1. Introduction

In recent years, metasurface, periodic, and quasi-periodic planar arrays of sub-wavelength elements have attracted increasing attention because of their unique electromagnetic (EM) properties and ability to manipulate EM waves [1–6]. Owing to the lower profile (easy integration into ultrathin devices) and less absorption (easy to obtain high efficiency) of metasurfaces [7,8], metasurface-based reflective linear-to-circular (LTC) polarization converters have been extensively investigated for converting linearly polarized waves into circularly polarized waves, showing outstanding potential in many fields such as electronic countermeasures and satellite communication [9,10]. For example, Orr et al. proposed an LTC polarization reflector using anisotropic frequency-selective surfaces, but the polarization reflector operates within two narrow bands centered at about 20.5 and 26 GHz [11]. Meanwhile, Li et al. proposed a transmitting wideband LTC polarization converter using a bi-layered metasurface [12], which covers a wide frequency range from 11.0 to 18.3 GHz. Later, Gao et al. reported a reflective circular polarization converter using an ultrathin micro-split Jerusalem-cross metasurface, which can convert linearly polarized waves into circularly polarized waves in a frequency range of 12.4–21 GHz [13]. However, the relative bandwidths (RBWs) of the two mentioned gigahertz designs are only 50%. Another two designs operating in the gigahertz regime with ultra-wideband have also been reported in the literature [14,15]. Recently, two broadband tunable terahertz polarization converters were proposed based on multi-layer graphene sheets [16,17]. Although these polarization converters can dynamically achieve LTC polarization conversion by electrically controlling the Fermi energy of the graphene sheets, they could lead to bulky configurations and high loss with the application of a biasing device. Moreover, Mahdi proposed reflection-mode LTC polarization converters used in the terahertz regime exhibiting the ultra-wideband property [18]. Nevertheless, this design is based on a multi-layer structure and is unsuitable for low profiles. As previously mentioned, LTC polarization converters operating in the terahertz regime, with all the properties of wideband, high efficiency, and low profile, have been underutilized.

In this study, a reflective LTC polarization converter is proposed based on a metasurface. It consists of an anisotropic double split resonant square ring, medium, and metal ground, and operates in the frequency range of 0.60–1.41 THz with an axis ratio (AR) ≤ 3dB and efficiency ≥ 88%. Moreover, the LTC polarization converter is excited by y-polarized and x-polarized incident waves, where the reflected wave comprises left-hand circular polarization (LHCP) and right-hand circular polarization (RHCP) waves, respectively. The design can also operate in the frequency range of 1.48–1.54 THz with an opposite rotation and efficiency ≥ 82%. Finally, the physical mechanisms are revealed by using the current distribution.

2. Theoretical design and results discussion

Figure 1 shows an illustration of the 3 × 3 unit design of the proposed LTC polarization converter. The upper layer is an anisotropic double split resonant square gold ring with a thickness of 200 nm. In the middle of the cell, there is a dielectric material of polyimide with a dielectric constant of 3, loss tangent of 0.001 and thickness h of 47 µm (if there is no specific mention). Then, a fully reflective gold mirror is bottomed. The specific parameters of the double split resonant square ring are as follows: p = 92 µm, s = 10 µm, l = 44 µm, and w = 5 µm.

 

Fig. 1 3 × 3 unit structure diagram of the proposed polarization converter.

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This design was simulated using frequency domain solver in CST Microwave Studio. In the simulation, periodic boundary conditions were employed in the x and y directions to simulate an infinite periodic array, and a plane wave was incident downward on the top surface of the proposed design with a y-polarized electric field (i.e., E_yi = E_yie_y). The reflected wave can be expressed as E_r = E_xre_x + E_yre_x = r_xyexp(jϕ_xy)E_yie_x + r_yyexp(jϕ_yy)E_yie_y, where r_xy = |E_xr/E_yi| and r_yy = |E_yr/E_yi| respectively represent the reflection coefficient magnitudes for y-to-x and y-to-y polarization conversion, and ϕ_xy and ϕ_yy are the corresponding phases. Because of the anisotropic characteristic of the metasurface, the magnitude and phase of E_xr and E_yr may be different [19]. If r_xy = r_yy and Δϕ = ϕ_yy – ϕ_xy = 2nπ ± π/2 (n is an integer), the purified LTC polarization conversion can be obtained, and “–” and “+” respectively represent RHCP and LHCP [20]. In contrast, their magnitudes should be as high as possible for high-efficiency polarization conversion.

