Full-space polarization conversion of electromagnetic waves at terahertz frequency based on metasurface

In this paper, a full-space electromagnetic wave polarization converter working in the terahertz frequency was put forward, and its physical mechanism was also analyzed. The polarization converter could realize the reflection cross-polarization conversion in the frequency range of 3.16–3.75 THz, with the Polarization Conversion Rate (PCR) of more than 90%. In the frequency range of 0.43–2.15 THz, it could realize transmission cross-polarization conversion, with the PCR close to 100%. In short, the designed metasurface polarization converter has a simple structure, realizes full-space manipulation of electromagnetic waves, facilitates the miniaturization and integration of the system, and has the potential applications in antennas, imaging systems, remote sensors, and radiometers.


Introduction
Electromagnetic metamaterials [1,2], as the structures composed of subwavelength artificial units arranged in periodic or non-periodic manner, have attracted extensive attention due to their unique electromagnetic properties [3][4][5]. In comparison to general three-dimensional metamaterials, metasurfaces have obvious advantages in terms of insertion loss, integrability and size. After the generalized Snell's law was proposed [6], the research of metasurfaces has developed rapidly, and metasurfaces have been continuously applied to modulate the loss [7], transmission properties [8], and polarization properties [9][10][11] of electromagnetic waves. Besides, a series of superior functions, such as negative refraction [12], perfect absorption [13], beam manipulation [14,15], holograms [16,17], and perfect lens [18], are realized, which are impossible or difficult to be achieved by traditional materials. Polarization is an important feature of electromagnetic waves, and it is always hoped to manipulate the polarization of electromagnetic waves in applications such as optical communication, sensing, and imaging [19]. Generally speaking, traditional polarization devices are designed using Faraday effect [20] and based on twisted nematic liquid crystals, but these traditional methods are very complicated. It is noteworthy that the proposal of metasurface provides a more convenient way for controlling the polarization direction of electromagnetic waves.
Nowadays, the single-function metasurfaces can no longer satisfy people's needs, and multi-function metasurfaces are attracting more and more increasing attention [21][22][23]. Active devices such as positiveintrinsic-negative (PIN) diodes and varactor diodes have been applied to achieve multi-function modulation of electromagnetic waves by metasurfaces [24,25]. For example, Y Li et al proposed an active metasurface with switchable absorption and polarization conversion [26], which could flexibly reduce RCS. Beyond that, Z Yang et al designed a metasurface based on dynamic regulation of PIN diodes [27], which realized a wideband linearto-circular polarization conversion in the OFF state of the diode as well as a dual-band linear-to-linear polarization conversion in the ON state of the diode. However, the traditional active devices cannot work well in the terahertz band. Due to the limitation of material size and processing technology, active devices cannot be well integrated into the terahertz metasurfaces. Therefore, it is still of great significance to explore passive terahertz metasurfaces that can realize multifunction. Most of the above-mentioned multifunctional metasurfaces achieve multifunctional modulation of electromagnetic waves in reflection or transmission modes by using multifunctional unit structures or coding arrays. With such a design, the metasurfaces can only regulate electromagnetic waves in half of the space, but the space resources are not fully utilized. Some researchers have begun to study the manipulation of electromagnetic waves in the full-space to achieve multifunctional electromagnetic metasurfaces. For instance, Y Tamayama et al designed a singlelayered metamaterial with three-dimensional structure coupled by two identical split-ring resonators [28], which is characterized by a half mirror and a quarter-wave plate and can realize a linear-tocircular polarization conversion of half reflection and half transmission. Furthermore, T Cai et al designed a metasurface composed of specially designed meta-atoms with polarization-dependent transmission and reflection properties that can efficiently manipulate electromagnetic waves in the full space [29]. Furthermore, the metasurface can bend or focus electromagnetic waves on the transmission and reflection sides of the metasurface, respectively. Q Fang et al designed a metamaterial capable of operating linear and circular polarization waves in both transmission and reflection modes [30], with the functions of polarization conversion, focusing and divergence. Apart from that, L Zhang et al proposed a transmission-reflectionintegrated multi-function coding metasurface for the full-space controls of electromagnetic waves [31], which realized multiple independent functionalities by changing the polarization and direction of incident waves. Additionally, L Bao et al proposed a dual-band metasurface working at microwave frequencies [32], which could realize independent manipulations of reflection and transmission waves in two half-spaces at two frequencies.
