We propose a broadband reflective linear-to-circular (LTC) polarization converter in a mid-infrared regime based on monolayer black phosphorus (phosphorene) metamaterial. The proposed converter consists of periodic unit cells, each cell of which is formed by multiple phosphorene layers, a dielectric layer, and a fully reflective gold mirror. In the frequency range of 14.20 and 23.10 THz, the magnitudes of the reflection coefficients are approximately equal and the phase difference value between the two orthogonal electric field components of the reflected wave is close to π/2 or −3π/2, which indicates the reflective wave can be deemed the circular polarization with the incidence of linearly polarized wave. The simulation results show that the relative bandwidth of LTC polarization conversion reaches 58% and 47.8%, respectively, when the pucker ridge alignment of the phosphorene is perpendicular to the y-direction and x-direction. Finally, the physical mechanism is revealed via the field decomposition and current distribution. This polarization converter has great potential for future applications in electronic measurement, photonic design, and in some other optoelectronic systems.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Polarization control device of electromagnetic waves — cross-polarization converter or linear-to-circular polarization converter — plays a critical role in a wide range of applications , such as photonics, optoelectronics, imaging , and telecommunications [3–5]. In past few decades, conventional polarization devices were designed by employing photonic , chiral structures , metamaterials [8,9], meander-line , slots of different structures , waveguide , grating structures , quarter wave plate , etc. However, these designs are incapable of real-time operational adjustment. Recently, two-dimensional (2D) materials, such as graphene [15,16] and transition metal dichalcogenides (TMDs) , with atomic-scale thicknesses, have attracted extensive attention in applications for the polarization control device, because of the steerable optical and electrical properties, which are not available in conventional materials.
Graphene, characterized by the absence of band gap, is limited in many applications where high on-off ratio is required . Conversely, TMDs, such as MoTe2, MoSe2, and MoS2, offers the noticeable band gap of 1.57 eV . Nevertheless, the applications of TMDs are obstructed on the basis of the moderate carrier mobility . More recently, monolayer black phosphorus (phosphorene) , as an alternative 2D material, has been extensively investigated in many areas, owning to unique optoelectronic properties, such as the intrinsic in-plane anisotropic (caused by the different atom arrangements in the armchair and zigzag direction), the suitable and tunable direct band gap ranging from 0.3 eV to 2.0 eV  (bridging the graphene and TMDs), the mobility of up to 50000 cm V−1 s−1 , and the maximum carrier density of ns = 2.6 × 1014 cm−2 . These features make phosphorene have extensive potential for developing polarization converter. So far, three achievements [24–26], to the author’s best knowledge, have been reported regarding the research of linear polarization conversion. In , Zhou et al. proposed a transmitted linear polarizer based on phosphorene-SiO2 metamaterials structure whose polarization state can be controlled by utilizing the in-plane anisotropic property of phosphorene. Then, Shen et al.  presented a reflective tunable phosphorene-based linear polarizer in a visible regime using the Fabry–Perot cavities method. On the other hand, the combined effect of the linear dichroism and birefringence in the phosphorene was utilized to modulate the phase and amplitude of incident polarized light on the platform of polarized Raman spectroscopy, and the phosphorene was used as a linear polarization element . However, the patterning of phosphorene, in the form of phosphorene metamaterial, has not been included in the investigation of LTC polarization conversion.
In this paper, we consider the in-plane anisotropic properties of phosphorene and propose a dual-L shaped reflective linear-to-circular polarization converter. The proposed design consists of a multilayered phosphorene-metamaterial/dielectric structure on an optically thick gold mirror, which blocked all transmission, and formed a Fabry-Perot resonator to enhance the light-matter interaction. The simulation results show that the relative bandwidth of the proposed polarization converter are about 58% and 47.8%, respectively, when the pucker ridge alignment (PRA) perpendicular to the y direction and x direction. And the physical mechanism is investigated through the field decomposition and current distribution of the multilayered phosphorene structure.
2. Design, results and discussion
The cell schematic diagram of the proposed LTC polarization converter is sketched in Fig. 1. As shown in Fig. 1(a) and (b), the upper part of the cell consists of N layers dual-L shaped (see Fig. 1 (c)) phosphorene-based metamaterials embedded in a dielectric layer. In the middle of the cell there is a layer of the same dielectric material holding a dielectric constant of 2.89 and thickness t of 0.2µm, with a fully reflective gold mirror at bottom. In the design, we employ the phosphorene thickness of d = 1 nm, and the other parameters are as follows: p = 4 µm, s = 0.2µm, l1 = 3 µm, l2 = 2.8 µm, w1 = 1.6 µm, and w2 = 1 µm. Note that, if there is no specific mention, h = 2.0 µm, N = 6 and ns = 1014 cm−2  (the permittivity is shown by the blue line and the dotted blue line in Fig. 1 (d)).
