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Abstract
We propose a terahertz chiral metamaterial as a multi-functional device to manipulate asymmetry transmission of linear polarized waves, linear-to-elliptical polarization conversion and circular dichroism in transmission mode while asymmetry reflection of circular polarized waves. For incidence of linear polarized waves, dual-band asymmetry transmission is shown around 0.42 THz and 1.04 THz where asymmetry transmission factors reach up to two peak values: ∼0.51 and ∼0.55, respectively. Intense linear-to-elliptical polarization conversion occurs at 0.81 THz and 0.97 THz, respectively. For incidence of circular polarized waves, a strong circular dichroism appears at 0.36 THz where circular dichroism parameter reaches to ∼0.64 and asymmetry reflection is displayed around 0.36 THz with the maximum of asymmetry reflection factors approaching to 0.55.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fifth generation mobile communication technology (5G) has become ubiquitous and sixth generation mobile communication technology (6G) is around the corner, for this reason, people attach significance to develop terahertz communication [1–8]. Terahertz communication has more advantages than microwave communication with greater transmission capacity, better security and anti-jamming capability, more accurate positioning, more miniaturized and faster. The concept of metamaterial [9–13] has been proposed in 1860s. It is a kind of artificial composite material, which has been widely concerned for its dozens of unique electromagnetic effects, such as perfect absorption [14], unidirectional reflectionlessness [15–20], asymmetric transmission [4,21–30], linear-to-circular polarization conversion [31–34]. Metamaterial can be divided into three types, including anisotropy [35,36], bianisotropy [28,37] and chiral metamaterials (CMM) [38–45]. CMM is introduced to achieve a strong polarization conversion response. Chirality plays an important role in materials science which is defined as, object itself after rotating, translating or scaling in the plane mismatching its image perfectly.
So far, a great deal of schemes to realize polarization conversion have been increased [4,21–34]. Asymmetric transmission (AT) and reflective polarization conversion device in terahertz region have been theoretically demonstrated by changing the phase of vanadium dioxide [23]. In this case, broadband asymmetric transmission has been realized in the range of 2.023 THz$\sim$5.971 THz. While linear-to-circular polarization conversion has been achieved in the ranges 2.058 THz$\sim$3.423 THz and 4.753 THz$\sim$5.6 THz, and at 6.496 THz in reflection mode. A terahertz CMM is proposed to achieve dual-band dichroic asymmetric transmission of linear polarized waves [27]. In their scheme, the peak value of AT response arrives 0.6 while circular dichroism (CD) occurs with CD parameter below 0.3. An anisotropic metasurface is utilized to bring out polarization conversion of linear and linear-to-circular polarized waves in GHz domain [32]. In their work, the structure serving as a multi-functional metasurface makes cross-polarization conversion come true over a fractional bandwidth from 8 GHz to 11 GHz with more than 0.95 reflection coefficient while linear-to-circular polarization conversion achieve in two frequency bands of 7.5 GHz$\sim$7.7 GHz and 11.5 GHz$\sim$11.9 GHz. Multiband efficient AT is realized by introducing three resonators into metasurface [39]. There are three bands, 10.9 GHz$\sim$11.2 GHz, 14.4 GHz$\sim$14.8 GHz and 18.4 GHz$\sim$18.5 GHz, in which AT factor surpasses 0.8. The structures mentioned above can implement some specific polarization conversion functions independently, however, we would like to combine these superior performances to make a multi-functional and simple device.
In this work, a CMM is designed to manipulate AT of linear polarized waves, linear-to-elliptical polarization conversion, CD and asymmetry reflection (AR) of circular polarized waves in THz domain. Two J-shape-like resonators are putting forward to act as chiral structure. When linear polarizated waves strike in the CMM, dual-band AT arises around frequencies of 0.42 THz and 1.04 THz, respectively, and the maximum of AT factor reaches up to $\sim$0.55. A salient CD turns up at 0.36 THz with CD parameter reaching $\sim$0.64. When the incident waves are circular polarized waves, the maximum of AR is shown at 0.36 THz with asymmetry reflection factor exceeding 0.55.
