光电工程  2019, Vol. 46 Issue (8): 180519      DOI: 10.12086/oee.2019.180519

Broadband terahertz tunable metasurface linear polarization converter based on graphene
Zhang Hongtao, Cheng Yongzhi, Huang Mulin
School of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan, Hubei 430081, China
Abstract: A terahertz broadband tunable reflective linear polarization converter based on oval-shape-hollowed graphene metasurface is proposed and verified by simulation and Fabry-Perot multiple interference theory in this paper. Our designed metasurface model is similar to a sandwiched structure, which is consisted of the top layer of anisotropic elliptical perforated graphene structure, an intermediate dielectric layer and a metal ground plane. The simulation results show that when the given graphene relaxation time and Fermi energy are τ=1 ps and μc=0.9 eV, respectively, the polarization conversion rate (PCR) of the designed metasurface structure is over 90% in the frequency range of 0.98 THz~1.34 THz, and the relative bandwidth is 36.7%. In addition, at resonance frequencies of 1.04 THz and 1.29 THz, PCR is up to 99.8% and 97.7%, respectively, indicating that the metasurface we designed can convert incident vertical (horizontal) linearly polarized waves into reflected horizontal (vertical) linearly polarized waves. We used the Fabry-Perot multi-interference theory to further verify the metasurface model. The theoretical predictions are in good agreement with the numerical simulation results. In addition, the designed metasurface reflective linear polarization conversion characteristics can be dynamically adjusted by changing the Fermi energy and electron relaxation time of graphene. Therefore, our designed graphene-based tunable metasurface polarization converter is expected to have potential application value in terahertz communication, sensing and terahertz spectroscopy.
Keywords: linear polarization converter    metasurface    graphene    interference theory

1 引言

2 单元结构设计和仿真

 图 1 超表面的设计方案。(a)，(b)单元结构的正视图和立体视图；(c)三维(3D)阵列结构 Fig. 1 The design scheme of the metasurface. (a), (b) The front and perspective views of the unit-cell structure; (c) Three dimen-sional (3D) array structure

 ${\mu _{\rm{c}}} = \mathit{ћ}{v_{\rm{F}}}\sqrt {\frac{{{\rm{ \mathsf{ π} }}{\varepsilon _0}{\varepsilon _{\rm{r}}}{V_{\rm{g}}}}}{{e{t_{\rm{s}}}}}}$ (1)

 $\begin{array}{l} {\sigma _{\rm{g}}}\left( {\omega, {\mu _{\rm{c}}}, \tau , T} \right) \approx \text{j}\frac{{{e^2}{\kappa_{\rm{B}}}T}}{{{\rm{ \mathsf{ π} }}{\mathit{ћ}^2}\left( {\omega + {\rm{j}}{\tau ^{ - 1}}} \right)}}\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \times \left( {\frac{{{\mu _{\rm{c}}}}}{{{\kappa_{\rm{B}}}T}} + 2\ln \left( {\exp \left( { - \frac{{{\mu _{\rm{c}}}}}{{{\kappa_{\rm{B}}}T}}} \right) + 1} \right)} \right), \end{array}$ (2)

 图 2 在固定的驰豫时间τ=1.0 ps时不同μc下电导率的(a)实部和(b)虚部 Fig. 2 The (a) real part and (b) imaginary part of the conductivity with fixed relaxation time τ=1.0 ps under different μc

 图 3 在固定的化学势μc=0.9 eV时不同τ下电导率的(a)实部和(b)虚部 Fig. 3 The (a) real part and (b) imaginary part of the conductivity with fixed μc=0.9 eV under different τ

 $\begin{array}{l} {r_{xx}} = \left| {E_x^{\rm{r}}} \right|/\left| {E_x^{\rm{i}}} \right|, {r_{yx}} = \left| {E_y^{\rm{r}}} \right|/\left| {E_x^{\rm{i}}} \right|, \\ {r_{xy}} = \left| {E_x^{\rm{r}}} \right|/\left| {E_y^{\rm{i}}} \right|, {r_{yy}} = \left| {E_y^{\rm{r}}} \right|/\left| {E_y^{\rm{i}}} \right| 。\end{array}$

