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Abstract
The reported dual-band asymmetric transmission is usually an effect of mutual polarization conversion, where one polarized wave is converted to its cross-polarization in the first band while the other polarized wave is converted to its cross-polarization in the second band. In this work, we experimentally demonstrate a dual-band asymmetric transmission effect only for one-polarized linear wave in the terahertz band. It is measured that the cross-polarization transmission coefficient Tyx reaches two peaks of 0.715 and 0.548 at the frequency of 0.74 THz and 1.22 THz, respectively. While the transmission coefficient Txy is lower than 0.2 in the wide-band from 0.5 THz to 1.5 THz. Firstly, the multiple interference model is used to discuss the physical mechanism of the dual-band asymmetric transmission. However, the second band of the calculated spectrum is offset due to the strong near field coupling between the two metal layers. The coupled-mode theory is then introduced and the fitting result of the coupled-mode theory is in good agreement with that of the experiment in the two bands. This research would provide new theoretical instructions in designing and analyzing multiband asymmetric transmission in the terahertz, microwave or the optical bands.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recently, the terahertz science and technology have been paid much attention, and a great deal of novel metamaterial functional devices were proposed to manipulate the THz waves [1–3]. Asymmetric transmission (AT) is a very attractive phenomenon, which is associated with the presence of magnetization of medium or the chirality of structure that wave transmitted through. The AT in metamaterial is mainly attributed to the different conversion between two orthogonal polarization waves’ propagation backward and forward directions [4–6], which is different from the Faraday Effect in magneto-optical media. Hence, the AT effect via polarization conversion has become a research hotspot since it is quite useful in realizing nonreciprocal light devices such as isolators, circulators, frequency selectors or filters [7–11]. The asymmetric transmission has been largely reported on planar metasurfaces in the microwave [12–17], terahertz [18–23] and optical [5,24,25–29] regime. These designs can be used as polarization-controlled devices for many potential applications in imaging, sensing, and communications. In previous studies, most work focused is on the AT structures with narrow-band [10,11,16], broad-band [9,19,20,23,26,29] or dual-band structures [17,22,24,28,30,31]. The dual-band AT is usually an effect of mutual polarization conversion in the microwave band with experiments [17] or the infrared band with simulations [24,28,30,31]. Where one polarized wave is converted to its cross-polarization in the first band, while the other polarized wave is converted to its cross-polarization in the second band. To our best knowledge, the goal to pursue a terahertz AT structure with only one polarized wave converting to its cross-polarization in all bands is still challenging. Which has promising applications in polarization manipulation and is highly valuable for the development of terahertz devices. Besides, several experimental works have been done for the AT metamaterials in the terahertz band. R. Singh et al. [6] firstly demonstrated a weak asymmetric transmission of circularly polarized waves through a planar chiral metamaterial in the terahertz region. M. Kenney et al. [32] showed a herringbone metasurface can realize a broadband asymmetry for the circular polarizations with the cross-polarization transmittance magnitude over 0.6 from 0.8 to 1.2 THz. M. Liu et al. [33] demonstrated a temperature-controlled AT of linearly polarized THz wave by exploiting the insulator-to-metal phase transition of VO2. The measured cross-polarization transmittance magnitude reaches a large maximum of 0.45 near 1.1 THz. Recently, T. Lv et al. [34] demonstrated experimentally a bilayer chiral metamaterial consisting of orthogonally chained S-shaped patterns to realize a dual-band dichroic AT effect for linearly polarized terahertz waves. However, the dual-band AT effect is still an effect of mutual polarization conversion. Where the cross-polarization coefficient ${T_{xy}}$ owns higher value in the first band, while the cross-polarization coefficient ${T_{yx}}$ reaches a higher value in the second band.