2. Results and discussion
The unit cell of the CMM is shown in Fig. 1(a). Two resonators are embedded in polyimide, a lossy dielectric layer, whose permittivity is 2.93 with loss tangent of 0.044 [38]. Aluminium is selected as metal resonators with conductivity of $3.56\times 10^7$ S/m [38] and thickness of 0.2$\mu$m. Silicon dioxide is chosen as substrate with dielectric constant $\varepsilon =3.8$ [23]. The front and back resonators of the CMM are shown in Fig. 1 (b) and (c), respectively. The back resonator is obtained by rotating the front one $90^{\circ }$ clockwise then flipping $180^{\circ }$ along $y$ axis. The optimal parameters in our scheme are as follows: $d=65\mu$m, $p=70\mu$m, $h=30\mu$m, $a=78\mu$m, $m=75\mu$m, $n=37.5\mu$m and $w=8\mu$m. The boundary conditions are set up in a finite-integration package (CST Microwave Studio) with unit cell in $x$ and $y$ axes and open in $z$ axis for numerical simulation.
Fig. 1. (a) The perspective view of the unit cell and parameters. The sectional views of the front resonator (b) and the back resonator (c) and parameters.
The time evolution of electric fields associated with incident and transmitted waves can be written as [46]
Fig. 2 (a) displays transmission spectra $t_{ij}={\left | T_{ij} \right |^{2}} (i, j=x, y)$ for forward direction of co- and cross$-$ polarization components based on numerical simulation when linear polarized waves are incident. From the transmission spectra in Fig. 2 (a), we can see that $t_{yx}$ (red solid line) and $t_{xy}$ (blue solid line) reach to $\sim$0.54 and $\sim$0.45 around frequencies 0.42 THz and 1.04 THz, respectively. It is obvious that the dual-band AT appears. Furthermore, according to Eq.(3), we calculate the AT factors for forward direction of linear polarized waves, and plot the curves of AT factors versus frequency as shown in Fig. 2 (b). Fig. 2 (b) depicts that AT factors $\Delta ^{y}$ (black dash line) and $\Delta ^{x}$ (red solid line) are exactly opposite, and $\Delta ^{x}$ and $\Delta ^{y}$ reach up to the peak values $\sim$0.51 and $\sim$0.55 at 0.42 THz and 1.04THz, respectively. Therefore, strong dual-band AT phenomenon occurs around the frequencies 0.42 THz and 1.04 THz in our scheme.
Fig. 2. (a) The transmission spectra for forward direction of linear polarized incident waves based on numerical simulation. (b) AT factors for incidence of $x$ and $y$ polarized waves. (c) Polarization conversion ratios for incidence of $x$ and $y$ polarized waves. (d) Polarization rotation angle $\chi$ and ellipticity $\eta$ based on analytical calculation.
Polarization conversion ratio (PCR) is introduced to indicate the extent of polarization conversion of linear polarized waves [47], as
For purpose of investigating linear-to-elliptical polarization conversion in transmission mode, Stokes parameters are introduced to calculate polarization rotation angle $\chi$ and ellipticity $\eta$. They can be written as [48]:
The ellipticity $\eta >0$ represents left-handed circular polarized waves (LCP), $\eta <0$ indicates right-handed circular polarized waves (RCP), $\eta =0$ represents linear polarized waves and $\eta =\pm 1$ represents circular polarized waves. It is clearly shown in Fig. 2 (d), $\eta$ (blue dash line) reaches peak value of $\sim$0.27 at 0.81 THz with $\chi$ (black solid line) closing to $70^{\circ }$ which results in a stronger optical activity. Likewise, $\eta$ is close to $-$0.32 at 0.97 THz with $\chi$ near $-61^{\circ }$. In addition, linear-to-elliptical polarization conversion has been attained in our structure.
Next, we discuss the circular dichroism (CD) and polarization maintenance ratio (PMR) in our scheme. Usually, symbols + and $-$ are adopted to indicate RCP and LCP, respectively. Jones matrix $T^{f}_{circ}$ of circular polarized waves is associated with the components of $T^{f}_{lin}$ [49], as
Figs. 3 (a),(b) and (c) show the transmission spectra, CD parameter and PMR, respectively. In Figs. 3 (a), the transmission spectra of circular polarized waves are depicted. $t_{++} (t_{--})$ denotes the transmission of RCP (LCP) when RCP (LCP) is incident, while $t_{-+} (t_{+-})$ means the transmission of LCP (RCP) when RCP (LCP) is incident. From Figs. 3 (a), there is a large difference between $t_{++}$ and $t_{--}$ in transmittance at 0.36 THz. From Figs. 3 (b), there is a strong CD response closing to 0.64 at 0.36 THz.