The proposed polarization converter was investigated via CST Microwave Studio, where the 1 nm thick phosphorene were meshed using fine grids, the periodic boundary conditions were employed in the x and y direction to simulate an infinite periodic array, and a u-polarized plane wave (i.e. Ei = euEui) was incident downward on the top surface of the proposed design (i.e. the incident angle θ = 0°) if there is no specific indication. Then, the reflected wave can be expressed as Er = Eur + Evr = ruuejϕuuEuieu + rvuejϕvuEuiev, where ruu and rvu respectively represent the reflection coefficient magnitudes for u-to-u and u-to-v polarization conversion, and ϕuu and ϕvu are the corresponding phases. Because of the anisotropic characteristics of the phosphorene and the patterned phosphorene metamaterial, the magnitudes and phases of Eur and Evr may be different. However, if ruu = rvu and Δϕ = ϕvu − ϕuu = 2nπ±π/2 (n is an integer), the perfect LTC polarization conversion can be obtained, where “−” and “+” respectively represent right-hand circular polarization (RHCP) and left-hand circular polarization (LHCP).
In the first simulation, the PRA of phosphorene is perpendicular to the y direction, and the simulation results are shown by dash line in Fig. 2. One can see that the reflection coefficient magnitudes are approximately equal and the phase difference is close to π/2 and −3π/2 (i.e., the v-component is π/2 ahead of the u-component) in the frequency range of 12.82-23.28 THz, thus, the reflected wave is a LHCP wave with the relative bandwidth of 58%. Similarly, ruu, rvu, and Δϕ for the PRA perpendicular to the x direction are also shown by the solid line in Fig. 2. Accordingly, from 14.20 to 23.10 THz, an RHCP reflected wave can be obtained with the relative bandwidth of 47.8%. It should be pointed out that, when the incident wave is v-polarized, the LTC conversion can also be achieved with the approximate bandwidth but opposite rotation, despite the absence in the results. In addition, the proposed design, in which the anisotropic phosphorene is replaced by an isotropic 2D-material with ɛav=(ɛx +ɛy)/2, is excited by the u-polarized incident wave and the results are shown by the magenta dash line in Fig. 2. Where, ruu >> rvu indicates the polarization of reflection wave is similar to that of incident wave. Therefore, we can obtain that the anisotropy of the phosphorene plays an important role in achieving LTC polarization conversion.3, for the PRA perpendicular to the y direction, e is in the range of 0.8 and 1.0 and the AR is less than 3 dB from 12.82 to 23.28 THz, this shows the reflection wave is an approximate LHCP. In contrast, the reflection wave is a RHCP wave from 14.20 to 23.12 THz for the PRA perpendicular to the x direction.
As discussed above, the alignment of the pucker ridge determines the rotation direction of the reflection wave and the bandwidth of the LTC conversion.
The complex permittivity of phosphorene is seriously dependent on the carrier density ns (as shown in Fig. 1(d)), which determines the light-matter interaction and affects the performance of polarization conversion. As PRA perpendicular to the y direction, the simulated ruu, rvu, Δϕ , and AR for ns = 1.0 × 1013, 5.0 × 1013, 1.0 × 1014, and 2.0 × 1014 cm−2 are shown in Figs. 4(a) ∼ (c). While ns ≤ 1.0 × 1014 cm−2, on the basis of the phase differences approximate to π/2 or −3π/2 (see Fig. 4(b)), the magnitudes of the two orthogonal components for reflection wave approach (see Fig. 4(a)) with the ns increasing, in addition, the operating band exhibits redshift and the relative bandwidth shows increase (see Fig. 4(c)). However, the performance of the proposed converter will degrade with ns = 2.0 × 1014 cm−2. One can observe that an optimal LTC polarization conversion performance can be obtained when ns = 1.0 × 1014 cm−2 (see the red solid line).
Here, we also investigate the relationship between the number N of phosphorene layers and the polarization conversion performance of the proposed converter. As shown in Figs. 4(d) ∼ (f), the simulated ruu, rvu, Δϕ, and AR are provided, where the N = 3, 5, 6, and 8, respectively. We can clearly observe that the value of N has a great impact on ruu and rvu, which results in the variety of polarization conversion. In detail, the ability of polarization conversion firstly enhances and then degenerates, and the widest bandwidth ranging from 12.82 to 23.28 THz can be obtained with N = 6 (see the red solid line).
We also investigate the effect on the performance of the LTC for the different h value. The simulated ruu, rvu, Δϕ are shown in Fig. 5 (a & b), where h = 1.6, 2.0, and 2.4 µm, respectively. Obviously, the value of h has a great effect on ruu and rvu, moreover the effective operating frequency band exhibits a red shift with increasing h (see Fig. 5(c)). Specially, the optimal LTC polarization conversion (the widest bandwidth with AR <3 dB) can be achieved when h = 2.0 µm.