In this work, we demonstrated a terahertz dual-band asymmetric transmission structure only for a single cross-polarized linear wave. In which, the normally incident x-polarized wave is transmitted and converted into the y-polarized wave in two adjacent frequency bands, while most of the normally incident y-polarized wave is blocked. That means only the cross-polarization transmission coefficient ${T_{yx}}$ have the high values in the two adjacent bands. The measured peaks for ${T_{yx}}$ are 0.715 and 0.548 at the frequency of 0.74 THz and 1.22 THz, respectively. While the ${T_{xy}}$ is lower than 0.2 in the wideband from 0.5 THz to 1.5 THz. Different from the dual-band AT structure reported before [17,24,28,30,31,34], our proposed AT structure experimentally realizes a dual-band AT effect only for ${T_{yx}}$. The multiple interference model is used to discuss the physical mechanism of the dual-band asymmetric transmission. However, due to the near field coupling between the two metal layers, the multiple interference model fails to illuminate the mechanisms of the asymmetric transmission perfectly. The coupled-mode theory (CMT) is introduced to further explain the dual-band AT effect effectively.
2. Structure design and simulations
Figure 1(a) shows the schematic diagram of the asymmetric transmission for the proposed 4×4 unit cells of terahertz metamaterial. When the incident wave propagates along the z-axis, the normally incident x-polarized wave can be transmitted and converted into the y-polarized wave in two adjacent frequency bands, while the normally incident y-polarized wave is blocked. The unit cell of the proposed metamaterial is shown in Fig. 1(b), which is composed of a split rectangular annulus and a metal strip on two sides of a dielectric substrate. The metallic patterns on both sides of the dielectric layer are identical but twisted, the bottom metal structure is formed by rotating the top metal structure with a clockwise angle of 90° along the z-axis and then is mirrored along the y-axis. In our design, the top and the bottom metallic layers are made of gold with a conductivity of $\mathrm{\sigma } = 4 \times {10^7}\; S/m$. The dielectric substrate is polyimide with the relative permittivity ɛr=3 and the loss tangent tgδ=0.035. The substrate thickness is d=32 µm. The geometric parameters of the structure shown in Fig. 1(b) are p=158 µm, L=92 µm, w=20 µm, g=48.5 µm, a=72.5 µm, s=38.25 µm.
Fig. 1. (a) Schematic view of the 4×4 unit cells of AT metamaterial. (b) The unit cell of the proposed AT metamaterial, where the yellow color represents the gold and the blue one is the polyimide. (c) Photograph of the experimental sample.
The numerical simulations are performed by the CST Microwave Studio. The finite element method in the frequency domain is used. For the setting of the simulation model, periodic boundary conditions are applied in the x and y directions, and the absorbing boundaries are applied in the z-direction. Figure 1(c) shows the optical microscope image of the sample fabricated by the standard Lithography technique. Firstly, a 10 nm/100 nm thick Ti/Au film was deposited on one side of the 32 µm polyimide and the metallic patterns were formed by a lift-off process. Next, the same metalized process was used on the other side of the polyimide. The fabricated AT metamaterial had a 100×100 square array cell with a period of 158 µm. A good uniformity was achieved across the 15.8×15.8 mm device area.
The sample was measured by using the terahertz time-domain spectroscopy. The experiment was carried out in an airtight box which was vacuumed to avoid the influence of water absorption. Figure 2 shows the part of the optical test system consisting of three polarizers. The first polarizer (P1) was placed parallel to the x-axis to ensure the incident wave illuminating on the sample is x-polarized. The second polarizer (P2) was set behind the sample, which can rotate to ${\pm} 45^\circ $ with respect to the x-axis under the control of the computer. Since the test system can obtain the amplitude and the phase of the electric field, we can measure and calculate the component electric field in two different polarization directions to acquire the polarization state of the whole transmitted electric field. The third polarizer (P3) was put behind P2 to collect the electric fields in the x-direction, which could guarantee the reliability of the measured results. It should be noted that the sample can be rotated 90 degrees by hand to let another polarized wave illuminate on the sample.