Fig. 3. (a) The transmission spectra for forward direction of RCP and LCP based on numerical simulation. (b) Circular dichroism response of RCP and LCP. (c) Polarization maintenance ratios of RCP and LCP.
PMR$(t_{+(-)})$ indicates whether RCP (LCP) can maintain its own rotation when RCP (LCP) is incident. PMR$(t_{+(-)})$=1 and 0 indicate that when RCP (LCP) is incident in structure, LCP (RCP) and RCP (LCP) can not be transmitted, respectively. As depicted in Figs. 3 (c), PMR$(t_{+})$ and PMR$(t_{-})$ are both extend 0.9 in frequency of 0.2 THz$\sim$0.3 THz, which means that both RCP and LCP can maintain their own rotation very well. PMR$(t_{+})$ is verging on 0 at 0.37 THz which illustrates that RCP can not be transmitted.
In addition, we investigate the AR for forward of circular polarized incident waves in our scheme. Jones reflection matrix $R^{f}_{circ}$ of circular polarized waves is associated with the components of Jones reflection matrix $R^{f}_{lin}$ for linear polarized waves, as
Fig. 4. The reflection spectra for forward direction of circular polarized incident waves based on numerical simulation. Among them, $r_{ij}={\left | R_{ij} \right |^{2}}, (i,j=+,-)$. (b) AR factors of RCP and LCP.
In Fig. 4 (a), the refection spectra of circular polarized waves are depicted. $r_{++}$ (green dash line) denotes the reflection of RCP when RCP is incident, while $r_{--}$ (black dash dot line) represents the reflection of LCP when LCP is incident. $r_{-+}$ (red solid line) means the reflection of LCP when RCP is incident, while $r_{+-}$ (blue solid line) denotes the reflection of RCP when LCP is incident. It is obvious that, there are remarkable AR factors occurence when LCP and RCP are incident, as shown in Fig. 4 (b). According to Eq.(10), the AR factor $\Delta ^{-}$ (black dash line) and $\Delta ^{+}$ (red solid line) are $-$0.55 and +0.55, respectively, at 0.36 THz which are opposite with each other.
In order to explain the physical mechanism of AT, $z-$component surface current distributions for forward direction at 0.42 THz and 1.04 THz are shown in Figs. 5 (a-d) and (e-h), respectively. Compared Figs. 5 (a) with (b), hardly vertical magnetic field is excited at 0.42 THz when $y$ polarized waves are incident which causes a low value of $t_{xy}$ verging on 0. While horizontal magnetic field is excited at 0.42 THz when $x$ polarized waves are incident, as shown in Figs. 5 (c) and (d). It results a high value of $t_{yx}$ closing to 0.54. Compared Fig.5 (e) with (f), vertical magnetic field is excited at 1.04 THz when $y$ polarized waves come in that results in a value of $t_{xy}$ near 0.45. And hardly horizontal magnetic field is excited at 1.04 THz when $x$ polarized waves illuminate, causing a small value of $t_{yx}$ approaching to 0, as shown in Figs. 5(g) and (h). Therefore, cross$-$polarization phenomenon occurs at 0.42 THz and 1.04 THz, simultaneously. We explain more clearly about the emerging of polarization conversion according to surface current distributions in Figs. 5 (c) and (d). The electric and magnetic fields of front resonator and back resonator are depicted in Figs. 6 (a) and (b), respectively. On the basis of vector operation rule, the currents $I_{1}$, $I_{2}$ and $I_{3}$ of the front resonator can be merged to get direction of electric field in Fig. 6 (a). Fig. 6 (b) shows the direction of electric field of the back resonator. Because the magnetic field direction is determined by directions of electric field and wave vector (forward entry), the magnetic field directions of the front and back resonators can be depicted as Figs. 6 (a) and (b), respectively. Fig. 6 (c) is the combination display of the direction of incident electric field and orthogonal decompositions of magnetic fields for two resonators. It is clear that magnetic field components $H_{x1}$ and $H_{x2}$ are parallel to the direction of $x$ polarized waves which causes a polarization conversion.
Fig. 5. Surface current distributions on front and back resonators when linear polarized waves are incident for forward direction in AT case at frequencies of 0.42 THz (a-d) and 1.04 THz (e-h), respectively.
