Abstract

The chiroptical response of the chiral metasurface can be characterized by circular dichroism, which is defined as the absorption difference between left-handed circularly polarized incidence and right-handed circularly incidence. It can be applied in biology, chemistry, optoelectronics, etc. Here, we propose a dynamically tunable chiral metasurface structure, which is composed of two metal split-ring resonators and a graphene layer embedded in dielectric. The structure reflects right-handed circularly polarized waves and absorbs left-handed circularly polarized waves under normal incidence. The overall unit structural parameters of the chiral metasurface were discussed and analyzed, and the circular dichroism was 0.85 at 1.181 THz. Additionally, the digital imaging function can be realized based on the chiral metasurface structure, and the resolution of terahertz digital imaging can be dynamically tuned by changing the Fermi level of graphene. The proposed structure has potential applications in realizing tunable dynamic imaging and other communication fields.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Traditionally, gratings, crystals and liquid crystals can be used to regulate the polarization state of electromagnetic waves [1], although they are bulk materials with large footprints that cannot meet the requirements of device integration and miniaturization. With research on electromagnetic metasurfaces, chiral metasurfaces have been used to regulate the polarization of electromagnetic waves. Chiral refers to substances whose original structural unit does not overlap with its mirror image after translation, rotation, etc. [2,3], and the different absorption between left-handed circularly polarized (LCP) waves and right-handed circularly polarized (RCP) waves can be characterized by circular dichroism (CD) [4]. In nature, there are many chiral substances such as amino acids and DNA. The chirality of these natural substances is weak [5]. Compared to natural chiral substances, chiral metasurfaces have considerably stronger CD [6]. Therefore, they have been widely used to regulate the polarization of electromagnetic waves at the subwavelength scale, and many important achievements have been made in imaging displays, encryption, quantum information, biosensors and other fields [712]. Li et al. designed a sensitive chirality selective metamaterial absorber with dual bands by using ‘I-shaped’ resonator with asymmetric twisted metallic wires. The simulation results show that the absorption of LCP is as high as 95.18% at 12.04 GHz and 91.77% at 14.22 GHz, while little absorption of RCP. Besides, the absorber can apply in midinfrared band after adjusting parameters [13]. However, further development is limited by the untunability of static metasurfaces. Therefore, there are extensive application requirements for dynamically tunable chiral metasurfaces in many fields, such as dynamic polarization regulation, signal tuning, and focusing. [1417]. Graphene is a novel two-dimensional material with dynamic control capability [18,19]. Recently, by combining a metasurface with graphene, many dynamically controllable metasurfaces have been designed to achieve tunable polarization coding, polarization conversion, wave front control, full gray scale development and other applications [2024].

In this study, a dynamically tunable chiral metasurface with simple structure is proposed. The unit cell of the metasurface structure consists of a metal layer at the bottom, two metal split-ring resonators (SRRs) with a certain rotation angle at the top, and a graphene layer embedded in the dielectric layer. The influence of the unit cell parameters on the CD of this structure is discussed in detail. Dynamic terahertz digital imaging was realized by changing the Fermi levels of graphene using this chiral metasurface.

2. Structure design and theoretical analysis

A schematic diagram of the unit cell structure is illustrated in Fig. 1, the chiral metasurface is constructed by periodically arraying the unit cell. The period of the unit cell was denoted by PX and PY. The dielectric layer is polyimide with a thickness, ${d_2}$, where ${d_2} = d + {d_0}$, ${d_0} = 2 \times d$. The metal material of the bottom layer and SRRs is Au with a thickness, ${d_1}$. R1 is the outer radius of the large split-ring resonator (SRR1), w1 is the distance of SRR1, and the small split-ring resonator (SRR2). where w is the width of the two SRRs. Gap1 and Gap2 are the split angles of SRR1 and SRR2, respectively, and β is the relative rotation angle between SRR1 and SRR2.

 figure: Fig. 1.

Fig. 1. Diagram of the chiral metasurface structure based on metal-graphene-dielectric.

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According to previous reports, the feasible manufacturing processes are as follows. Firstly, a bottom gold film is grown on a substrate (silicon) by thermal evaporation [25]. Then, a polyimide is covered on the bottom gold film by spin-coating and curing processes [26]. Secondly, monolayer graphene grown on copper foil through chemical vapor deposition (CVD) is transferred to the polyimide prepared in the previous step [27]. Then, form the second polyimide film by spin-coating and curing processes. Finally, Semiconductor process is used to fabricate a template of the top gold split-ring resonators, and cover it on the second polyimide. After sputter coating, remove the template to form the top gold split-ring resonators.

If a circularly polarized wave (CP) propagates along the z-axis, the Jones matrix connecting the complex amplitudes of the incident RCP, LCP electrical fields ($\textrm{E}_R^i$, $ \textrm{E}_L^i$) and reflected RCP, LCP electrical fields ($\textrm{E}_R^r,\textrm{E}_L^r$) can be represented as [2830]:

$$\left( {\begin{array}{{c}} {\textrm{E}_R^r}\\ {\textrm{E}_L^r} \end{array}} \right) = \left( {\begin{array}{{cc}} {{r_{ +{+} }}}&{{r_{ +{-} }}}\\ {{r_{ -{+} }}}&{{r_{ -{-} }}} \end{array}} \right)\left( {\begin{array}{{c}} {\textrm{E}_R^i}\\ {\textrm{E}_R^i} \end{array}} \right) = {R_{\rm circ}}\left( {\begin{array}{{c}} {\textrm{E}_R^i}\\ {\textrm{E}_L^i} \end{array}} \right),$$
where ${\textrm{r}_{ +{+} }}\; ({{\textrm{r}_{ -{-} }}} )\; \textrm{i}$s the co-polarization reflection coefficient under $\textrm{RCP}\; ({\textrm{LCP}} )$ incidence, and ${r_{ +{-} }}$ (${r_{ -{+} }}$) is the cross-polarization reflection coefficient under RCP (LCP) incidence. Because two linearly polarized waves (LP) with the same amplitude and a certain phase difference can be combined to form a circularly polarized light, when the incident wave is in the LP state, the relationship between incident liner electrical fields ($\textrm{E}_x^i$, $; \textrm{E}_y^i$) and reflection liner electrical fields ($\textrm{E}_x^r$, $ \textrm{E}_y^r$) can be expressed as follows:
$$\left( {\begin{array}{{c}} {\textrm{E}_x^r}\\ {\textrm{E}_y^r} \end{array}} \right) = \left( {\begin{array}{{cc}} {{r_{xx}}}&{{r_{xy}}}\\ {{r_{yx}}}&{{r_{yy}}} \end{array}} \right)\left( {\begin{array}{{c}} {\textrm{E}_x^i}\\ {\textrm{E}_y^i} \end{array}} \right) = {R_{\rm line}}\left( {\begin{array}{{c}} {\textrm{E}_x^i}\\ {\textrm{E}_y^i} \end{array}} \right),$$
where ${r_{xx}}({{r_{yy}}} )$ and $ {r_{xy}}({{r_{yx}}} )$ represent the co-polarization reflection coefficient and cross-polarization reflection coefficient under LP incidence, respectively. Combining Eqs. (1) and (2) and the normalized basis matrix $\mathrm{\Lambda } = \frac{1}{{\sqrt 2 }}\left( {\begin{array}{{cc}} 1&1\\ \textrm{i}&{ - \textrm{i}} \end{array}} \right)$ [29], we obtain [31]:
$${R_{\rm circ}} = \left( {\begin{array}{{cc}} {{r_{ +{+} }}}&{{r_{ +{-} }}}\\ {{r_{ -{+} }}}&{{r_{ -{-} }}} \end{array}} \right) = {\mathrm{\Lambda }^{ - 1}}{R_{\rm line}}\mathrm{\Lambda } = \frac{1}{2}\left( {\begin{array}{{cc}} {{r_{xx}} + {r_{yy}} + \textrm{i}({{r_{xy}} - {r_{yx}}} )}&{{r_{xx}} - {r_{yy}} - \textrm{i}({{r_{xy}} + {r_{yx}}} )}\\ {{r_{xx}} - {r_{yy}} + \textrm{i}({{r_{xy}} + {r_{yx}}} )}&{{r_{xx}} + {r_{yy}} - \textrm{i}({{r_{xy}} - {r_{yx}}} )} \end{array}} \right).$$

As a tunable part of the chiral metasurface, graphene is a good material that can be dynamically tuned in the terahertz band. By random phase approximation (RPA) [32,33], the conductivity of graphene can be expressed by the Kubo formula, which consists of inter-band and intra-band conductivity [34,35]:

$$\sigma (\omega )= \frac{{i{e^2}}}{{\pi {\hbar ^2}}}\frac{{{E_F}}}{{\omega + i{\tau ^{ - 1}}}} - \frac{{i{e^2}}}{{4\pi {\hbar ^2}}}\ln \left[ {\frac{{2{E_F} + \hbar ({\omega + i{\tau^{ - 1}}} )}}{{2{E_F} - \hbar ({\omega + i{\tau^{ - 1}}} )}}} \right],$$
where $\hbar $ is the reduced Planck constant, $\omega $ is the angular frequency, ${E_\textrm{F}}$ is the Fermi level, $\tau = \mu {E_F}/({eV_\textrm{f}^2} )$ is the carrier relaxation time, $\mu $ is the carrier mobility, and ${V_\textrm{F}}$ is the Fermi velocity. In the terahertz band, with the condition of the low frequency limit $(\hbar \omega < 2{E_\textrm{F}})$ [36], the conductivity is dominated by the intra-band response, and the weak response of the inter-band can be ignored, thus, the conductivity can be simplified as [37]:
$$\sigma (\omega )= \frac{{i{e^2}}}{{\pi {\hbar ^2}}}\frac{{{E_F}}}{{\omega + i{\tau ^{ - 1}}}}.$$

From Eq. (5), the conductivity of graphene can be influenced by $ {E_\textrm{F}}$. The relationship between ${E_\textrm{F}}\; $and the voltage bias V can be expressed as ${E_\textrm{F}} = \hbar {V_\textrm{F}}\sqrt {\frac{{\pi {\varepsilon _0}{\varepsilon _r}V}}{{e{d_2}}}} $, where ${\varepsilon _0}$ is the permittivity of free space, ${\varepsilon _r}$ is the relative permittivity, and ${d_2}$ is the thickness of the polyimide.