Moreover, the oblique incidence case is considered in the simulation. We respectively chose θ = 0°, 30°, and 60° to simulate the LTC converter performance. As shown in Fig. 5(d & e), it’s obviously observe that the value of θ affect the magnitude and phase difference of reflected wave greatly, where the cross-polarization component decreases with increasing θ. Furthermore, the bandwidth of ruu ≈ rvu becomes narrower with increasing θ, which will lead to the degradation of the LTC performance (see Fig. 5(f)).
3. Physical mechanisms
To quantificationally elucidate the physical mechanism of the polarization conversion, we decompose both the incident wave and the reflected wave into two orthogonal components, as shown in the inset of Fig. 6, i.e. x component and y component. Specifically, the u-v coordinate system comes from the x-y coordinate system rotating 45o around the z-axis, as shown in Fig. 1. Assuming the incident wave is a u-polarized wave propagating along the –z-axis, the electric field can be written as
Where, rxx, rxy, ryx, and ryy represent the magnitudes of the reflection coefficients for the x-to-x, y-to-x, x-to-y, and y-to-y polarization conversions, respectively, and ϕxx, ϕxy, ϕyx and ϕyy are the corresponding phases. When rxy = ryx = 0, rxx = ryy = r and Δϕ′ = ϕyy− ϕxx = 2nπ ± π/2, the reflected electric field will be
Furthermore, the physical mechanism of the polarization conversion can be qualitatively elaborated upon the current and surface current distribution in the x-y coordinate system. According to the resonant theory, the electric resonance and magnetic resonance would be formed in the proposed design, respectively, while the currents crossing the plane of the phosphorene metamaterial are paralleling and anti-paralleling to the surface currents on the gold mirror. Correspondingly, the equivalent electric dipoles (EED) and equivalent magnetic moments (EMM) will be formed.
Here, we choose two frequencies of 15 THz and 20 THz, to analyze the physical mechanism of the LTC converter through the currents crossing the plane of the phosphorene metamaterial and the surface currents on the gold mirror.
At 15 THz, the overall direction of the currents crossing the plane of the phosphorene metamaterial (as shown in Figs. 7(a) and (d)) and that of the surface currents on the gold mirror (as shown in Figs. 7(b) and (e)) are anti-parallel to each other and form magnetic resonances under the x-polarization and y-polarization, and then generate EMM m1 and m2 (as shown in Figs. 7(c) and (f)). m1 and m2 manipulate the magnitudes and phases of the reflected electric field along the y-axis and x-axis respectively. If the x-component and y-component of the reflected electric field have the equal magnitudes and a phase difference of π/2 or −3π/2, an ideal LTC polarization conversion will be achieved. In the proposed design, as the dynamic current distributions crossing the plane of the phosphorene metamaterial for various time phases shown in Figs. 8(a) ∼ (f), the reflective wave operates in LHCP state with the u-polarized incident wave. At 20 THz, in contrast, the overall currents crossing the plane of the phosphorene metamaterial (see Figs. 7(g) and (j) and the surface currents on the gold mirror (see Figs. 7(h) and (k)) are parallel to each other and form electric resonances under the x-polarization and y-polarization, and then generate the EED p1 and p2. Similarly, p1 and p2 can also manipulate the magnitude and phases of the reflected electric fields along the x-axis and y-axis. Then, the LTC polarization conversion will be achieved if the magnitudes of the y-axis and x-axis of the reflected electric fields approximate and the phase difference is π/2 or −3π/2. At the other frequencies, the similar principle can be carried out to elaborate the physical mechanism.
This work proposed and investigated an LTC polarization converter based on phosphorene metamaterial in a mid-infrared regime. It comprises metamaterial with N layers dual-L shaped patterned phosphorene embedded in dielectric and a fully reflective gold mirror. The phosphorene-based metamaterial structure can convert a linearly polarization incident wave into a circular polarization reflective wave in the frequency ranges of 12.82-23.28 THz and 14.2-23.12THz, respectively, when the PRA of the phosphorene perpendicular to y-direction and x-direction. Moreover, the physical mechanism of the proposed converter was analyzed via the quantificational field decomposition and the qualitative current distribution. The proposed LTC polarization converter can be used as the key components in the applications of photonics measurement, antenna design, and some others infrared systems.
National Natural Science Foundation of China (NSFC) (61661012); Natural Science Foundation of Guangxi Zhuang Autonomous Region (2017GXNSFBA198121, 2018GXNSFAA281190); Dean Project of Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing (GXKL06160108, GXKL06170104); Dean Laboratory of Cognitive Radio and Information Processing.
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