For the purpose of investigating AT of linear polarized incident waves, we plot transmission $t_{yx}$ and $t_{xy}$ as the functions of incident angle and frequency for forward direction in Fig. 7. As Fig. 7 (a) described, high $t_{yx}$ appears around 0.42 THz with the increase of $\theta$ from 0 to $60^{\circ }$. While as Fig. 7 (b) described in this frequency domain, transmission is nearly to zero. Fig. 7 (b) shows that $t_{xy}$ is high around 1.04 THz with the increase of $\theta$ from 0 to $70^{\circ }$, and has a blue shift. While as Fig. 7 (a) described in this frequency domain, transmission is nearly to zero. Compared Figs.7 (a) with (b), we know that dual band AT phenomenon are displayed in the wide range of incident angle $\theta$ from 0 to $60^{\circ }$. For the sake of exploring the physical mechanism of AR, $z-$component electrical field distributions of front and back resonators for forward direction at 0.36 THz are shown in Fig. 8. Compared Fig. 8 (a) with (b), symmetry modes are excited at 0.36 THz for LCP incident waves which lead induced currents in the same directions. It makes phase diference of resonators near 2$\pi$ which causes a low value of $r_{+-}$ closing to 0. Compared with Fig. 8 (c) and (d), asymmetry modes are excited at 0.36 THz for RCP incident waves which lead induced currents opposite. It makes phase diference of resonators near $\pi$ which results in a high value of $r_{-+}$ approaching to 0.55.
Fig. 6. Electric and magnetic fields according to surface current distributions (Figs. 5 (c) and (d)) of front resonator (a) and back resonator (b) at 0.42 THz. (c) The relationship between the incident electric field (${\rm {E}}_{in}$) and the component in $x$ direction of magnetic fields.
Fig. 7. $t_{yx}$ (a) and $t_{xy}$ (b) as the functions of incident angle $\theta$ and frequency for forward direction.
Fig. 8. Electric field distributions about front and back resonators when LCP (a,b) and RCP (c,d) are incident for forward direction in AR case at frequency of 0.36 THz.
For the purpose of investigating AR of circular polarized incident waves, we plot reflections $r_{-+}$ and $r_{+-}$ as the functions of incident angle and frequency for forward direction in Fig. 9. As Fig. 9 (a) described, high $r_{-+}$ appears around 0.36 THz with the increase of $\theta$ from 0 to $80^{\circ }$ and has a slight blue shift. Fig. 9 (b) shows that $r_{+-}$ is nearly zero around 0.36 THz with the increase of $\theta$ from 0 to $80^{\circ }$, and has a small blue shift. Compared Figs. 9 (a) with (b), we know that strong AR phenomenon is displayed in the wide range of incident angle $\theta$ from 0 to $80^{\circ }$.
Fig. 9. $r_{-+}$ (a) and $r_{+-}$ (b) as the functions of incident angle $\theta$ and frequency for forward direction.
Table 1. indicates the comparison of the proposed device with other Refs. [23,27,32,34]. A switchable and tuneable broadband AT and LCP device in THz region by changing phase of vanadium dioxide is shown in Ref. [23]. Dual-band dichroic AT of linearly polarized waves and CD in terahertz chiral metamaterial are shown in Ref. [27]. LCP in GHz domain can be obtained by using anisotropic metasurface as shown in Ref. [32]. Controllable broadband asymmetric transmission of terahertz wave based on Dirac semimetals is designed in Ref. [34]. Compared with above designs, we design a multi-functional device which can achieve AT, CD and AR by adjusting the polarization states of the incident waves.
Table 1. Comparison with recent reported functional devices
3. Conclusion
We have designed a chiral metamaterial structure that integrates multiple asymmetric transmission functions. In this structure, asymmetric transmission, polarization conversion, circular dichroism and asymmetric reflection can be switched by converting the polarization of the incident waves to linear polarized waves or circular polarized waves, respectively. When linear polarization waves are incident, AT can be realized in a wide frequency range, especially the conversion of linear-to-elliptical polarization waves can be realized during 0.3 THz to 1.2 THz. When circular polarized waves enter, the right- and left-handed circular polarized waves show significant dichroism effect at the frequency of 0.36 THz. In addition, AR can be realized in a wide frequency range. It can be seen that this structure can be used to prepare multifunctional asymmetric transmission devices without changing the material structure, just adjusting the polarization states of the incident waves to achieve a variety of asymmetric transmission functions. This result offers promising applications in designing metamaterials to achieve variety functions such as AT, CD and AR by adjusting the polarization of the incident waves. Our research can be used for military stealth, optical diode devices, isolators, polarization conversion devices and so on.