3. Simulation and discussion

To evaluate the CD of the proposed chiral metasurface, numerical simulations of a unit cell were performed using frequency domain solver of the electromagnetic simulation software, CST Studio Suite. The graphene is regarded as a two-dimensional layer and we use surface impedance to model it. In the three-dimensional simulations, unit cell is applied in the x and y directions while the open (add space) boundary conditions are imposed at the boundaries in z direction. The simulation parameters were as follows: ${P_X} \times {P_Y} = 65\;\mu \textrm{m} \times 65\;\mu \textrm{m}$, ${d_1} = 0.2\;\mu \textrm{m}$, ${d_2} = 36\;\mu \textrm{m}$, ${R_1} = 24\;\mu \textrm{m}$, $w = 4\;\mu \textrm{m}$, ${w_1} = 2\;\mu \textrm{m}$, $\beta = 45^\circ $, ${\rm Gap_1} = 55^\circ$, ${\rm Gap_2} = 65^\circ$, the conductivity of the Au is $4.56 \times {10^7}S \cdot {m^{ - 1}}$ and taken from [38], the dielectric constant of polyimide is $\varepsilon = 3.5 + 0.00945\textrm{i}$ [39], and the relaxation time and Fermi level of graphene are set to $\tau = 1\textrm{ps}$ and ${E_\textrm{F}} = 1.0\textrm{eV}$ [40]. The simulated chiral response results are presented in Fig. 2. Figure 2(a) shows the simulated results for the reflectivity of the chiral metasurface. The cross-polarized reflectance ${R_{ -{+} }}$ and ${R_{ +{-} }}$ of RCP and LCP are equal over the entire operating frequency range, whereas the co-polarized reflectance ${R_{ +{+} }}$ and ${R_{ -{-} }}$ of RCP and LCP are different. When $f = 1.181$ THz, the metasurface reflected most of the RCP wave but suppressed the reflection of the LCP wave. Figure 2(b) shows the simulated results for the absorptivity and CD of the chiral metasurface. It can be observed that the CD is 0.85, when the frequency of the incident wave is 1.181 THz. Here, the CD is defined as the absorption difference of different circular polarization waves, that is, $CD = {A_{LCP}}$-${A_{RCP}}$, where ${A_{LCP}} = 1 - {R_{ -{-} }} - {R_{ +{-} }}$ is the absorption of the LCP wave and ${A_{RCP}} = 1 - {R_{ +{+} }} - {R_{ -{+} }}$ is the absorption of the RCP wave. To understand the mechanism of circular dichroism more clearly, we simulated the electric field distribution ($|E |$) and surface current density at the resonant frequency of SRRs structure under LCP and RCP waves, as shown in Figs. 2(c)–2(f). When the incident wave is RCP, there is a monopole resonance on one side of the two SRRs, while the incident wave is LCP, the two SRRs produce ring dipole resonance and there is a strong coupling between them. Through the surface current distribution of SRRs in Figs. 2(e) and 2(f), we find that when the incident wave is RCP, the two SRRs are in phase, while the incident wave is LCP, they are out phase. This difference in the electric field and surface current distributions is an essential reason for the CD.

 figure: Fig. 2.

Fig. 2. Chiral response of the metasurface under the incident wave is LCP and RCP. Reflectivity (a), absorption and CD (b) under the incident wave is LCP and RCP, respectively. Electric field distribution ($|E |$) (c) and (d) and surface currents (e) and (f) at 1.181THz of SRRs structure under LCP and RCP waves, respectively.

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We further evaluate the influences of the unit-cell parameters on the chiral response, and the simulation results are shown in Fig. 3. Except for the parameter being discussed, the other parameters are the same as those used in Fig. 2. To study the influence of the polyimide thickness ${d_2}$ on the CD, the CD at different thickness ${d_2}$ was calculated, and the results are shown in Fig. 3(a). It can be observed that the CD increases first when ${d_2}$ increases from 24 µm to 36 µm and then decreases when ${d_2}$ is further increased. And the resonance frequency exhibits the blueshift as ${d_2}\; $increases from 24 µm to 48 µm. This is due to an increase of the effective thickness of the F-P resonator, which consists of a graphene layer and the Au layer on the bottom. Additionally, the surface SRRs can be equivalent to an L-C circuit [41]. The influences of the parameters of the SRRs on the CD are calculated and shown in Figs. 3(b)–3(f). In Fig. 3(b), the CD at different relative rotation angles β between SRR1 and SRR2 are calculated. It shows that the CD reaches a maximum when β=45°, and gradually decreases to 0 as β increases. Figure 3(c) shows the results for the CD with different widths of the two SRRs. When w increases from 2 µm to 8 µm, the CD increases first and then decreases, and reaches a maximum when the width is 4 µm. Additionally, the resonance frequency increases with an increase in w, which depicts a blueshift in the operating frequency range. Because the L-C resonance frequency is inversely proportional to the inductance and capacitance introduced by SRRs. Increasing the width decreases the induced current density and inductance, resulting in a higher frequency. Figure 3(d) shows the results for the CD with different distances of SRR1 and SRR2, the resonance frequency increases as w1 increases, which indicates a blueshift. Moreover, the CD reaches a maximum when w1 = 2 µm. Figures 3(e)–3(f) show the simulated results of the CD with different spilt angles Gap1 and Gap2 of SRR1 and SRR2. The change in Gap1 had a slight effect on the CD, as shown in Fig. 3(e). The resonance frequency exhibits the blueshift as Gap2 increases, as can be observed in Fig. 3(f). Additionally, the CD reaches a maximum when $\textrm{Gap}_1 = {55^\circ }$, $\textrm{Gap}_2 = {65^\circ }$. The two split gaps can be equivalent to the capacitances of the L-C circuit and both sides of the split gaps will accumulate positive and negative charges and form capacitors. The charging and discharging capacity of the capacitor is affected by the distance between the upper and lower electrodes of the capacitor [17]. Increasing the split gap causes the capacitance to decrease and the frequency of the absorption peak to increase.

 figure: Fig. 3.

Fig. 3. Influence of different parameters on the CD of chiral metasurface. CD of chiral metasurface for different values of (a) d2, (b) β, (c) w, (d) w1, (e) gap1, and (f) gap2.