Fig. 2. The test system setup. P1, P2 and P3 represent the three polarizers, P1 and P3 are fixed while P2 can rotate to ±45°with respect to the y-axis under the control of the computer
The results of ${T_{xy}}$, ${T_{yx}}$, ${T_{xx}}$ and ${T_{yy}}$ can be calculated based on the following measurement. For the terahertz wave transmitting through the second polarizer P2, the electric field can be written as
This equation contains the electric field with magnitude and phase in the x and y directions. When $\mathop{{{\boldsymbol E}_2}}\limits^\rightharpoonup $ passes through the third polarizer, the electric field can be written as
When P2 rotated to be the other side with -45°, we can get the electric field after the P3 is
Then, we can get the
If rotating the sample 90O along the z-direction by hand, we can get the values of the ${E_{yx}}$ and ${E_{xx}}$. Based on the reference signal of the vacuum, we can obtain the ${T_{xy}}$, ${T_{yx}}$, ${T_{xx}}$ and ${T_{yy}}\; $from the Fourier transform.
Figures 3(a) and 3(b) demonstrate the simulated and the measured cross- and co-polarized transmission coefficients of the dual-band AT structure, while ${T_{xx}}\; $and ${T_{yx}}\; $are the transmission coefficients of the electromagnetic wave on the x and y directions for an x-polarized incident wave, respectively. ${T_{yy}}\; $and ${T_{xy}}\; $are the transmission coefficients on the y and x directions for a y-polarized incident wave, respectively. We can see the measured results have good uniformity with the simulated results. As can be seen from Fig. 3(a), it is clear that the measured cross-polarized transmission coefficient ${T_{xy}}$ is very different from ${T_{yx}}$. The transmission coefficients ${T_{yx}}\; $can reach two peaks of 0.715 and 0.548 at the frequency of 0.72 THz and 1.22 THz, respectively. While the transmission coefficients ${T_{xy}}$ is lower than 0.2 from 0.5 THz to 1.5 THz. The co-polarized transmission coefficients ${T_{xx}}$ and ${T_{yy}}$ are equal due to the rotational symmetry of the metal structures on both sides of the substrate, which can be shown in Fig. 3(b).
Fig. 3. The simulated and measured results. (a) cross-polarization coefficient and (b) co-polarization coefficient.
To better understand the mechanism of the AT properties, we firstly use the multi-reflection and transmission interference model [35–37] shown in Fig. 4(a). The proposed metamaterial can be regarded as the F-P-like cavity in which the EM wave will experience the multi-reflection process. When the x-polarized wave passes through the left interface of the cavity, two transmitted waves can be generated: one is the co-polarized transmitted wave with a transmission coefficient $\mathop{T_{xx}^1}\limits^\rightharpoonup $ and the other is the cross-polarized wave with a transmission coefficient $\mathop{T_{yx}^1}\limits^\rightharpoonup $. Both of the two transmitted waves continue to propagate to the right interface of the cavity and the corresponding co- and cross-polarized transmitted and reflected wave are generated, the reflected wave is partially reflected back to the cavity when it returns to the left interface and continues the previous process.
When the x-polarized incident wave passes through the proposed structure, the y-polarized transmitted wave can be described using the following equation [35–37]:
Thus, the overall y-polarized transmitted wave is written as:
In this case, the transmitted wave for each n can be written as
The cross-polarized transmission coefficient can be written as:
Using the above equations, the evolution of the cross-polarized transmitted wave as a function of roundtrips n was tracked at f=0.745 THz in Fig. 4(b). The x-axis and y-axis denote the real part and imaginary part of the transmitted cross-polarized electric field, respectively. The numbers 0, 1, 2, and 3 denote the number of reflection roundtrips. The red and black dashed lines denote the combined electric field Eyx and Exy after several roundtrips of inferences, respectively. The inset is the enlarged part for the variation of the Exy. It is noticeable that the y-component of the transmitted wave is enhanced when the incident wave is x-polarized at f=0.745 THz after multiple interferences in the cavity. While for the y-polarized incident wave, the combined x-polarized transmitted wave is too weak to be seen due to the little polarization conversion in the proposed AT structure.