Funding
National Natural Science Foundation of China (11364044, 11864043, 12064045).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. J. Zhao, J. Song, T. Xu, T. Yang, and J. Zhou, “Controllable linear asymmetric transmission and perfect polarization conversion in a terahertz hybrid metal-graphene metasurface,” Opt. Express 27(7), 9773 (2019). [CrossRef]
2. P. Pitchappa, A. Kumar, S. Prakash, H. Jani, R. Medwal, M. Mishra, R. S. Rawat, T. Venkatesan, N. Wang, and R. Singh, “Volatile ultrafast switching at multilevel nonvolatile states of phase change material for active flexible terahertz metadevices,” Adv. Funct. Mater. 31(17), 2100200 (2021). [CrossRef]
3. J. Yang and Y. S. Lin, “Design of tunable terahertz metamaterial sensor with single- and dual-resonance characteristic,” Nanomaterials 11(9), 2212 (2021). [CrossRef]
4. X. Dong, X. Luo, Y. Zhou, Y. Lu, F. Hu, X. Xu, and G. Li, “Switchable broadband and wide-angular terahertz asymmetric transmission based on a hybrid metal-VO2 metasurface,” Opt. Express 28(21), 30675 (2020). [CrossRef]
5. Y. Bai, T. Wang, H. Ullah, Y. Qu, A. Abudukelimu, and Z. Zhang, “Asymmetric transmission in the planar chiral nanostructure induced by electric and magnetic resonance at the same wavelength,” Ann. Phys. (Berlin, Ger.) 531(7), 1800469 (2019). [CrossRef]
6. X. Chen, Z. Tian, Y. Lu, Y. Xu, X. Zhang, C. Ouyang, J. Gu, J. Han, and W. Zhang, “Electrically tunable perfect terahertz absorber based on a graphene salisbury screen hybrid metasurface,” Adv. Opt. Mater. 8(3), 1900660 (2020). [CrossRef]
7. H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional hybrid metasurfaces for dynamic tuning of terahertz waves,” Adv. Opt. Mater. 6(14), 1800257 (2018). [CrossRef]
8. X. Tao, L. Qi, J. Yang, and F. Liu, “Experimental verification of a broadband asymmetric transmission metamaterial in the terahertz region,” RSC Adv. 10(11), 6179–6184 (2020). [CrossRef]
9. G. Kenanakis, A. Xomalis, A. Selimis, M. Vamvakaki, M. Farsari, M. Kafesaki, C. M. Soukoulis, and E. N. Economou, “A three-dimensional infra-red metamaterial with asymmetric transmission,” ACS Photonics 2(2), 287–294 (2015). [CrossRef]
10. S. Yang, Z. Liu, H. Yang, A. Jin, S. Zhang, J. Li, and C. Gu, “Intrinsic chirality and multispectral spin-selective transmission in folded Eta-shaped metamaterials,” Adv. Opt. Mater. 8(4), 1901448 (2020). [CrossRef]
11. M. Kang and Y. D. Chong, “Coherent optical control of polarization with a critical metasurface,” Phys. Rev. A 92(4), 043826 (2015). [CrossRef]
12. Y. Zhao, X. Cao, J. Gao, X. Liu, and S. Li, “Jigsaw puzzle metasurface for multiple functions: polarization conversion, anomalous reflection and diffusion,” Opt. Express 24(10), 11208 (2016). [CrossRef]
13. B. Kamal, J. Chen, Y. Ying, R. Jian, S. Ullah, and W. U. R. Khan, “High efficiency and ultra-wideband polarization converter based on an L-shaped metasurface,” Opt. Mater. Express 11(5), 1343 (2021). [CrossRef]
14. Y. Liu, Y. Q. Zhang, X. R. Jin, S. Zhang, and Y. P. Lee, “Dual-band infrared perfect absorber for plasmonic sensor based on the electromagnetically induced reflection-like effect,” Opt. Commun. 371, 173–177 (2016). [CrossRef]
