# Reconfigurable Polarizer Based on Bulk Dirac Semimetal Metasurface

^{*}

## Abstract

**:**

_{F}) of the BDS. In the frequency range of 0.51 THz and 1.06 THz, the incident linear polarized wave is converted into a circular polarized wave with an axial ratio (AR) less than 3 dB when E

_{F}= 30 meV. When E

_{F}= 45 meV, the cross-polarization conversion is achieved with the polarization conversion ratio (PCR) greater than 90% in the band of 0.57−1.12 THz. Meanwhile, the conversion efficiencies for both polarization conversions are in excess of 90%. Finally, the physical mechanism is revealed by the decomposition of two orthogonal components and the verification is presented by the interference theory.

## 1. Introduction

^{3}hybridization, offers attractive alternatives to narrow-gap semiconductors for optoelectronics across mid-infrared and THz frequencies [20]. For example, [21] proposed a broadband reflective LTC polarizer in a mid-infrared regime based on monolayer BP (phosphorene) metamaterial. Generally, 2D matearials have been attracting increasing attention as a candidate in the design of THz polarizer. However, their moderate carrier mobility (e.g., 2 × 10

^{5}cm

^{2}V

^{−1}s

^{−1}at 5 K for graphene [22] and 5 × 10

^{5}cm

^{2}V

^{−1}s

^{−1}at 30 K for BP [23]) are still a limitation in their application.

^{6}cm

^{2}V

^{−1}s

^{−1}at 5 K [24,25], recently, Bulk Dirac semimetals (BDSs) showed promise in the design potential of a THz polarizer. For instance, Dai et al. investigated a broadband tunable THz cross-polarizer based on BDSs [26]. With increasing E

_{F}, the cross-conversion bandwidth is widened and exhibits a blue-shift. Furthermore, they proposed a dynamically tunable broadband LTC polarizer based on metasurface [27], where the proposed metasurface consists of a center-cut cross-shaped metallic patterned structure with a sandwiched BDS ribbon. Both of the above-mentioned designs in [26] and [27] achieve the adjustable performance in terms of frequency, but the absence of polarization reconfigurability is still a limitation to their application.

## 2. Materials and Methods

_{r}= 3.0 and a loss tangent tanθ = 0.001, and a fully reflective gold mirror. The circular-polarized (CP) wave or x-polarized (XP) wave can be reflected when the y-polarized (YP) wave is incident on the polarizer. The geometric parameters of the polarizer include unit length L = 94.0 μm, dielectric thickness h = 50.0 μm, the distance from the center of the arc to the edge of the cell a = 22.0 μm, outer radius R

_{o}= 70.7 μm, inner radius R

_{i}= 57.7 μm, and half of the angle corresponding to the outer arc α = 31.5° and inner arc β = 25.2°.

_{intra}and σ

_{inter}represent the intraband and interband contributions, respectively. ħ and g are respectively the reduced Planck constant and the degeneracy factor, E

_{F}, v

_{F}, and k

_{F}are respectively the Fermi level, Fermi speed, and Fermi Momentum, moreover k

_{F}is calculated by E

_{F}/ħv

_{F}. G(E) = n(−E) − n(E), and n(E) is the Fermi distribution function. In the case of electron-hole (e−h) symmetry of the Dirac spectrum for the nonzero temperature T, the real and imaginary parts of the longitudinal dynamic conductivity of the Dirac semimetal can be expressed as

_{F}, in the electron-hole (e−h) symmetry of the Dirac spectrum, the complex conductivity is expressed as [28]

_{F}+ jv

_{F}/(E

_{F}k

_{F}μ) is the normalized frequency, and the relative permittivity of the BDSs can be expressed as ε = ε

_{b}+ iσ/ωε

_{0}, where ε

_{b}= 1 is the effective background dielectric constant and ε

_{0}is the permittivity of vacuum.