Figure 5(a) shows the cross-polarization transmission ${T_{yx}}$ by using the multiple interference model (dot line) and the simulation software CST (solid line). It is seen that the first band of the calculated spectrum with the multiple interference model is well fitted with the simulated spectrum. However, the second band of the calculated spectrum is offset compared with the simulated spectrum. This phenomenon can be explained by the fact that the multiple interference model neglects the near-field interaction or magnetic resonance [35,36]. In our proposed AT structure, the near field coupling between the two metal layers on the two sides of the substrate has a great impact on the second passband of ${T_{yx}}$, which is not taken into account in the derived formulation. Figure 5(b) shows the ${T_{yx}}$ by using the calculation model and the simulation method for the substrate thickness of 80 µm. Compared with Fig. 5(a), the calculated result is more consistent with the simulation one for the substrate thickness increasing to 80µm. The increase of substrate thickness makes the distance between the two metal layers large, then the near field coupling between the two metal layers becomes weaker. Therefore, the calculated result for substrate thickness 80 µm is closer to the simulated result. To further investigate the near field coupling between the two metal layers, Figs. 5(c) and 5(d) present the simulated and calculated ${T_{yx}}$ for substrate thickness d varying from 20 µm to 80 µm, respectively. For the lower frequency band, the variation trend of the calculated ${T_{yx}}$ are well consistent with the simulated ${T_{yx}}$ as d increases. For the higher frequency band, there is firstly large offset between the calculated and simulated results of ${T_{yx}}$. Then, the calculated and simulated results tend to be close as d is larger than 60 µm.
Fig. 4. (a) Multiple interference model of the proposed metamaterial. (b) The cross-polarized transmitted waves on multiple interference method for the x- and y-polarized wave at the frequency of 0.745 THz.
Fig. 5. Theoretically calculated and numerically simulated cross-polarization transmission ${T_{yx}}$ with (a) d = 32 µm and (b) d = 32 µm. Color map of the (c) simulated and (d) calculated ${T_{yx}}$ with varying substrate thickness d varying from 20 µm to 80 µm.
As the multiple interference model fails to illuminate the mechanisms of the asymmetric transmission perfectly in the second band, the coupled-mode theory (CMT) is introduced to further explain the dual-band AT effect. The proposed metal-dielectric-metal structure can be viewed as a two-port model with two resonators due to the two metal structures on the top and bottom of the dielectric substrate, these two resonators can couple with each other through near-field coupling with a strength of k. The time evolution of the amplitudes of the two resonant modes are described by the following equations [38–40]:
Through carefully setting the above four fitting parameters k, Γ+, Γ-, and Γa, the measured results of ${T_{yx}}$ shown in Fig. 3(a) can be well described by the coupled-mode theory. We divide the corresponding frequency range into two parts, the first part is from 0.4 THz to 1 THz with the resonant frequency 0.74 THz, while the second part is from 1 THz to 1.4 THz with the resonant frequency 1.22 THz. The calculated results of each part using the CMT method are combined in Fig. 6. The calculated fitting parameters for the two bands using the CMT method are given in Table 1, all are in units of THz. The fitting parameters of the first band is set as k=0.0841, Γ+=0.068, Γ-=0.065, and Γa=0.026. In the second band, the fitting parameters is set as k=0.00065, Γ+=0.0025, Γ-=0.0315, and Γa=0.0144. As is seen from Fig. 6, the fitting results of the two bands are in good agreement with the experiment. The insets are the simulated current distribution of the top metal structure at the peak frequency of 0.74 THz and 1.22 THz, respectively. The current distribution in the top split rectangular annulus oscillates in phase at 0.74 THz, that is, the electric dipoles excite in the split rectangular annulus oscillate in phase, while the current distribution in the top split rectangular annulus oscillates out of phase at 1.22 THz. These two different current direction modes give rise to different transmissions at the two resonant frequencies of 0.74 THz and 1.22 THz, respectively [41–43].