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To evaluate the tunability of the proposed chiral metasurface by changing the Fermi level (${E_\textrm{F}}$) of graphene, we further simulated the chiral response of the chiral metasurface under different ${E_\textrm{F}}$ values when the incident wave was LCP and RCP. The results are shown in Fig. 4. Figure 4(a) shows the simulated results of the absorptivity and CD of the chiral metasurface under different ${E_\textrm{F}}$ values of graphene. When the ${E_\textrm{F}}$ varies from 0.4 eV to 1.0 eV, it mainly affects the absorption of the RCP wave, whereas the absorption of the LCP wave is barely affected. This leads to an increase in the CD from 0.68 to 0.85. Figures 4(b)–4(e) show the simulated results of the electric field distribution of the chiral metasurface under different ${E_\textrm{F}}$ values of graphene when the incident wave is LCP and RCP. It can be observed that with the increase in ${E_\textrm{F}}$, the resonance of the SRRs decreases when the normal incidence wave is RCP, whereas the resonance is always in a strong state when the normal incidence wave is LCP. This further illustrates the relationship between the graphene and chiral metasurface resonance. Figures 4(f)–4(i) show the electric field distribution of the cross section at a resonance frequency of 1.181 THz. It can be observed that when ${E_\textrm{F}} = 0.4\; \textrm{eV}$, the energy permeates from the graphene to the underlying dielectric layer and is distributed in the dielectric layer and SRRs. With an increase in ${E_\textrm{F}}$, the graphene changes from a dielectric state to a metallic state [17], and acts as a “thin metal”. The energy is reflected off the graphene and is zero in the underlying dielectric layer.

 figure: Fig. 4.

Fig. 4. Chiral response of the chiral metasurface under different ${E_\textrm{F}}$ when incident wave is LCP and RCP. (a) Absorptivity and CD of the chiral metasurface under different $ {E_\textrm{F}}$. (b)-(e) Surface electric field distribution ($|E |$) at 1.181 THz of SRRs structure at different ${E_\textrm{F}}$ when incident wave is LCP and RCP, respectively. (f)-(i) Electric field distribution ($|E |$) of the cross section (x-z plane, y = −5 µm) at different ${E_\textrm{F}}$ when the resonance frequency is 1.181THz, respectively.

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In addition to the normal-incidence CP wave, the absorption and CD of the chiral metasurface at different incident angles were evaluated, and the results are shown in Fig. 5. Figures 5(a1)–5(b3) show the simulated results of the absorption and CD of the chiral metasurface when the incident angles θ of the CP wave range from $- 60^\circ $ to $60^\circ $ in the x-z plane and y-z plane; it has obvious absorption differences and maintains good CD quality. When θ reaches 60°, the absorption of the LCP exceeds 80% in the x-z plane and 70% in the y-z plane. Even at large incident angles, indicating that the chiral metasurface has good wide-angle absorption performance. The absorption has a slight red and blue shift when incident at a larger angle because both the mirror and rotational symmetry are broken simultaneously. Additionally, when the incident angle θ was maintained at $20^\circ $, we further evaluated the absorption and CD of the chiral metasurfaces by rotating the direction of the incident, that is, at different polar angles φ. The simulated results are shown in Figs. 5(c1)–fu5(c3) that the CD remains stable at any polar angle φ.

 figure: Fig. 5.

Fig. 5. Absorption and CD of the chiral metasurface at different incidence angles ($\theta $) and polarization angles when the incident wave is LCP and RCP. (a1)–(a3) Absorption and CD of the chiral metasurface when incident angles ($\theta $) are in the x-z plane, respectively. (b1)–(b3) Absorption and CD of the chiral metasurface when incident angles ($\theta $) are in the y-z plane, respectively. (c1)–(c3) When the incident angle θ is maintained at ${20^\circ }$, the absorption and CD of the chiral metasurface at any polarization angle.

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Based on the previous analysis, for the incident wave at different CP states, the chiral metasurface could reflect the RCP wave and absorb the LCP wave. Figure 6 shows a simple application of the chiral metasurface in near-field digital imaging, in which the unit cell is arrayed as 16 × 16 and the structures in quadrants 1 and 3 are mirror images of the original structures in quadrants 2 and 4, as shown in Fig. 6(a). The response of the CP wave is different and complementary between the original and mirror of the unit cell. According to the distribution of the quadrants, we mark the quadrants that have weak electric field distribution with “0” and mark the strong quadrants with “1”. Figures 6(c) and 6(e) show the simulated results that when ${E_\textrm{F}} = 1.0\textrm{eV}$, the digital images of “0101”and “1010” are displayed clearly under the incident wave of RCP and LCP, respectively. When we tune ${E_\textrm{F}}$ to 0.4 eV, the display resolution of the near-field digital imaging becomes blurred, as shown in Figs. 6(b) and 6(d). This method has potential applications in image encryption. Additionally, a 0–2π Pancharatnam-Berry (PB) phase delay can be achieved when the SRRs are rotated by a certain angle, and the PB phase delay of the LCP wave is unchanged at different Fermi levels with the rotation of the SRRs. Thus, the chiral metasurface can be potentially used for tunable applications such as vortex focusing, beam splitting, and holography.

 figure: Fig. 6.

Fig. 6. Unit-cell for dynamic terahertz near-field digital imaging. (a) Array diagram of the unit-cell. (b)–(e) Near-field distributions of array structure when ${E_\textrm{F}} = 0.4\; \textrm{eV}$ and ${E_\textrm{F}} = 1.0\; \textrm{eV}$, respectively.

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4. Conclusion

In summary, a dynamically tunable chiral metasurface based on metal-graphene-dielectric was proposed by analyzing the chiral theory and theoretical model of graphene. The effects of the unit-cell parameters, incident angle, and Fermi levels of graphene on CD were then discussed, and the circular dichroism was 0.85 at 1.181 THz. Additionally, it was shown that the reflection and CD could be tuned by changing the Fermi level of graphene. Therefore, we arrayed a unit structure to achieve dynamic THz near-field digital imaging. Further, it has potential applications in vortex focusing and holography.