15. R. Bai, C. Zhang, X. Gu, X. R. Jin, Y. Q. Zhang, and Y. Lee, “Unidirectional reflectionlessness and perfect nonreciprocal absorption in stacked asymmetric metamaterial based on near-field coupling,” Appl. Phys. Express 10(11), 112001 (2017). [CrossRef]
16. C. Zhang, R. Bai, X. Gu, X. R. Jin, Y. Q. Zhang, and Y. P. Lee, “Dual-band unidirectional reflectionless phenomena in an ultracompact non-Hermitian plasmonic waveguide system based on near-field coupling,” Opt. Express 25(20), 24281 (2017). [CrossRef]
17. C. Zhang, R. Bai, X. Gu, Y. Jin, Y. Q. Zhang, X. R. Jin, S. Zhang, and Y. P. Lee, “Unidirectional reflectionless phenomenon in ultracompact non-Hermitian plasmonic waveguide system based on phase coupling,” J. Opt. 19(12), 125005 (2017). [CrossRef]
18. H. Yin, R. Bai, X. Gu, C. Zhang, G. R. Gu, Y. Q. Zhang, X. R. Jin, and Y. Lee, “Unidirectional reflectionless propagation in non-Hermitian metamaterial based on phase coupling between two resonators,” Opt. Commun. 414, 172–176 (2018). [CrossRef]
19. Y. M. Liu, L. Yu, X. R. Jin, Y. Q. Zhang, and Y. P. Lee, “Highly-dispersive unidirectional reflectionless phenomenon based on high-order plasmon resonance in metamaterials,” Opt. Express 27(21), 30589 (2019). [CrossRef]
20. L. Yu, H. Yang, Y. M. Liu, C. An, X. R. Jin, and Y. Q. Zhang, “Theoretical investigation of a controlled unidirectional reflectionlessness by applying external voltage in an electro-optical plasmonic waveguide system,” Opt. Express 28(16), 24069 (2020). [CrossRef]
21. S. H. A. Bokhari and H. M. Cheema, “Broadband asymmetric transmission via angle-induced chirality enhancement in split ring resonators,” J. Appl. Phys. 128(6), 063102 (2020). [CrossRef]
22. Y. H. Wang, I. Kim, R. C. Jin, H. Jeong, J. Q. Li, Z. G. Dong, and J. Rho, “Experimental verification of asymmetric transmission in continuous omega-shaped metamaterials,” RSC Adv. 8(67), 38556–38561 (2018). [CrossRef]
23. H. Zhang, C. Yang, M. Liu, and Y. Zhang, “Dual-function tuneable asymmetric transmission and polarization converter in terahertz region,” Results Phys. 25, 104242 (2021). [CrossRef]
24. R. Zhao, H. Y. Chen, L. Zhang, F. Li, P. Zhou, J. Xie, and L. Deng, “Design and implementation of high efficiency and broadband transmission-type polarization converter based on diagonal split-ring resonator,” Prog. Electromagn. Res. 161, 1–10 (2018). [CrossRef]
25. H. B. Wang, X. Zhou, D. F. Tang, and J F. Dong, “Diode-like broadband asymmetric transmission of linearly polarized waves based on Fabry-Perot-like resonators,” J. Mod. Opt. 64(7), 750–759 (2017). [CrossRef]
26. A. Somayyeh and R. Mahdi, “Tunable circular conversion dichroism and asymmetric transmission of terahertz graphene metasurface composed of split rings,” Opt. Commun. 456, 124623 (2020). [CrossRef]
27. T. Lv, X. Chen, G. Dong, M. Liu, D. Liu, C. Ouyang, Z. Zhu, Y. Li, C. Guan, J. Han, W. Zhang, S. Zhang, and J. Shi, “Dual-band dichroic asymmetric transmission of linearly polarized waves in terahertz chiral metamaterial,” Nanophotonics 9(10), 3235–3242 (2020). [CrossRef]
28. C. Pfeiffer and A. Grbic, “Bianisotropic metasurfaces: ultra-thin surfaces for complete control of electromagnetic wavefronts,” arXivarXiv:1404, 3313 (2014).
