Achieving circular-to-linear polarization conversion and beam deflection simultaneously using anisotropic coding metasurfaces

An anisotropic coding metasurface (CM) is proposed for achieving circular-to-linear polarization conversion and beam deflection. Different phase coding consequences were independently achieved for two orthogonal linear polarized (LP) waves. Thus by elaborately designing coding sequences of the metasurfaces, different functions can be achieved, respectively for waves polarized along two orthogonal directions. More importantly, for circularly polarized (CP) wave, anisotropic CM can achieve circular-to-linear polarization conversion and beam deflection simultaneously. As a proof, a 1-bit anisotropic CM with 0101…/0101… and 0000…/1111… coding sequences respectively for two orthogonal LP waves was designed. The simulation results indicated that the incident CP wave is deflected into two x-polarized waves in x-o-z plane and two y-polarized waves in y-o-z plane. Both the simulation and experimental results verify the circular-to-linear polarization conversion performance of the anisotropic coding metasurfaces. The proposed anisotropic coding metasurfaces have the potential for the applications of multifunctional devices.


Results
Operating principle and theoretical analysis. In order to clarify multifunctionality of anisotropic CMs and their ability to transform CP waves into LP waves, we expound the principle by a simple 1-bit anisotropic CM. For the 1-bit anisotropic CM, coding sequences are composed of four basic encodings [0/0, 0/1, 1/0, 1/1]. The digit code before '/' represents the phase state of the unit cell under x-polarization, while the digit code after '/' represents the phase state of the unit cell under y-polarization. For a CM which is encoded with coding sequence [0,1;0,1], the incident x-polarization wave is reflected into two equal waves along x direction ( Fig. 1(a)). Similarly, if the CM is encoded with coding sequence [0,0;1,1], the incident y-polarization wave is reflected into two equal waves along y direction ( Fig. 1(b)). As it is known to all, a CP wave can be decomposed into two orthogonal LP waves with same amplitude and phase difference is 90°. Therefore, when anisotropic CM is illuminated by CP wave, the CP wave is transformed into LP wave and achieving beam deflection simultaneously, as shown in Fig. 1(c).
To mathematically describe the anisotropic CM, a tensor R mn is used to express the reflection coefficient of a unit cell indicated below: where R mn x and R mn y denote reflection coefficients under x-and y-polarizations, respectively. For isotropic unit cells, R mn x = R mn y ; for anisotropic unit cells, the two reflection coefficients are different.  www.nature.com/scientificreports www.nature.com/scientificreports/ The anomalous reflection angle (θ, ϕ) can be obtained from theory of beam superposition of array antenna 22 , and the formulas is as follows: x y x y x y 1 1  The 'split ring' pattern is used as anisotropic unit cell (Fig. 2). The top is metal 'split ring' , and then dielectric substrates (ε r = 2.65, tan δ = 0.001), the below is metal backboard. The other geometrical parameters are r = 2.3 mm, w r = 0.1 mm, s = 2 mm, l = 1.48 mm, w l = 0.2 mm. The reflected phases and amplitudes of the 'split ring' pattern under incident x-polarized and y-polarized wave are shown in Fig. 2(c). The phase difference between the two is about 180°, and the reflective amplitudes are more than 98%. Therefore, it is treated as '1' and '0' numeric state under x-and y-polarizations respectively.
The 'Crusades' pattern is used as isotropic unit cell (Fig. 3). The top is metal 'Crusades' , the other two layers are the same as the anisotropic unit cell. By optimizing design, the 'Crusades'-shaped metallic pattern with b = 0.5 mm and b = 2.16 mm are treated as '1' and '0' numeric state respectively and the corresponding reflection phases and amplitudes are shown in Fig. 3(c). The four basic structures of 1-bit anisotropic CM are shown in the Fig. 4.
In this paper, two different coding sequences are presented to demonstrate the special ability of anisotropic metasurface. The first coding sequence is composed of a periodic coding matrix C 1 : The completed view of the anisotropic CM with matrix C 1 is show in Fig. 5(a). The three-dimensional (3D) and two-dimensional (2D) far-field scattering patterns of anisotropic CM with matrix C 1 under incident x-polarized  Fig. 6(a,d) respectively. The simulated results show that the incident x-polarized wave is reflected into two symmetrical waves in ϕ = 0° cutting plane, and θ = 31.5°. The theoretical deviation angle is calculated as 31°, which is consistent with the numerical simulation. For the y-polarization, the incident wave is reflected into two symmetrical waves in ϕ = 90° plane, and the deviation angle θ = 31.5°, as shown in Fig. 6(b,e). So far we have proved the anisotropic properties of the designed CM. For the left-handed circularly polarized (LCP) incident wave, the wave is deflected to four symmetrical waves (ϕ = 0°, 90°, 180°, 270°, θ = 31°), as shown in Fig. 6(c,f). The simulated results indicates that the reflection characteristics of the anisotropic CM under CP wave incidence simultaneously possesses the both reflection characteristics under two orthogonal LP waves. To further verify the polarization characteristics of reflected beam, the axial ratio are analyzed. As shown in Fig. (7), two cutting planes ϕ = 0°, 90° are selected, and the axial ratio of the reflected waves (θ = ±31°) exceed 18 dB. Therefore the CP incident wave is converted to LP wave as expected.
The results of these simulations are consistent with the theoretic analysis, it indicates that anisotropic CMs can convert the CP wave into LP wave and achieve beam deflection simultaneously.  To validate the performance of the designed anisotropic CMs, one sample (as shown in Fig. 10(a)) is fabricated, which corresponds to the coding matrix C 1 . The measurement was carried out in a microwave anechoic chamber, and the sketch maps of the test setup is given in Fig. 10(b). The measured 2D far-field scattering patterns of the anisotropic CM with matrix C 1 at 14 GHz are show in Fig. 10. The results show that the measured deviation angle is accordance with the simulated result roughly, which demonstrates that anisotropic CMs can convert CP incident wave into LP wave and achieve beam deflection simultaneously.

conclusions
In conclusion, we have proposed an anisotropic CM, which can achieve circular-to-linear polarization conversion and beam deflection simultaneously. Due to the characteristic of anisotropic, the coding sequences depend on the EM wave's states of polarization, and the manipulation of EM waves becomes more flexible. In other word, the same metasurfaces can achieve different functions under the different polarized incident waves. Moreover, by analyzing the axial ratio of reflected EM waves, it is found that the anisotropic CMs can convert CP wave into LP wave. Both the simulated and measured results indicate that anisotropic CM can achieve circular-to-linear polarization conversion and beam deflection simultaneously. The proposed anisotropic CMs have the potential for the applications of multifunctional devices. Measurements. The measurement was made in a microwavechamber. A CP horn antenna served as transmitter, and maintained 2 m distance from the sample. Both the sample and the CP horn were bolted to the revolving stage, which could rotate 360°. In addition, a LP horn antenna was used as the receiving antenna to receive the scattering fields.