The transmission mode works at 7 GHz, in which the amplitude and phase modulations can be used to form multifocal points on focal planes with different distances and intensities. By contrast, the reflection mode works at 17GHz, which can generate and control reflected beams of different intensities in the far-field. At present, most electromagnetic metamaterials capable of full-space manipulation of electromagnetic waves work in the microwave band with lower frequencies.
In this paper, a full-space electromagnetic wave polarization converter (FPC) working in the terahertz frequency range was proposed. With a simple structure, it is based on the coupled resonance of twisted electromagnetic fields. The proposed metasurface can perfectly convert the reflected wave to the crosspolarization wave of the incident wave in the frequency range of 3.16-3.75 THz. Besides, in the frequency range of 0.43-2.15 THz, the metasurface can perfectly convert the transmitted wave to the cross-polarization wave of the incident wave. In comparison to the previous studies, the metasurface designed in this paper has a simple structure, is easy to manufacture at tiny dimensions, can perform full-space manipulation of electromagnetic waves in the terahertz band, realizes the miniaturization and integration of optical systems, and has potential applications in terahertz antennas, superlenses, beam splitters, etc.

Model design and discussion
The structure of FPC unit is shown in figure 1(a), and its top structure and bottom structure are presented in figures 1(b) and (c). For a square dielectric substrate with a thickness of t and a side length of P with copper cladded on both sides, on the front, we first removed two 1/4 circles with a radius of R by centering the two vertices symmetrically, leaving the arrow-like part. On both sides of the arrow, we symmetrically placed two metal circles with radius r. On the back, we made a metal slit with width d from the middle. The material of the The frequency domain solver of electromagnetic wave simulation software CST Microwave Studio was used to conduct a full-wave simulation of FPC, and the boundary conditions in the x-direction and y-direction were set as unit cell, while the boundary condition in the direction z was set as open boundary condition. In order to improve the computational efficiency of the simulation software, we used quadrilateral grid dissection with 26,858 meshes.
For the y-polarization wave incident on the FPC, we denoted the incident electric field by E . yi For the reflected wave, we denoted its components in the x-direction and y-direction of E xr and E , yr respectively. In terms of the transmitted wave, we used E xt and E yt to represent its components in the x-direction and y-direction. Then, the co-polarization reflection coefficient r yy and the cross-polarization reflection coefficient r xy could be defined as [33]: Likewise, we could also obtain the co-polarization transmission coefficient t yy and cross-polarization transmission coefficient t , xy which could be described as: In order to describe the polarization conversion of the incident wave, we defined the PCR of reflected wave and transmitted wave as PCR r and PCR , t respectively, which could be expressed as [34,35]: In order to further evaluate the polarization conversion capability of the FPC, we defined the Polarization Extinction Ratio (PER) of the reflected and transmitted waves as PER r and PER , t respectively, which could be derived as [36]: Finally, in order to describe the absorption of incident waves by FPC, the expression of absorption rate is defined as: w represents the angular frequency of the incident electromagnetic wave. When the TE wave is incident on the FPC surface, r xy is close to 0dB in the frequency of 3.16-3.75 THz, while r yy is below −10 dB. Especially near the frequency of 3.24 THz, r yy is less than −30 dB. It can be observed from figure 2(a) that the TE wave is perfectly converted to TM wave. In addition, figure 2(c) presents that the PCR r is above 90% in the above frequency range, of which it is close to 100% near the frequency of 3.24 THz, which achieves a nearly perfect crosspolarization conversion. At the same time, the PER r is almost above 10dB in the frequency range, and close to 30dB near the frequency of 3.24 THz, as shown in figure 2(e), indicating that the reflected wave is mainly the cross-polarization wave of incident wave. Namely, FPC has excellent cross-polarization conversion capability for reflected waves in the wide frequency range of 3.16-3.75 THz. Similar to the analysis of reflection characteristics, when the TE wave