Fig. 6. Transmission coefficient ${T_{yx}}$ obtained by experiment (red solid line) and CMT method (blue scatter diagram, star symbol for the first band and hollow circle symbol for the second band). The two insets are the simulated current distributions of the top metal structure at 0.74 THz and 1.22 THz, respectively.
Table 1. The calculated fitting parameters for the two bands using the CMT method
Finally, we compare our work with the reported similar references about the AT metamaterials, as is shown in Table 2. Although the single-band, dual-band and broadband AT metamaterials have been realized in Refs. [11], [17] and [26], but their work belongs to the microwave and the near-infrared regions. Although Ref. [32] proposes an asymmetric transmission in the terahertz band, the polarization conversion mode changes from circular to circular. Reference [22] presents a terahertz dual-band AT metamaterials, it lacks experimental validation and the three layers of metal structure make it harder to fabricate. Reference [34] can realize a dual-band AT effect for linearly polarized terahertz waves. However, there are two differences. Firstly, in Ref. [34], the dual-band AT effect is mutual for the two polarization. While the dual-band AT effect is only for one single polarization. Secondly, only the multiple interference model is used for the theoretical analysis of the dual-band AT transmission. In this work, we use two analytical methods to better understand the mechanism of the AT properties, and we find that the coupled-mode theory is better to explain the dual-band AT effect than the multiple interference model for our proposed model.
Table 2. The comparison between references and our work.
3. Conclusion
In conclusion, we demonstrated a terahertz dual-band asymmetric transmission only for a single cross-polarized linear wave. The measured peaks for ${T_{yx}}$ are 0.715 and 0.548 at the frequency of 0.74 THz and 1.22 THz, respectively. While the ${T_{xy}}$ is lower than 0.2 in the wideband from 0.5 THz to 1.5 THz. The multiple interference model is used to discuss the physical mechanism of the dual-band asymmetric transmission. It is easy to see that combined Eyx is enhanced while the combined Exy is too weak by tracking the evolution of the cross-polarized transmitted wave as a function of roundtrips. We also found that the first band of the calculated spectrum with the multiple interference model is well fitted with the simulated spectrum, while the second band of the calculated spectrum is offset due to the strong near field coupling between the two metal layers. This phenomenon is confirmed by investigating the influence of the substrate thickness on the two bands of the ${T_{yx}}$.
As the multiple interference model does not take the near field coupling effect into account and fails to illuminate the mechanisms of the asymmetric transmission perfectly in the second band, the coupled-mode theory is introduced to further explain the dual-band AT effect. The fitting result of the CMT method is in good agreement with that of the experiment in the two bands. Our research would provide new instructions in designing and analyzing multiband AT structures in the terahertz band, microwave or optical bands.
Funding
This work is supported by the National Natural Science Foundation of China (61875017 and 61107030) and BUPT Excellent Ph.D. Students Foundation (CX2020110) .
Acknowledgments
We would like to thank Dr. Bo Wang and Dr. Chun Wang in the Institute of Physics, Chinese Academy of Sciences for providing the measurement with Terahertz time-domain-spectroscopy.
Disclosures
The authors declare no conflicts of interest.