Funding

National Key Research and Development Program of China (2019YFB2203904); National Natural Science Foundation of China (62075047, 61965006, 61975038, 6194005, 62065006); Natural Science Foundation of Guangxi Province (2020GXNSFDA297019, 2020GXNSFAA238040, 2021GXNSFAA075012, 2019GXNSFAA245024, 2020GXNSFBA159059, 2018GXNSFAA281272); Science and Technology Major Project of Guangxi (AD19245064); Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (YQ20107, YQ19108); the Innovation Project of GUET Graduate Education (2020YCXS089).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data of the conductivity of Au underlying the results presented in this paper are available in Ref. [38]. Data of the dielectric constant of polyimide underlying the results presented in this paper are available in Ref. [39]. Data of the relaxation time and Fermi level of graphene underlying the results presented in this paper are available in Ref. [40].

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26. S. Liu, H. Zhang, L. Zhang, Q. Yang, Q. Xu, J. Gu, Y. Yang, X. Zhou, J. Han, Q. Cheng, W. Zhang, and T. Cui, “Full-state controls of terahertz waves using tensor coding metasurfaces,” ACS Appl. Mater. Interfaces 9, 21503–21514 (2017). [CrossRef]  

27. H. Yan, Z. Li, X. Li, W. Zhu, P. Avouris, and F. Xia, “Infrared spectroscopy of tunable dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012). [CrossRef]  

28. E. Plum, V. A. Fedotov, and N. I. Zheludev, “Extrinsic electromagnetic chirality in metamaterials,” J. Opt. A: Pure Appl. Opt. 11, 074009 (2009). [CrossRef]  

29. M. Mutlu and E. Ozbay, “A transparent 90° polarization rotator by combining chirality and electromagnetic wave tunneling,” Appl. Phys. Lett. 100, 051909 (2012). [CrossRef]  

30. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108, 213905 (2012). [CrossRef]  

31. C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced Jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82, 053811 (2010). [CrossRef]  

32. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008). [CrossRef]  

33. K. F. Mak, M. Y. Sfeir, Y. Wu, C. Lui, J. A. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008). [CrossRef]  

34. S. A. Mikhailov and K. Ziegler, “A new electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007). [CrossRef]  

35. C. Qiu, W. Gao, V. Robert, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 µm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14, 6811–6815 (2014). [CrossRef]  

36. J. Li, J. Tao, Z. Chen, and X. Huang, “All-optical controlling based on nonlinear graphene plasmonic waveguides,” Opt. Express 24, 22169–22176 (2016). [CrossRef]  

37. S. Luo, B. Li, A. Yu, J. Gao, X. Wan, and D. Zuo, “Broadband tunable terahertz polarization converter based on graphene metamaterial,” Opt. Commun. 413, 184–189 (2018). [CrossRef]  

38. J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Broadband terahertz absorber with a flexible, reconfigurable performance based on hybrid-patterned vanadium dioxide metasurfaces,” Opt. Express 28, 17832–17840 (2020). [CrossRef]  

39. J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam–Berry coding metasurfaces,” Nanoscale 11, 5746–5753 (2019). [CrossRef]  

40. Q. Li, Z. Tian, X. Zhang, R. Singh, L. Du, J. Gu, J. Han, and W. Zhang, “Active graphene–silicon hybrid diode for terahertz waves,” Nat. Commun. 6, 7082 (2015). [CrossRef]  

41. M. Ricardo, M. Francisco, J. Martel, and M. Francisco, “Comparative analysis of edge- and broadside coupled split ring resonators for metamaterial design—theory and experiments,” IEEE Trans. Antennas Propagat. 51, 2572–2581 (2003). [CrossRef]  

References

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    [Crossref]
  27. H. Yan, Z. Li, X. Li, W. Zhu, P. Avouris, and F. Xia, “Infrared spectroscopy of tunable dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
    [Crossref]
  28. E. Plum, V. A. Fedotov, and N. I. Zheludev, “Extrinsic electromagnetic chirality in metamaterials,” J. Opt. A: Pure Appl. Opt. 11, 074009 (2009).
    [Crossref]
  29. M. Mutlu and E. Ozbay, “A transparent 90° polarization rotator by combining chirality and electromagnetic wave tunneling,” Appl. Phys. Lett. 100, 051909 (2012).
    [Crossref]
  30. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108, 213905 (2012).
    [Crossref]
  31. C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced Jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82, 053811 (2010).
    [Crossref]
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    [Crossref]
  33. K. F. Mak, M. Y. Sfeir, Y. Wu, C. Lui, J. A. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
    [Crossref]
  34. S. A. Mikhailov and K. Ziegler, “A new electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
    [Crossref]
  35. C. Qiu, W. Gao, V. Robert, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 µm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14, 6811–6815 (2014).
    [Crossref]
  36. J. Li, J. Tao, Z. Chen, and X. Huang, “All-optical controlling based on nonlinear graphene plasmonic waveguides,” Opt. Express 24, 22169–22176 (2016).
    [Crossref]
  37. S. Luo, B. Li, A. Yu, J. Gao, X. Wan, and D. Zuo, “Broadband tunable terahertz polarization converter based on graphene metamaterial,” Opt. Commun. 413, 184–189 (2018).
    [Crossref]
  38. J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Broadband terahertz absorber with a flexible, reconfigurable performance based on hybrid-patterned vanadium dioxide metasurfaces,” Opt. Express 28, 17832–17840 (2020).
    [Crossref]
  39. J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam–Berry coding metasurfaces,” Nanoscale 11, 5746–5753 (2019).
    [Crossref]
  40. Q. Li, Z. Tian, X. Zhang, R. Singh, L. Du, J. Gu, J. Han, and W. Zhang, “Active graphene–silicon hybrid diode for terahertz waves,” Nat. Commun. 6, 7082 (2015).
    [Crossref]
  41. M. Ricardo, M. Francisco, J. Martel, and M. Francisco, “Comparative analysis of edge- and broadside coupled split ring resonators for metamaterial design—theory and experiments,” IEEE Trans. Antennas Propagat. 51, 2572–2581 (2003).
    [Crossref]