29. M. Kang, H. T. Wang, W. Zhu, and W. Zhu, “Dual-band unidirectional circular polarizer with opposite handedness filtration using hybridized metamaterial,” Opt. Express 22(8), 9301 (2014). [CrossRef]
30. T. Wang, H. Zhang, Y. Zhang, Y. Zhang, and M. Cao, “Tunable bifunctional terahertz metamaterial device based on Dirac semimetals and vanadium dioxide,” Opt. Express 28(12), 17434 (2020). [CrossRef]
31. X. F. Zang, S. J. Liu, H. H. Gong, Y. Wang, and Y. M. Zhu, “Dual-band superposition induced broadband terahertz linear-to-circular polarization converter,” J. Opt. Soc. Am. B 35(4), 950 (2018). [CrossRef]
32. M. I. Khan, Z. Khalid, and F. A. Tahir, “Linear and circular-polarization conversion in X-band using anisotropic metasurface,” Sci. Rep. 9(1), 4552 (2019). [CrossRef]
33. A. Fahad, M. I. Khan, and F. A. Tahir, “A multi-functional polarization transforming metasurface for C, X and K band applications,” Antennas Wirel. Propag. Lett. 20(11), 2186–2190 (2021). [CrossRef]
34. L. Dai, Y. Zhang, J. F. O’Hara, and H Zhang, “Controllable broadband asymmetric transmission of terahertz wave based on Dirac semimetals,” Opt. Express 27(24), 35784 (2019). [CrossRef]
35. S. Zhang, F. Liu, T. Zentgraf, and J. Li, “Interference induced asymmetric transmission through a monolayer of anisotropic chiral metamolecules,” Phys. Rev. A 88(2), 023823 (2013). [CrossRef]
36. Y. Cheng, J. Fan, H. Luo, and F. Chen, “Dual-band and high-efficiency circular polarization convertor based on anisotropic metamaterial,” Opt. Mater. Express 9(3), 1365 (2019). [CrossRef]
37. C. Pfeiffer, C. Zhang, V. Ray, L. J. Guo, and A. Grbic, “High performance bianisotropic metasurfaces: asymmetric transmission of light,” Phys. Rev. Lett. 113(2), 023902 (2014). [CrossRef]
38. M. Liu, Q. Xu, X. Chen, E. Plum, H. Li, X. Zhang, C. Zhang, C. Zou, J. Han, and W. Zhang, “Temperature-controlled asymmetric transmission of electromagnetic waves,” Sci. Rep. 9(1), 4097 (2019). [CrossRef]
39. M. I. Khan, B. Hu, Y. Chen, N. Ullah, M. J. I. Khan, and A. R. Khalid, “Multiband efficient asymmetric transmission with polarization conversion using chiral metasurface,” Antennas Wirel. Propag. Lett. 19(7), 1137–1141 (2020). [CrossRef]
40. J. Shi, X. Liu, S. Yu, T. Lv, Z. Zhu, H. F. Ma, and T. J. Cui, “Dual-band asymmetric transmission of linear polarization in bilayered chiral metamaterial,” Appl. Phys. Lett. 102(19), 191905 (2013). [CrossRef]
41. F. Lv, L. Wang, Z. Xiao, M. Chen, Z. Cui, and Q. Xu, “Asymmetric transmission polarization conversion of chiral metamaterials with controllable switches based on VO2,” Opt. Mater. 114, 110667 (2021). [CrossRef]
42. T. Ullah and A. Rashid, “Angularly stable and broadband chiral metamaterial based design for asymmetric transmission of linearly polarized waves,” Microw Opt Technol Lett 63(1), 226–234 (2021). [CrossRef]
43. C. Liu, Y. Huang, F. Hu, Y. E X. Dong, Y. Yang, Y. Jin, and X. Xu, “Giant asymmetric transmission and circular dichroism with angular tunability in chiral terahertz metamaterials,” Ann. Phys. (Berlin, Ger.) 532(3), 1900398 (2020). [CrossRef]
44. M. Kang, J. Chen, and Y. D. Chong, “Chiral exceptional points in metasurfaces,” Phys. Rev. A 94(3), 033834 (2016). [CrossRef]
45. Y. Cheng, J. C. Zhao, X. Mao, and R. Gong, “Ultrabroadband diode-like asymmetric transmission and high-efficiency cross-polarization conversion based on composite chiral metamaterial,” Prog. Electromagn. Res. 160, 89–101 (2017). [CrossRef]
46. C. Menzel, C. Helgert, C. Rockstuhl, E.-B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010). [CrossRef]
47. J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007). [CrossRef]
48. C. H. Papas, Theory of Electromagnetic Wave Propagation (McGraw-Hill, 1965).
49. D. Liu, Z. Xiao, X. Ma, Q. Ma, X. Xu, and Z. Wang, “Asymmetric transmission of chiral metamaterial slab with double L resonators,” Opt. Commun. 338, 359–365 (2015). [CrossRef]
