A Broadband Transmission Metasurface with Polarization-Transforming Functionality

A transmission metasurface with polarizationtransforming functionalities is presented. The unit cell is characterized by broad band, low profile and low loss. Due to the asymmetric structure, the proposed metasurface shows different responses to different linear-polarized incidences. For a particular linear-polarized incidence, the polarization direction of transmitted waves will be rotated by 90° in 3.72–8.28 GHz with high polarization conversion ratio (PCR). However, for the orthogonal-polarized ones, the incidence will be reflected totally and the polarization remains. The operating mechanism of the proposed metasurface is analyzed both by theoretical investigations and numerical simulations. Measured results of the fabricated samples are in good agreement with the simulated ones.


Introduction
In recent years, the constantly updating communication technology has wonderfully advanced the living standards of human beings, and the upcoming 5G mobile communication era will be fascinating because of its high information transmission rate.Compared to 4G communication network, 5G communication system not only is far ahead of the rate, but also significantly improves user density and user capacity based on the polarization isolation characteristics of electromagnetic waves.Polarization, as an important feature of electromagnetic waves, not only has important applications prospects in the field of modern communications, but also in radar, detection, and imaging [1].Meanwhile, the polarization control is completely required in microwave regime, as well as in terahertz, infrared, and visible frequencies [2].Therefore, the research of how to manipulate the polarization of electromagnetic wave is in great demands.
The manipulation of the electromagnetic wave by the metamaterials normally aims at the control of its amplitude [3][4][5][6], phase [7][8][9][10][11] and polarization [12][13][14][15][16][17][18][19][20][21][22].According to the propagation direction of electromagnetic waves, polarization-manipulating metamaterials consist of reflective and transmitting types.Currently, lots of polarization rotating reflective metamaterial are reported.By using multi-layer cascading [12], metallized via [13], multiple plasmon resonances [14] and other anisotropic structures, many reflective polarization convertors with broadband and high polarization conversion ratio performance have been successfully presented.The conventional applications of the reflective polarization-manipulating metamaterials include: acting as reflective surface to achieve polarization transformation [15] or implement a reflectarray antenna [16], constituting a reflective screen to reduce radar cross section (RCS) [17].For transmitting ones, it is usually employed as filters for waveguide transmission systems [18], as polarization convertors for antennas [19] and as antennas' transmitarrays to achieving beam focusing, beam steering and beam shaping [20].However, the precondition for the application is that these polarization-manipulating metamaterials exhibit low loss, high polarization conversion efficiency and low fabrication cost.But, how to take all these factors into consideration still remains a big challenge for the researches of polarization convertors.
In this paper, a kind of polarization-dependent transmission metasurface is proposed.In the frequency range of 3.72-8.28GHz, the polarization direction of the transmitted wave will be rotated by 90° when a particular linearpolarized wave irradiates the metasurface.The proposed polarization-transforming metasurface is characterized by broadband, high efficiency, low loss and low profile.Because of these noticeable performances, the proposed metasurface has potential applications in waveguide transmission systems and transmitarray antenna domain.

Structure Design
The unit cell structure of the polarization-transforming transmission metasurface is shown in Fig. 1(a).The tri- During the designing process of the proposed unit cell, Ansoft HFSS 14.0 is used for full-wave simulation.Floquet port and periodic boundary are adopted for a unit cell to simulate an infinite periodic array.
It is worth noting that the proposed metasurface is characterized by polarization-dependent functionalities.When a y-polarized electromagnetic wave irradiates from the region 1, the y-polarized incidence can be transformed into the x-polarized transmitted wave.And if the polarization direction of the incident wave is parallel to the x-axis, the x-polarized incidence will be reflected totally, and polarization direction of the reflected wave is also parallel to x-axis.However, when the electromagnetic waves irradiate from region 2, the electromagnetic response will be the opposite case.