2020 (5)

X. Mao, Y. Hang, Y. Zhou, J. Zhu, Q. Ren, J. Zhuo, and Y. Cai, “Probing composite vibrational fingerprints in the terahertz range with graphene split ring resonator,” IEEE Photonics J. 12, 1–8 (2020).
[Crossref]

F. Li, T. Tang, Y. Mao, L. Luo, J. Li, J. Xiao, K. Liu, J. Shen, C. Li, and J. Yao, “Metal–graphene hybrid chiral metamaterials for tunable circular dichroism,” Ann. Phys. 532, 2000065 (2020).
[Crossref]

J. Li, J. Li, C. Zheng, S. Wang, M. Li, H. Zhao, J. Li, Y. Zhang, and J. Yao, “Dynamic control of reflective chiral terahertz metasurface with a new application developing in full grayscale near field imaging,” Carbon 172, 189–199 (2020).
[Crossref]

J. Li, J. Li, Y. Yang, J. Li, Y. Zhang, L. Wu, Z. Zhang, M. Yang, C. Zheng, J. Li, J. Huang, F. Li, T. Tang, H. Dai, and J. Yao, “Metal-graphene hybrid active chiral metasurfaces for dynamic terahertz wave front modulation and near field imaging,” Carbon 163, 34–42 (2020).
[Crossref]

J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Broadband terahertz absorber with a flexible, reconfigurable performance based on hybrid-patterned vanadium dioxide metasurfaces,” Opt. Express 28, 17832–17840 (2020).
[Crossref]

2019 (4)

J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam–Berry coding metasurfaces,” Nanoscale 11, 5746–5753 (2019).
[Crossref]

D. Chen, J. Yang, J. Huang, W. Bai, J. Zhang, Z. Zhang, S. Xu, and W. Xie, “The novel graphene metasurfaces based on split-ring resonators for tunable polarization switching and beam steering at terahertz frequencies,” Carbon 154, 350–356 (2019).
[Crossref]

L. Wang, X. Huang, M. Li, and J. Dong, “An ultra-thin chiral metamaterial absorber with high selectivity for LCP and RCP waves,” Opt. Express 27, 25983–25993 (2019).
[Crossref]

H.-X. Xu, G. Hu, Y. Li, L. Han, J. Zhao, Y. Sun, F. Yuan, G. Wang, Z. Jiang, X. Ling, T. Cui, and C. Qiu, “Interference-assisted kaleidoscopic meta-plexer for arbitrary spin-wave front manipula-tion,” Light: Sci. Appl. 8, 3 (2019).
[Crossref]

2018 (2)

S. Luo, B. Li, A. Yu, J. Gao, X. Wan, and D. Zuo, “Broadband tunable terahertz polarization converter based on graphene metamaterial,” Opt. Commun. 413, 184–189 (2018).
[Crossref]

Q. Wang, E. Plum, Q. Yang, X. Zhang, Q. Xu, Y. Xu, J. Han, and W. Zhang, “Reflective chiral meta-holography: multiplexing holograms for circularly polarized waves,” Light: Sci. Appl. 7, 25 (2018).
[Crossref]

2017 (2)

S. Liu, H. Zhang, L. Zhang, Q. Yang, Q. Xu, J. Gu, Y. Yang, X. Zhou, J. Han, Q. Cheng, W. Zhang, and T. Cui, “Full-state controls of terahertz waves using tensor coding metasurfaces,” ACS Appl. Mater. Interfaces 9, 21503–21514 (2017).
[Crossref]

H. Jiang, W. Zhao, and Y. Jiang, “High-efficiency tunable circular asymmetric transmission using dielectric metasurface integrated with graphene sheet,” Opt. Express 25, 19732–19739 (2017).
[Crossref]

2016 (3)

J. Li, P. Yu, H. Cheng, W. Liu, Z. Li, B. Xie, S. Chen, and J. G. Tian, “Optical polarization encoding using graphene-loaded plasmonic metasurfaces,” Adv. Optical Mater. 4, 91–98 (2016).
[Crossref]

J. Li, J. Tao, Z. Chen, and X. Huang, “All-optical controlling based on nonlinear graphene plasmonic waveguides,” Opt. Express 24, 22169–22176 (2016).
[Crossref]

S. Xiao, X. Zhu, B. Li, and N. Asger Mortensen, “Graphene-plasmon polaritons: from fundamental properties to potential applications,” Front. Phys. 11, 117801 (2016).
[Crossref]

2015 (2)

S. S. Kruk, A. N. Poddubny, D. A. Powell, C. Helgert, M. Decker, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Polarization properties of optical metasurfaces of different symmetries,” Phys. Rev. B 91, 195401 (2015).
[Crossref]

Q. Li, Z. Tian, X. Zhang, R. Singh, L. Du, J. Gu, J. Han, and W. Zhang, “Active graphene–silicon hybrid diode for terahertz waves,” Nat. Commun. 6, 7082 (2015).
[Crossref]