is incident on the FPC surface, t yy is basically below −30 dB in the frequency range of 0.43-2.15THz, whereas t xy is basically above −10 dB and close to 0 dB in the frequency of 1.82 THz, as shown in figure 2(b), indicating that the TE wave is converted to TM wave after being transmitted by the FPC. Figure 2(d) shows that the PCR t is close to 100% in the frequency range, which realizes perfect cross-polarization conversion. In addition, the PER r is almost above 20 dB in the above frequency range, and even above 30 dB near 1 THz, as shown in figure 2(f), suggesting that the transmitted wave is mainly the cross-polarization wave of the incident wave. In other words, FPC has excellent crosspolarization conversion capability for transmitted waves in the wide frequency range of 0.43-2.15 THz. When the TE wave is incident on the surface of the FPC, the absorption is basically below 0.2 in the two frequency ranges of 0.43-2.15 THz and 3.16-3.75 THz, as shown in figure 2(g), meaning that most of the incident wave is mainly reflected or transmitted. It can be observed from the above analysis that the polarization directions of reflected and transmitted waves are basically perpendicular to those of incident waves, so that obvious cross-polarization transformation occurs. In addition, PCR r is above 90% in the frequency range of 3.16-3.75THz, and PCR t is close to 100% in the frequency range of 0.43-2.15 THz, indicating that FPC can realize reflection and transmission cross-polarization conversion at different frequencies, with high conversion efficiency. All in all, FPC can make full use of the whole electromagnetic space in the terahertz band, which is favorable to the miniaturization and integration of electronic and optical systems.

Theoretical analysis
In order to further study the physical principle of reflection and transmission cross-polarization conversion of FPC, we started with the surface current distribution. In CST Microwave Studio, we added some field monitors to view the surface current, which is used to view the surface current at the resonant frequencies. Figure 3 shows the surface current distribution at the resonant frequencies of f1 = 1.84 THz, f2 = 3.24 THz and f2 = 3.67 THz. At the resonant frequency of f1, an obvious transmission cross-polarization conversion occurs, and a reflection cross-polarization conversion is evident at the resonant frequencies of f2 and f3. Besides, when the TE incident wave is vertically incident on the surface of FPC, the current of the top metal mainly flows to the lower left along is perpendicular to the incident electric field and cannot produce a polarization deflection. Likewise, at the resonant frequency of f2 = 3.24THz, the current on the top metal flows to the upper right along the two circular metal patches, which is parallel to the current on the bottom of FPC, forms electric resonance, and excites the induced magnetic field H . 2 Meanwhile, its y-direction component can still lead to orthogonal polarization deflection. The case of f3 = 3.67 THz is similar to that of f2 = 3.24 THz, in which the induced magnetic field H 3 is excited by the electrical resonance, whose y-direction component leads to a 90°polarization deflection.
In addition, we analyzed the polarization deflection of electromagnetic waves from the azimuth angle q and ellipticity .
h When the TE wave is perpendicularly incident on the FPC along the z + direction, the expression of q and h could be defined as follows: xy yy j = -( ) ( ) When h is 0°, it indicates that the electromagnetic wave is a linear polarization wave, whereas q represents the azimuth angle between the reflected or transmitted wave and the incident wave. Therefore, when h is 0°and q is 90 ,   it indicates that the TE wave is completely converted into the TM wave, and cross-polarization conversion occurs. Based on calculation, we obtained the results of the variation of the q and h of the reflected and transmitted waves with frequency when the TE wave is incident vertically on the surface of FPC, as shown in figures 4 (a) and (b). It can be observed from figure 4(a) that the q of the reflected wave is close to 90°and h of that is close to 0°in the frequency range of 3.16-3.75 THz, suggesting that the TE wave reflected by FPC is basically converted into the TM wave in the frequency range. Meanwhile, the q of the transmitted wave is almost equal to  90°and h of that is close to 0°in the frequency range of 0.43-2.15 THz, as shown in figure 4(b). That is to say, the crosspolarization conversion of the TE wave transmitted by FPC is almost perfectly achieved in the above frequency range.