Simulation and Analysis
For the sake of analysis, we define r mn xy as reflection coefficient, and t mn xy as transmission coefficient.Here x and y represent the electric field directions of the electromagnetic wave, and m and n denote the different regions.For example, t 21 xy represents the x-polarized field transmit-ted into region 2 when the y-polarized plane wave is incident from region 1.
The simulation results are shown in Fig. 2. When the y-polarized field is incident from region 1, the results are shown in Fig. 2(a).The curves manifest that, in the frequency range of 3.72-8.28GHz, t 21 xy is greater than -0.5 dB and t 21 yy is below -35 dB, which indicates that the polarization direction of transmitted wave is parallel to the x-axis; Meanwhile, it is also observed that r 11 yy is less than -10 dB, and r 11 yy is less than -35 dB, which demonstrates that the reflected wave is mainly y-polarized.Figure 2(b) shows the simulation results of the S parameters when the incidence is x-polarized.It can be seen that r 11 xx is approximately 0 dB.At the same time, both r 11 yx and t 21 xx are lower than -35 dB and t 21 yx is less than -70 dB.These numerical simulations manifest that the x-polarized incident waves will be totally reflected when incident from region 1.To explain the operating mechanism of the metasurface, we rotate the xy-coordinate system by 45° and thus the uv-coordinate system is obtained, as shown in Fig. 3.
When the y-polarized incidence propagates along the z-axis, the electric field can be expressed as E i = E i exp(jkz) y.The electric field of the incident wave can be decomposed into two components along u axis and v axis as: Then the electric field of the reflective and transmitted wave can be presented as ( 2) and (3), respectively.
As seen from Fig. 4(b), we can derive that: .
By inserting ( 4) and ( 5) to ( 2) and ( 3), we can get the reflected field E r = r 11 yy E i exp(-jkz) y and the transmitted field E t = t 21 xy E i exp(jkz) x.In this case, the reflected field remains y-polarized and the transmitted field is twisted to be x-polarized.This conclusion coincides well with the simulation results of y-polarized incidence, as shown in Fig. 2(a).
Similarly, when the polarization direction of incident wave is parallel to x-axis, the reflected field will be E r = r 11 xx E i exp(-jkz) x, and the transmitted field is E t = r 21 yx E i exp(jkz) y.Therefore, the x-polarized reflected wave and the y-polarized transmitted field are obtained theoretically.Remarkably, in this occasion, the x-polarized incident waves will be reflected totally, just as demonstrated in Fig. 2(b).
Figure 5 exhibits the current distribution of the RDSRR at four peak transmission coefficient frequencies.As the charts show, the RDSRR resembles a pair of symmetrical vibrators.At 3.86 GHz, the RDSRR operates like a pair of half-wave oscillator.At 8.04 GHz, the RDSRR works corresponding to a pair of full-wave oscillator.Besides, at 4.85 GHz and 6.60 GHz, its operating states are between the half-wave and full-wave oscillators.According to the working principle of the symmetrical oscillator, its operation wavelength depends on the arm length of the oscillator.Similarly, the operation wavelength of the proposed metasurface is closely related to the size of the RDSRR.So, based on the same principle, we can obtain the relationship between the unit's operation wavelength λ and the arm length L (L is the sum of long side and short side of the RDSRR).The analytical expression can be depicted as 0.5  L  .By calculating, L  l1 + w -w1 -(w1 + w2)/2  22.7 mm.Assume the relative permittivity of the dielectric is denoted by  r , the operating frequency range can be calculated approximately: The relative permittivity of the dielectric is 2.65.So, a (4-8) GHz operating frequency range can be obtained according to (6).This result coincides well with the simulation results.To verify functions of the MGs, we also compare the polarization conversion ratio (PCR) and the reflection ratio (RR) of the metasurface with and without the orthogonal MGs.As shown in Fig. 6, the PCR of the metasurface with MGs is greater than 0.9 in the frequency range of 3.72-8.28GHz.But the PCR of the metasurface without MGs is lower than 0.22.Besides, in the same frequency range, the RR of the metasurface with MGs is no more than 0.1, while the RR of the metasurface without MGs will be higher than 0.4.Consequently, it is concluded that the MGs can raise PCR and reduce RR significantly.