2014 (5)

Y. Cui, L. Kang, S. Lan, S. Rodrigues, and W. Cai, “Giant chiral optical response from a twisted-arc metamaterial,” Nano Lett. 14, 1021–1025 (2014).
[Crossref]

M. Li, L. Guo, J. Dong, and H. Yang, “Chirality selective metamaterial absorber with dual bands,” J. Phys. D: Appl. Phys. 47, 185102 (2014).
[Crossref]

S. Mousavi, E. Plum, J. Shi, and N. I. Zheludev, “Coherent control of birefringence and optical activity,” Appl. Phys. Lett. 105, 011906 (2014).
[Crossref]

J. Shi, X. Fang, E. T. F. Rogers, E. Plum, K. F. MacDonald, and N. I. Zheludev, “Coherent control of Snell’s law at metasurfaces,” Opt. Express 22, 21051–21060 (2014).
[Crossref]

C. Qiu, W. Gao, V. Robert, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 µm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14, 6811–6815 (2014).
[Crossref]

2012 (4)

M. Mutlu and E. Ozbay, “A transparent 90° polarization rotator by combining chirality and electromagnetic wave tunneling,” Appl. Phys. Lett. 100, 051909 (2012).
[Crossref]

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108, 213905 (2012).
[Crossref]

H. Yan, Z. Li, X. Li, W. Zhu, P. Avouris, and F. Xia, “Infrared spectroscopy of tunable dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
[Crossref]

Z. Fang, Y. Wang, Z. Liu, A. Schlather, P. M. Ajayan, F. H. L. Koppens, P. Nordlander, and N. J. Halas, “Plasmon-induced doping of graphene,” ACS Nano 6, 10222–10228 (2012).
[Crossref]

2010 (1)

C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced Jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82, 053811 (2010).
[Crossref]

2009 (2)

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Extrinsic electromagnetic chirality in metamaterials,” J. Opt. A: Pure Appl. Opt. 11, 074009 (2009).
[Crossref]

M. Decker, M. Ruther, C. E. Kriegler, J. Zhou, C. M. Soukoulis, S. Linden, and M. Wegener, “Strong optical activity from twisted-cross photonic metamaterials,” Opt. Lett. 34, 2501–2503 (2009).
[Crossref]

2008 (2)

R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. Lui, J. A. Misewich, and T. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

2007 (2)

S. A. Mikhailov and K. Ziegler, “A new electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76, 153410 (2007).
[Crossref]

2005 (1)

2003 (2)

J. Lub, P. van de Witte, C. Doornkamp, J. P. A. Vogels, and R. T. Wegh, “Stable photopatterned cholesteric layers made by photoisomerization and subsequent photopolymerization for use as color filters in liquid-crystal displays,” Adv. Mater. 15, 1420–1425 (2003).
[Crossref]

M. Ricardo, M. Francisco, J. Martel, and M. Francisco, “Comparative analysis of edge- and broadside coupled split ring resonators for metamaterial design—theory and experiments,” IEEE Trans. Antennas Propagat. 51, 2572–2581 (2003).
[Crossref]

2001 (1)

A. G. White, D. F. V. James, W. Munro, and P. Kwiat, “Exploring Hilbert space: accurate characterization of quantum information,” Phys. Rev. A 65, 012301 (2001).
[Crossref]

2000 (1)

B. Max and W. Emil, “Principles of optics: electromagnetic theory of propagation, interference and diffraction of light,” Phys. Today 53, 77–78 (2000).
[Crossref]

1988 (1)

Ajayan, P. M.

C. Qiu, W. Gao, V. Robert, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 µm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14, 6811–6815 (2014).
[Crossref]

Z. Fang, Y. Wang, Z. Liu, A. Schlather, P. M. Ajayan, F. H. L. Koppens, P. Nordlander, and N. J. Halas, “Plasmon-induced doping of graphene,” ACS Nano 6, 10222–10228 (2012).
[Crossref]

Akosman, A. E.

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108, 213905 (2012).
[Crossref]

Asger Mortensen, N.

S. Xiao, X. Zhu, B. Li, and N. Asger Mortensen, “Graphene-plasmon polaritons: from fundamental properties to potential applications,” Front. Phys. 11, 117801 (2016).
[Crossref]

Avouris, P.

H. Yan, Z. Li, X. Li, W. Zhu, P. Avouris, and F. Xia, “Infrared spectroscopy of tunable dirac terahertz magneto-plasmons in graphene,” Nano Lett. 12, 3766–3771 (2012).
[Crossref]

Bai, W.

D. Chen, J. Yang, J. Huang, W. Bai, J. Zhang, Z. Zhang, S. Xu, and W. Xie, “The novel graphene metasurfaces based on split-ring resonators for tunable polarization switching and beam steering at terahertz frequencies,” Carbon 154, 350–356 (2019).
[Crossref]

Bassiri, S.

Blake, P.

R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref]

Booth, T. J.

R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320, 1308 (2008).
[Crossref]

Cai, W.

Y. Cui, L. Kang, S. Lan, S. Rodrigues, and W. Cai, “Giant chiral optical response from a twisted-arc metamaterial,” Nano Lett. 14, 1021–1025 (2014).
[Crossref]

Cai, Y.

X. Mao, Y. Hang, Y. Zhou, J. Zhu, Q. Ren, J. Zhuo, and Y. Cai, “Probing composite vibrational fingerprints in the terahertz range with graphene split ring resonator,” IEEE Photonics J. 12, 1–8 (2020).
[Crossref]

Chen, D.

