude ratio b and phase difference
Finally, to realize an experimental validation for our design, one prototype of the proposed metasurface was fabricated by using the standard PCB lithography and substrate bonding technique, which consists of 42×42 unit cells with an area of 252 mm×252 mm, as shown in Fig.
This work presents an anisotropic metasurface, which is symmetric with respect to the u and v axes. Numerical simulated results show that the metasurface can realize wideband LP-to-CP polarization conversion; moreover, its transmission coefficients at x- and y-polarized incidences are completely equal. Furthermore, we analyze the cause of the polarization conversion, and conclude that the metasurface has two independent transmission coefficients tu and tv, which results from the orthotropy of the metasurface structure; according to the two independent transmission coefficients tu and tv, the total transmission properties of the metasurface can completely be determined. Finally, we have carried out an experiment in which the polarization conversion performance of the proposed metasurface, together with some effective conclusions, has been confirmed effectively. Compared with the previous designs, the proposed metasurface, as a novel LP-to-CP polarization converter, has wider bandwidth. At the same time, it has no asymmetric transmission effect, so it is of great application value in polarization control devices, stealth surfaces, antennas, etc.
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