_{b}and g. In this study, AlCuFe was selected as the BDS material and its dynamic conductivity is shown in Figure 2, where g = 40, E

_{c}= 3, v

_{F}= 106 m/s, and μ = 3 × 10

^{4}cm

^{2}V

^{−1}s

^{−1}. The hatched regions indicate the normalized frequency range for the THz gap, ħω/E

_{F}≈ 1.30, 0.87, and 0.65 corresponding to E

_{F}= 30 meV, 45 meV, and 65 meV when f = 10 THz. It is clear that in the low frequency of THz gap, the real component can be neglected because it is far lower than the imaginary component.

_{r}= r

_{xy}exp(jφ

_{xy})E

_{yi}e

_{x}+ r

_{yy}exp(jφ

_{yy})E

_{yi}e

_{y}, where r

_{xy}and r

_{yy}are, respectively, the magnitudes of the reflection coefficient for y-to-x and y-to-y polarization conversion, φ

_{xy}and φ

_{yy}are the corresponding phases. Then, phase difference is defined by Δφ = φ

_{yy}− φ

_{xy}. When r

_{xy}= r

_{yy}= √2/2 and Δφ = 2n ± π/2 (n is an integer), the perfect LTC polarization conversion is brought; with “−” and “+”, the reflected waves are, respectively, the right-hand circular polarization (RHCP) wave and the left-hand circular polarization (LHCP) wave. On contrast, the total cross polarization conversion is brought with r

_{xy}= 1 and Δφ = 2n ± π [29]. In order to achieve a high efficiency of polarization conversion, the reflection coefficient amplitudes should be controlled as highly as possible within the demanded Δφ.

## 3. Results and Discussions

_{F}= 30 meV of BDS (AlCuFe), the reflection coefficient magnitudes and the phase difference are shown in Figure 3a. One can observe that r

_{xy}≈ r

_{yy}≈ √2/2 and Δφ ≈ −90° or 270° in the frequency range of 0.51–1.06 THz. Similarly, Δφ ≈ 90° in the range of 0.41–0.46 THz with r

_{xy}≈ r

_{yy}≈ √2/2. The results indicate that the incident linear polarized wave is converted into a RHCP wave within a broadband and a LHCP wave within a narrow band. When the E

_{F}is adjusted to 45 meV, r

_{yy}< 0.3 and r

_{xy}> 0.9 in the frequency range of 0.57–1.12 THz, as shown in Figure 3b, which means that the YPincident waves are converted into the cross-polarized reflected waves by the polarizer.

_{LTC}= r

_{xy}

^{2}+ r

_{yy}

^{2}and the axial ratio, AR = 10 lg(tanβ) with β = arcsin(V/I)/2 [13], obtained from the stokes parameter in Equation (3) [30]. In contrast, for cross-polarization conversion, the cross polarization conversion efficiency is estimated as η

_{cross}= r

_{xy}

^{2}and PCR = r

_{xy}

^{2}/(r

_{xy}

^{2}+ r

_{yy}

^{2}) is defined to further investigate the performance [31].

_{F}, the calculated PCR and AR are presented in Figure 4a. One can observe that the relative bandwidth (RBW) with PCR > 0.8 reaches 71% and the RBW of RHCP and LHCP with AR < 3 dB are, respectively, 71% and 11%. More significantly, a RBW of 64% is obtained in the identical frequency band; moreover, both η

_{LTC}and η

_{cross}are greater than 90%, as shown in Figure 4b, which indicates the high performance of the proposed polarizer.

_{F}, the conductivity of the BDS (AlCuFe) is adjustable, which causes the reconfigurability of the proposed BDS-based polarizer. Therefore, it is reasonable to study the effects of various E

_{F}on the conversion performance. The AR for E

_{F}= 25, 30, and 35 meV are shown in Figure 6a. It can be seen that an optimal LTC polarization conversion performance can be obtained when E

_{F}= 30 meV. Figure 6b shows the PCR gradually improves with increasing E

_{F}from 25 to 45 meV, and the operating frequency band exhibits a blue shift. Furthermore, the bandwidth of PCR becomes narrower gradually with increasing E

_{F}, which will lead to the degradation of the conversion performance. From Figure 6, one can conclude that the design polarizer achieves the optimized performances of cross polarization conversion with E

_{F}= 45 meV and the LTC polarization conversion with E

_{F}= 30 meV.