D. Chen, J. Yang, J. Huang, W. Bai, J. Zhang, Z. Zhang, S. Xu, and W. Xie, “The novel graphene metasurfaces based on split-ring resonators for tunable polarization switching and beam steering at terahertz frequencies,” Carbon 154, 350–356 (2019).
[Crossref]

Chen, S.

J. Li, P. Yu, H. Cheng, W. Liu, Z. Li, B. Xie, S. Chen, and J. G. Tian, “Optical polarization encoding using graphene-loaded plasmonic metasurfaces,” Adv. Optical Mater. 4, 91–98 (2016).
[Crossref]

Chen, Z.

Cheng, H.

J. Li, P. Yu, H. Cheng, W. Liu, Z. Li, B. Xie, S. Chen, and J. G. Tian, “Optical polarization encoding using graphene-loaded plasmonic metasurfaces,” Adv. Optical Mater. 4, 91–98 (2016).
[Crossref]

Cheng, Q.

S. Liu, H. Zhang, L. Zhang, Q. Yang, Q. Xu, J. Gu, Y. Yang, X. Zhou, J. Han, Q. Cheng, W. Zhang, and T. Cui, “Full-state controls of terahertz waves using tensor coding metasurfaces,” ACS Appl. Mater. Interfaces 9, 21503–21514 (2017).
[Crossref]

Cui, T.

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Data availability

Data of the conductivity of Au underlying the results presented in this paper are available in Ref. [38]. Data of the dielectric constant of polyimide underlying the results presented in this paper are available in Ref. [39]. Data of the relaxation time and Fermi level of graphene underlying the results presented in this paper are available in Ref. [40].

38. J. Huang, J. Li, Y. Yang, J. Li, J. Li, Y. Zhang, and J. Yao, “Broadband terahertz absorber with a flexible, reconfigurable performance based on hybrid-patterned vanadium dioxide metasurfaces,” Opt. Express 28, 17832–17840 (2020). [CrossRef]  

39. J. Li, Y. Zhang, J. Li, X. Yan, L. Liang, Z. Zhang, J. Huang, J. Li, Y. Yang, and J. Yao, “Amplitude modulation of anomalously reflected terahertz beams using all-optical active Pancharatnam–Berry coding metasurfaces,” Nanoscale 11, 5746–5753 (2019). [CrossRef]  

40. Q. Li, Z. Tian, X. Zhang, R. Singh, L. Du, J. Gu, J. Han, and W. Zhang, “Active graphene–silicon hybrid diode for terahertz waves,” Nat. Commun. 6, 7082 (2015). [CrossRef]  

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Figures (6)

Fig. 1.
Fig. 1. Diagram of the chiral metasurface structure based on metal-graphene-dielectric.
Fig. 2.
Fig. 2. Chiral response of the metasurface under the incident wave is LCP and RCP. Reflectivity (a), absorption and CD (b) under the incident wave is LCP and RCP, respectively. Electric field distribution ( $|E |$ ) (c) and (d) and surface currents (e) and (f) at 1.181THz of SRRs structure under LCP and RCP waves, respectively.
Fig. 3.
Fig. 3. Influence of different parameters on the CD of chiral metasurface. CD of chiral metasurface for different values of (a) d2, (b) β, (c) w, (d) w1, (e) gap1, and (f) gap2.
Fig. 4.
Fig. 4. Chiral response of the chiral metasurface under different ${E_\textrm{F}}$ when incident wave is LCP and RCP. (a) Absorptivity and CD of the chiral metasurface under different $ {E_\textrm{F}}$ . (b)-(e) Surface electric field distribution ( $|E |$ ) at 1.181 THz of SRRs structure at different ${E_\textrm{F}}$ when incident wave is LCP and RCP, respectively. (f)-(i) Electric field distribution ( $|E |$ ) of the cross section (x-z plane, y = −5 µm) at different ${E_\textrm{F}}$ when the resonance frequency is 1.181THz, respectively.
Fig. 5.
Fig. 5. Absorption and CD of the chiral metasurface at different incidence angles ( $\theta $ ) and polarization angles when the incident wave is LCP and RCP. (a1)–(a3) Absorption and CD of the chiral metasurface when incident angles ( $\theta $ ) are in the x-z plane, respectively. (b1)–(b3) Absorption and CD of the chiral metasurface when incident angles ( $\theta $ ) are in the y-z plane, respectively. (c1)–(c3) When the incident angle θ is maintained at ${20^\circ }$ , the absorption and CD of the chiral metasurface at any polarization angle.
Fig. 6.
Fig. 6. Unit-cell for dynamic terahertz near-field digital imaging. (a) Array diagram of the unit-cell. (b)–(e) Near-field distributions of array structure when ${E_\textrm{F}} = 0.4\; \textrm{eV}$ and ${E_\textrm{F}} = 1.0\; \textrm{eV}$ , respectively.

Equations (5)

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( E R r E L r ) = ( r + + r + r + r ) ( E R i E R i ) = R c i r c ( E R i E L i ) ,
( E x r E y r ) = ( r x x r x y r y x r y y ) ( E x i E y i ) = R l i n e ( E x i E y i ) ,
R c i r c = ( r + + r + r + r ) = Λ 1 R l i n e Λ = 1 2 ( r x x + r y y + i ( r x y r y x ) r x x r y y i ( r x y + r y x ) r x x r y y + i ( r x y + r y x ) r x x + r y y i ( r x y r y x ) ) .
σ ( ω ) = i e 2 π 2 E F ω + i τ 1 i e 2 4 π 2 ln [ 2 E F + ( ω + i τ 1 ) 2 E F ( ω + i τ 1 ) ] ,
σ ( ω ) = i e 2 π 2 E F ω + i τ 1 .

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