References
1. A. Ahmadivand, B. Gerislioglu, and Z. Ramezani, “Gated graphene island-enabled tunable charge transfer plasmon terahertz metamodulator,” Nanoscale 11(17), 8091–8095 (2019). [CrossRef]
2. A. Ahmadivand, B. Gerislioglu, R. Ahuja, and Y. K. Mishra, “Terahertz plasmonics: The rise of toroidal metadevices towards immunobiosensings,” Mater. Today 32, 108–130 (2020). [CrossRef]
3. B. Gerislioglu, A. Ahmadivand, and N. Pala, “Tunable plasmonic toroidal terahertz metamodulator,” Phys. Rev. B 97(16), 161405 (2018). [CrossRef]
4. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric Propagation of Electromagnetic Waves through a Planar Chiral Structure,” Phys. Rev. Lett. 97(16), 167401 (2006). [CrossRef]
5. A. S. Schwanecke, V. A. Fedotov, V. V. Khardikov, S. L. Prosvirnin, Y. Chen, and N. I. Zheludev, “Nanostructured Metal Film with Asymmetric Optical Transmission,” Nano Lett. 8(9), 2940–2943 (2008). [CrossRef]
6. R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, and N. I. Zheludev, “Terahertz metamaterial with asymmetric transmission,” Phys. Rev. B 80(15), 153104 (2009). [CrossRef]
7. C. Menzel, C. Rockstuhl, and F. Lederer, “An advanced Jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82(5), 053811 (2010). [CrossRef]
8. 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]
9. Z. Wei, Y. Cao, Y. Fan, X. Yu, and H. Li, “Broadband polarization transformation via enhanced asymmetric transmission through arrays of twisted complementary split-ring resonators,” Appl. Phys. Lett. 99(22), 221907 (2011). [CrossRef]
10. M. Kang, J. Chen, H. X. Cui, Y. Li, and H. T. Wang, “Asymmetric transmission for linearly polarized electromagnetic radiation,” Opt. Express 19(9), 8347–8356 (2011). [CrossRef]
11. C. Huang, Y. J. Feng, J. M. Zhao, Z. B. Wang, and T. Jiang, “Asymmetric electromagnetic wave transmission of linear polarization via polarization conversion through chiral metamaterial structures,” Phys. Rev. B 85(19), 195131 (2012). [CrossRef]
12. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Asymmetric transmission of linearly polarized waves and polarization angle dependent wave rotation using a chiral metamaterial,” Opt. Express 19(15), 14290–14299 (2011). [CrossRef]
13. L. Wu, Z. Y. Yang, Y. Z. Cheng, and M. Zhao, “Giant asymmetric transmission of circular polarization in layer-by-layer chiral metamaterials,” Appl. Phys. Lett. 103(2), 021903 (2013). [CrossRef]
14. 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(21), 213905 (2012). [CrossRef]
15. J. H. Shi, H. F. Ma, C. Y. Guan, Z. P. Wang, and T. J. Cui, “Broadband chirality and asymmetric transmission in ultrathin 90°-twisted Babinet-inverted metasurfaces,” Phys. Rev. B 89(16), 165128 (2014). [CrossRef]
16. Y. Cheng, Y. Nie, X. Wang, and R. Gong, “An ultrathin transparent metamaterial polarization transformer based on a twist-split-ring resonator,” Appl. Phys. A 111(1), 209–215 (2013). [CrossRef]
17. J. H. Shi, X. C. Liu, S. W. Yu, T. 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]
18. S. Y. Fang, L. Kang, H. F. Ma, W. J. Lv, Y. X. Li, Z Zhu, C. Y. Guan, J. H. Shi, and T. J. Cui, “Asymmetric transmission of linearly polarized waves in terahertz chiral metamaterials,” J. Appl. Phys. 121(3), 033103 (2017). [CrossRef]
19. L. L. Dai, Y. P. Zhang, J. F. O’Hara, and H. Zhang, “Controllable broadband asymmetric transmission of terahertz wave based on Dirac semimetals,” Opt. Express 27(24), 35784–35796 (2019). [CrossRef]
20. S. T. Xu, F. T. Hu, M. Chen, F. Fan, and S. J. Chang, “Broadband Terahertz Polarization Converter and Asymmetric Transmission Based on Coupled Dielectric-Metal Grating,” Ann. Phys. 529(10), 1700151 (2017). [CrossRef]