## 4. Mechanism and Verification

_{uu}, r

_{vu}, r

_{vv}, and r

_{uv}represent the reflection coefficient amplitudes for the polarization conversion of u−u, u−v, v−v, and v−u respectively, φ

_{uu}, φ

_{vu}, φ

_{vv}and φ

_{uv}represent the corresponding phases. When r

_{vu}= r

_{uv}= 0, r

_{uu}= r

_{vv}= r and Δφ = φ

_{vv}− φ

_{uu}= 2n ± π/2, the reflected wave is expressed as

_{vu}= r

_{uv}= 0, r

_{uu}= r

_{vv}= r and Δφ = φ

_{vv}– φ

_{uu}= 2n ± π the reflected wave is a cross-polarized wave and can be expressed as

_{F}= 30 meV, as shown in Figure 8a, r

_{uu}= r

_{vv}≈ 1, r

_{vu}= r

_{uv}≈ 0 and Δφ = φ

_{vv}− φ

_{uu}closing to −90°/270° are obtained in the frequency range of 0.5 and 1.08 THz, incidentally Δφ being approximately 90° is obtained in the band of 0.41–0.46 THz, i.e., the reflected waves are respectively RHCP wave and LHCP wave in these two bands. In contrast, when E

_{F}= 45 meV, r

_{uu}= r

_{vv}≈ 1, r

_{vu}= r

_{uv}≈ 0 and Δφ ≈ −180°/180° is obtained, as shown in Figure 8b, the cross-polarization conversion is realized. It is observed that the polarization conversions are consistent with that in Figure 3.

_{12}= r

_{12}exp(iφ

_{12}) and transmitted into the substrate with a transmission coefficient of t

_{12}= t

_{12}exp(iθ

_{12}). The transmitted wave continues to propagate with a propagation phase β = √εkd until it reaches the metal mirror, where ε and d are, respectively, the permittivity and the thickness of the substrate, and k is the propagation constant in the substrate. After the reflection at the metal mirror and the addition of another β, partial reflection and transmission occur again at the double-arc interface with coefficients r

_{21}= r

_{21}exp(iφ

_{21}) and t

_{21}= t

_{21}exp(iθ

_{21}). Similarly to the wave propagation in a stratified media, the total reflection is the superposition of the multiple reflections [32]:

## 5. Conclusions

_{F}. This design is of great significance in the wide application of metamaterials and the rapid development of THz technology.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 8.**The calculated and simulated reflection coefficients of u- and v-polarized reflected waves. (

**a**) LTC polarization conversion, (

**b**) Cross-polarization conversion.

Dirac Semimetal | ε_{b} | g |
---|---|---|

AlCuFe | 1 | 40 |

TaAs | 6.2 | 24 |

Eu2IrO7 | 6.2 | 24 |

Na3Bi | 12 | 4 |

Cd3As2 | 12 | 4 |

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**MDPI and ACS Style**

Jiang, Y.; Zhao, J.; Wang, J.
Reconfigurable Polarizer Based on Bulk Dirac Semimetal Metasurface. *Crystals* **2020**, *10*, 228.
https://doi.org/10.3390/cryst10030228

**AMA Style**

Jiang Y, Zhao J, Wang J.
Reconfigurable Polarizer Based on Bulk Dirac Semimetal Metasurface. *Crystals*. 2020; 10(3):228.
https://doi.org/10.3390/cryst10030228

**Chicago/Turabian Style**

Jiang, Yannan, Jing Zhao, and Jiao Wang.
2020. "Reconfigurable Polarizer Based on Bulk Dirac Semimetal Metasurface" *Crystals* 10, no. 3: 228.
https://doi.org/10.3390/cryst10030228