In the frequency range of 0.60–1.41 THz, the reflection coefficient magnitudes are approximately equal and the phase difference is close to 90° or –270° (i.e., the y-component is 90° ahead of the x-component), as shown in Fig. 2. One can see that the reflected wave is an LHCP wave. Moreover, from 1.48 to 1.54 THz (see the shaded regions), the reflection coefficient magnitudes are approximately equal and the phase difference is close to –90°, which leads to an RHCP reflected wave.

 

Fig. 2 Reflection coefficients for x-component and y-component. (a) Magnitude, (b) phase, and phase difference.

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Next, Stokes parameters [12,13,21] are introduced to describe the performance of the polarization converter:

The normalized ellipticity of V/I is further defined to characterize the polarization conversion ability. Specifically, V/I = –1 and V/I = + 1 indicate that the reflected wave is an RHCP wave and LHCP wave, respectively. Based on Eq. (1) and Fig. 2, we can obtain the frequency-dependent ellipticity, as shown in Fig. 3. It can be found that the ellipticity is close to unity in the frequency range of 0.60–1.41 THz, which further indicates that the reflected wave is of LHCP. A frequency of 0.8 THz, as an example, is taken to demonstrate the dynamic electric field distribution on the metasurface for different time phases, as shown in the insets of Fig. 3. One can clearly see that left-hand rotation is exhibited at certain time phases. An ellipticity approaching –1 is analogously obtained from 1.48 to 1.54 THz (see the shaded region in Fig. 3) and the reflected wave is an RHCP wave. Despite the absence in the results, it should be pointed out that the reflected wave is still circularly polarized with the same bandwidth but opposite rotation, when the incident wave is x-polarized.

 

Fig. 3 Ellipticity of this design excited by y-polarized plane wave. The insets from (a) to (i) show the electric field distribution at 0.8 THz for different time phases from 0° to 160° with a step of 20°.

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Here, we define tan2α = U/Q and sin2β = V/I and introduce an axis ratio AR = 10log(tanβ) to quantify the circular polarization performance [12], where α is the polarization azimuth angle and β is the ellipticity angle. According to the black line shown in Fig. 4, AR is less than 3 dB from 0.60 to 1.41 THz and from 1.48 to 1.54 THz, indicating that the proposed design performs well at circular polarization conversion.

 

Fig. 4 AR and efficiency.

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The energy conversion efficiency is also calculated by η = (|E_xr|² + |E_yr|²)/|E_yi|² = |r_xy|² + |r_yy|², represented by the blue dashed line in Fig. 4. We can notice that the efficiency of the LHCP is greater than 88% and that of the RHCP is greater than 82%. The results indicate that the proposed design exhibits the high-efficiency conversion property.

Furthermore, the AR of this design as a function of angle of incidence and frequency is simulated, as shown in Fig. 5 (a). One can see that the proposed converter can maintain a good circular polarization conversion performance with one ultra-wideband and one narrowband while the angle of incidence varies from 0° to about 20°. From about 20° to about 40°, the reflected wave is circularly polarized with one wideband and two narrowbands; it is circularly polarized only within one narrowband while the angle of incidence ≳ 40°. In addition, the thickness h of substrate can affect the performance of the proposed design significantly. The magnitudes and phase differences of the reflection coefficient, the axis ratio and the efficiency for h = 43, 47, and 51 μm are shown in Figs. 5 (b) and (c). It can be seen that an optimal LTC polarization conversion performance can be obtained when h = 47 μm.

 

Fig. 5 LTC polarization conversion performance for various parameters. (a) Angle of incidence and frequency-dependent AR; (b) the h-dependent reflection coefficient magnitudes and phase differences; (c) the h-dependent AR and η.

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3. Physical mechanisms

To better understand the physical mechanism of the polarization conversion, we decompose both the incident wave and reflected wave into two orthogonal components (i.e., u and v components), as shown in the inset of Fig. 6 (a). Specifically, the u–v coordinate system is the coordinate system that rotates about the z-axis 45° from the x–y coordinate system (see Fig. 1). Assuming the incident wave is a y-polarized wave propagating along the –z-axis, the electric field can be written as E_i = E_iexp(jkz)e_y = E_iexp(jkz)e_u/ + E_iexp(jkz)e_v/; the reflected electric field is thus E_r = {r_uuE_iexp[j(–kz + φ_uu)] + r_uvE_iexp[j(–kz + φ_uv)]}e_u/ + {r_vuE_iexp[j(–kz + φ_vu)] + r_vvE_iexp[j(–kz + φ_vv)]}e_v/. Here, r_uu, r_vu, r_uv, and r_vv represent the magnitudes of the reflection coefficients for the u-to-u, u-to-v, v-to-u, and v-to-v polarization conversions, respectively; and φ_uu, φ_vu, φ_uv, and φ_vv are the corresponding phases. When r_vu = r_uv = 0, r_uu = r_vv = r, and Δφ = φ_vv – φ_uu = 2nπ ± π/2, the reflected electric field will be E_r = rE_iexp(–jkz){exp(jφ_uu)e_u + exp[j(φ_uu + 2nπ ± π/2)]e_v}/ and a circular polarization wave will be obtained [20]. As shown in Fig. 6, it can be observed that r_vu and r_uv are nearly equal to 0, r_uu is approximately equal to r_vv, and the phase difference is close to 90° or –270° in the frequency range of 0.60–1.41 THz; thus, LTC polarization conversion has been achieved. A similar situation occurs from 1.48 to 1.54 THz but with a phase difference close to –90°.