Besides, the interference effect in the Fabry-Perot-like cavity formed between the top metal array and the bottom metal plate of the FPC is also important for the polarization conversion [37,38]. The plane wave of y polarization incident on FPC mainly excites dipole oscillation along the long axis of the top metal element. Since the long axis is at an angle of 45°to the y axis, this dipole oscillation can be decomposed into two orthogonal oscillations. The multiple reflections induced by the Fabry-Perot-like cavity may lead to interference effects of polarization coupling, which enhance or weaken the entire reflected field of co-polarization and crosspolarization. A Fabry-Perot-like cavity of suitable length can produce constructive interference to the crosspolarization field and destructive interference to the co-polarization field, thus obtaining the cross-polarization transition effect. Next, we decompose the incident wave along the long axis of the top metal and its orthogonal axis, and apply the transmission matrix for further analysis of this. Assuming that the electromagnetic wave incident on the surface of FPC is TE wave, the incident electric field is still denoted by E .
yi We let the incident electromagnetic wave decomposed orthogonally along the direction of 45°to the y-axis, and represented the components of the decomposed electromagnetic wave by E ui and E vi respectively. Likewise, the field intensity of the reflected wave was defined as E , r and the two components decomposed by E r along the direction of u and v were represented by E ur and E vr respectively, as shown in figure 5(a). Then, the reflected electric field could be expressed as: where r uu and r vu represent the co-polarization reflection coefficient and cross-polarization reflection coefficient of the reflected wave components in the u-direction, respectively, whereas r vv and r uv represent the crosspolarization reflection coefficient and co-polarization reflection coefficient of the reflected wave components in the v-direction, respectively. When the TE wave is incident on the surface of the FPC, the results of the reflection coefficients of the components decomposed by the reflected wave along the uand v-directions with the variation of frequency are illustrated in figure 6(a). It is obvious that the amplitude of r uu and r vv is close to 0dB in the frequency range of 3.16-3.75 THz, whereas the amplitude of r uv and r vu is less than −20dB, which can be neglected. According to the above transmission matrix, the following expressions could be obtained approximately:  Figure 6(c) presents the results of the R and j of the reflected waves with the variation of frequency. It can be observed that R is basically equal to 0 and j is close to 180   in the frequency range of 3.16-3.75 THz, indicating that the TE incident wave mainly achieves the cross-polarization conversion. Likewise, for transmitted waves, as shown in figure 5(b), the transmitted electric field could be expressed as: When the TE wave is incident on the surface of the FPC, figure 6(b) depicts the results of the transmission coefficients of the components decomposed by the transmitted wave along uand v-directions with the variation of frequency. Obviously, the magnitude of t uv and t vv is close to −5dB, whereas that of t uu and t vu is less than −20dB, which can be neglected. According to the above transmission matrix, the following expressions could be obtained approximately:    comparison to r of 10 m, m when r is 8 m, m the strong electromagnetic resonance will never be caused by the circular metal sheet at any frequency. Therefore, the two circular metal sheets lose their value of existence. Next, we discussed the effect of the radius R of a quarter metal circle intercepted at the top of FPC on polarization conversion. When the radius R changes from

Conclusion
In this paper, a full-space electromagnetic wave polarization converter working in the terahertz frequency range was put forward. In order to verify the advantages of the metasurface proposed in this paper, we compared it with the references with relevant characteristics published in recent years, as shown in table 1. According to the results of simulation, the FPC had the excellent cross-polarization conversion ability for reflected waves in the wide frequency range of 3.16-3.75 THz with the PCR above 90%, whereas the PCR was close to 100% near 3.24 THz. In addition, the FPC had the perfect cross-polarization conversion ability for transmitted waves in the wide frequency range of 0.43-2.15THz with the PCR close to 100%. Furthermore, the physical mechanism of polarization conversion achieved by FPC was analyzed from surface current distribution, azimuth angle, ellipticity and transmission matrix. Finally, the effects of some parameters on the polarization modulation of