Fabrication and Measurement
A 400-cell (20 × 20) metasurface prototype is fabricated and measured.The prototype and measurement setup are illustrated in Fig. 7.During the measurement, two broadband horn antennas are utilized as the emitter and the receiver, respectively.When measuring the reflection coefficient, two horn antennas are on the same side of the sample.When measuring the transmission coefficient, two horn antennas are located on either sides of the prototype.When the y-polarized electromagnetic wave is incident from the region 1, the transmission coefficient measurement results are shown in Fig. 8(a).It is observed that the measured curves of the cross-polarization transmission coefficient t 21 xy coincide well with the simulation ones in the observed frequency range.However, the measurement result has a slight error around 4 GHz.The key reason for this consequence is that the size of the sample is finite, which is not consistent with the infinite boundary.In addition, the co-polarization reflection coefficient measurement curve is also consistent with the simulation ones.But the measurement curve is lower than the simulation results around 6 GHz.By analyzing, the machining error is the main points for this consequence.This inevitable factor also results in the deviation between the measurement and the simulation results of the co-polarization reflection coefficient around 6 GHz when the incidence is x-polarized, as shown in Fig. 8(b).In summary, the measurement results confirm the effectiveness of the design.

Conclusion
In this paper, a polarization-dependent transmission metasurface covering the C band is presented.The proposed metasurface is characterized by low profile, broadband and high polarization conversion ratio.Numerical simulations demonstrate that, when a particular linear-polarized incidence irradiates the proposed metasurface, the polarization direction of the transmitted wave will be rotated by 90° in the frequency range of 3.72-8.28GHz.Based on the superposition principle of space wave vector, we have explained the reason of polarization-converting function.At the same time, by analyzing the current distribution of the RDSRR, we have investigated the operation frequency range of the metasurface in detail.Finally, a metasurface prototype is fabricated and measured, and the measurement results are in good agreement with the simulation ones.

Fig. 1 .
Fig. 1.Illustration of the presented unit cell:(a) Schematic of the simulation; (b) the RDSRR; (c) the stripe MG with surface slots parallel to x-axis.layers unit cell consists of a rectangle diagonal-split-ring resonator (RDSRR) structure and two orthogonal stripe metal grids (MG).The RDSRR, as shown in Fig. 1(b), is clamped by two substrates, and it is employed by achieving polarization conversion.Two orthogonal MGs, as shown in Fig. 1(c), are etched on the surface of the upper and lower substrate, and are designed to constitute a Fabry-Pérot-like cavity for more efficient polarization conversion [21].The optimized parameters are as follows: l1 = 16 mm, l2 = 12 mm, w = 12.4 mm, w1 = 3.2 mm, w2 = 1.8 mm, S1 = 2 mm, S2 = 1.1 mm, g = 5.9 mm, P = 18 mm.The relative permittivity of the adopted dielectric is 2.65.The total thickness of the unit cell is 5 mm, approximately 0.1λ at 6 GHz.During the designing process of the proposed unit cell, Ansoft HFSS 14.0 is used for full-wave simulation.Floquet port and periodic boundary are adopted for a unit cell to simulate an infinite periodic array.

Fig. 4 .
Fig. 4. Simulation results of the S parameters when the incident wave is parallel to u-axis and v-axis: (a) reflection coefficients and phase difference; (b) transmission coefficients and phase difference.

Figure 4
Figure4shows the S parameters of the element for upolarized and v-polarized incidence.As observed from Fig.4(a), we can conclude that: uu vv 1 uv vu 2 uu vv uv vu

Fig. 8 .
Fig. 8.The S parameters comparison between simulation and measurement results when the presented metasurface is irradiated by different polarized incident wave: (a) ypolarized incident wave; (b) x-polarized incident wave.Due to the limited measurement conditions, we have only measured t 21 xy and r 11 yy of the y-polarized incidence and r 11 xx of the x-polarized incidence.The comparison between the measurement results and the simulation ones are shown in Fig. 8.