 $\begin{array}{l} {\gamma _x} = {\left| {{r_{yx}}} \right|^2}/\left( {{{\left| {{r_{yx}}} \right|}^2} + {{\left| {{r_{xx}}} \right|}^2}} \right), \\ {\gamma _y} = {\left| {{r_{xy}}} \right|^2}/\left( {{{\left| {{r_{xy}}} \right|}^2} + {{\left| {{r_{yy}}} \right|}^2}} \right), \end{array}$

3 结果分析和讨论 3.1 仿真结果分析

 图 4 设计的超表面在τ=1.0 ps, μc=0.9 eV下仿真的(a)反射系数和(b)偏振转换率 Fig. 4 The simulated reflection coefficients (a) and γx(y) (b) of the designed metasurface with τ =1.0 ps, μc=0.9 eV

3.2 物理机制分析

 $\begin{array}{l} \;{\mathit{\pmb{E}}_{\rm{i}}} = \left( {{\mathit{\pmb{E}}_{{\rm{i}}u}}{\mathit{\pmb{e}}_u} + {\mathit{\pmb{E}}_{{\rm{i}}v}}{\mathit{\pmb{e}}_v}} \right){\text{e}^{{\rm{i}}\left( { - kz + \omega t} \right)}}, \\ {\mathit{\pmb{E}}_{\rm{r}}} = \left( {{r_u}{\mathit{\pmb{E}}_{{\rm{i}}u}}{\mathit{\pmb{e}}_u} + {r_v}{\mathit{\pmb{E}}_{{\rm{i}}v}}{\mathit{\pmb{e}}_v}} \right){\text{e}^{{\rm{i}}\left( {kz + \omega t} \right)}}, \end{array}$
 图 5 (a) 线偏振波与超表面单元结构相互作用后的电场矢量分解示意图；(b), (c)分别为表层结构在谐振频点1.04 THz和1.28 THz处的表面电流密度分布。其中黑色的粗线箭头表示电流流动方向 Fig. 5 (a) Schematic diagram of electric field vector decomposition after interaction of linearly polarized waves and unit-cell structure of metasurface; (b), (c) are the surface current density distributions of front layer surface structures at resonance frequencies of 1.04 THz and 1.28 THz, respectively. Where the thick black arrow indicates the direction of current flow

3.3 干涉理论模型

 图 6 在法布里-佩罗谐振腔中x轴偏振波传播的示意图 Fig. 6 Schematic sketch of the x-pol. wave propagation in a Fabry-Perot like resonance cavity

 ${r_{yx}} = {\vec r_{yx}} + \sum\limits_{j = 1}^\infty {{r_{yj}}} , {r_{xx}} = {\vec r_{xx}} + \sum\limits_{j = 1}^\infty {{r_{xj}}} \circ$

 图 7 设计的超表面在τ=1.0 ps, μc=0.9 eV时正入射x轴偏振波的仿真和计算得到的(a)反射系数和(b)偏振转换效率(γx) Fig. 7 The simulated and calculated (a) reflection coefficients and (b) γx of the designed metasurface with τ=1.0 ps, μc=0.9 eV under normal incident x-pol. wave
3.4 不同费米能级和驰豫时间下的偏振转换特性

 图 8 设计的超表面在固定的驰豫时间τ =1.0 ps时正入射x轴偏振波下不同μc时的(a)仿真和(b)计算得到的偏振转换效率(γx) Fig. 8 The (a) simulated and (b) calculated γx of the designed metasurface with fixed relaxation time τ =1.0 psand different μc under normal incident -pol. wave

 图 9 设计的超表面在固定的费米能级μc=0.9 eV时正入射x轴偏振波下不同τ时的(a)仿真和(b)计算得到的偏振转换效率(γx) Fig. 9 The (a) simulated and (b) calculated γx of the designed metasurface with the fixed μc=0.9 eV and different τ under normal incident x-pol. wave

4 总结