 

Fig. 6 (a) Magnitudes, (b) phases, and phase differences of the reflection coefficients in the u–v coordinate system.

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The physical mechanism of the polarization conversion can be further elaborated upon the current distribution on the metasurface and metal ground in the u–v coordinate system [7,8,14]. While the currents on the metasurface are parallel to those induced on the metal ground, electric resonance will be generated [7,8]. In contrast, magnetic resonance will be formed by current loops in the dielectric substrate if the surface currents on the metasurface are antiparallel to the induced currents [22,23]. Here, we choose four frequencies, 0.7, 1.0, and 1.35 THz with LHCP and 1.5 THz with RHCP, to analyze the current distribution on the metasurface and metal ground, as shown in Fig. 7.

 

Fig. 7 Current distributions and diagrams of the equivalent electric and magnetic moments. The images from the 1^st to 4^th row show the case for 0.7, 1.0, 1.35, and 1.5 THz, respectively. The 1^st and 3^rd columns show the current distributions on the metasurface, and the 2^nd and 4^th columns show those on the metal ground; the 1^st and 2^nd columns show those for the u-polarized incident wave, and the 3^rd and 4^th columns show those for the v-polarized incident wave. The 5^th column shows diagrams of the equivalent electric moments (red double-headed arrows) and equivalent magnetic moments (blue circles).

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At 0.7 and 1.0 THz, the currents on the metasurface (see Figs. 7 (a) and (f)) and those on the metal ground (see Figs. 7 (b) and (g)) form magnetic resonances and generate equivalent magnetic moments m₁ and m₃ under the u-polarized incident wave. Similarly, m₂ and m₄ are generated while the incident wave is v-polarized. In Fig. 7 (e), m₁ and m₂ manipulate the magnitudes and phases of the reflected electric fields along the u-axis and v-axis, respectively. If the u-component and v-component of the reflected electric fields have equal magnitudes and a phase difference of 90°, an ideal LTC polarization conversion will be achieved. In Fig. 7 (j), the principle is identical. At 1.35 and 1.5 THz, magnetic resonances still form and the magnetic moments m₆ and m₈ can still be obtained under the v-polarized incident wave. However, the electric resonances are generated under the u-polarized incident wave and, thus, the electric moments p₅ and p₇ can be obtained because the currents on the metasurface (see Figs. 7 (k) and (p)) are parallel to those induced on the metal ground (see Figs. 7 (l) and (q)). In Fig. 7 (o), p₅ and m₆ respectively manipulate the magnitudes and phases of the reflected electric fields along the u-axis and v-axis. An LTC polarization conversion can be achieved if approximate magnitudes of the u-component and v-component of the reflected electric fields exist and the phase difference is 90°. The same principle is used as presented in Fig. 7 (t). Because of its multiple resonance characteristic [8,24], the proposed design can operate in an ultra-wideband by optimizing the geometric parameters.

4. Conclusions

In this study, an ultra-wideband and high-efficiency LTC reflective polarization converter is designed based on a metasurface at terahertz frequencies. Due to the multiple resonance characteristic in the proposed design, the ultra-wideband can be obtained. For the two orthogonal electric field components of the reflected wave, the magnitudes of the reflection coefficients are approximately equal and as high as 0.7, and the phase difference is close to 90° or –270° from 0.60 to 1.41 THz (i.e., RBW ≈80%) when the incident wave is y-polarized. This results in ultra-wideband and high-efficiency LHCP. There is also a narrowband RHCP in the range of 1.48–1.54 THz. The converter can operate in LTC polarization conversion with an opposite rotation under x-polarized incident wave. The physical mechanism of the polarization conversion was analyzed according to the current distribution. With the increase in angle of incidence, the design can operate in one ultra-wideband and one narrowband, one wideband and two narrowbands, and just one narrowband. The LTC converter can be used as a key component in applications of EM measurement, antenna design, and stealth technology.