21. Y. Zhou, Y. Q. Dong, R. H. Fan, Q. Hu, R. W. Peng, and M. Wang, “Asymmetric transmission of terahertz waves through a graphene-loaded metal grating,” Appl. Phys. Lett. 105(4), 041114 (2014). [CrossRef]
22. J. S. Li and F. Q. Bai, “Dual-band terahertz polarization converter with high-efficiency asymmetric transmission,” Opt. Mater. Express 10(8), 1853–1861 (2020). [CrossRef]
23. X. Tao, L. M. Qi, J. Yang, and F. Y. Liu, “Experimental verification of a broadband asymmetric transmission metamaterial in the terahertz region,” RSC Adv. 10(11), 6179–6184 (2020). [CrossRef]
24. Y. Xu, Q. Shi, Z. Zhu, and J. H. Shi, “Mutual conversion and asymmetric transmission of linearly polarized light in bilayered chiral metamaterial,” Opt. Express 22(21), 25679–25688 (2014). [CrossRef]
25. S. Wu, S. Xu, Y. Zhang, Y. Wu, J. Jiang, Q. Wang, X. Zhang, and Y. Zhu, “Asymmetric transmission and optical rotation of a quasi-3D asymmetric metallic structure,” Opt. Lett. 39(22), 6426–6429 (2014). [CrossRef]
26. R. Ji, S. W. Wang, X. Liu, and W. Lu, “Giant and broadband circular asymmetric transmission based on two cascading polarization conversion cavities,” Nanoscale 8(15), 8189–8194 (2016). [CrossRef]
27. Y. Wang, X. Wen, Y. Qu, L. Wang, R. Wan, and Z. Zhang, “Co-occurrence of circular dichroism and asymmetric transmission in twist nanoslitnanorod Arrays,” Opt. Express 24(15), 16425–16433 (2016). [CrossRef]
28. D. F. Tang, C. Wang, W. K. Pan, M. H. Li, and J. F. Dong, “Broad dual-band asymmetric transmission of circular polarized waves in near-infrared communication band,” Opt. Express 25(10), 11329–11339 (2017). [CrossRef]
29. 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(1), 1–7 (2017). [CrossRef]
30. X. M. Zhai, L. F. Yao, H. B. Wang, and J. F. Dong, “Multi-band asymmetric transmission and mutual conversion in near-infrared band,” Int. J. Appl. Electromagnetics and Mechanics 50(3), 395–405 (2016). [CrossRef]
31. M. Kang, H. T. Wang, and W. R. Zhu, “Dual-band unidirectional circular polarizer with opposite handedness filtration using hybridized metamaterial,” Opt. Express 22(8), 9301–9306 (2014). [CrossRef]
32. M. Kenney, S. Li, X. Zhang, X. Su, T. T. Kim, D. Wang, and H. Sun, “Pancharatnam-Berry Phase Induced Spin-Selective Transmission in Herringbone Dielectric Metamaterials,” Adv. Mater. 28(43), 9567–9572 (2016). [CrossRef]
33. M. Liu, Q. Xu, X. Chen, E. Plum, H. Li, X. Zhang, and W. Zhang, “temperature-Controlled Asymmetric transmission of electromagnetic Waves,” Sci. Rep. 9(1), 4097 (2019). [CrossRef]
34. T. T. Lv, X. Y. Chen, G. H. Dong, M. Liu, D. M. Liu, C. M. Ouyang, Z. Zhu, Y. X. Li, C. Y. Guan, J. G. Han, W. L. Zhang, S. Zhang, and J. H. Shi, “Dual-band dichroic asymmetric transmission of linearly polarized waves in terahertz chiral metamaterial,” Nanophotonics 9(10), 3235–3242 (2020). [CrossRef]
35. H. T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20(7), 7165–7172 (2012). [CrossRef]
36. X. P. Shen, Y. Yang, Y. Z. Zhang, J. Q. Gu, J. G. Han, W. L. Zhang, and T. J. Cui, “Triple-band terahertz metamaterial absorber: Design, experiment, and physical interpretation,” Appl. Phys. Lett. 101(15), 154102 (2012). [CrossRef]
37. G. Duan, J. Schalc, X. Zhao, J. Zhang, R. D. Averitt, and X. Zhang, “Identifying the perfect absorption of metamaterial absorbers,” Phys. Rev. B 97(3), 035128 (2018). [CrossRef]
38. T. Fu, F. Liu, Y. B. An, Q. Li, G. L. Xiao, T. Y. Sun, and H. O. Li, “Narrow-band asymmetric transmission based on the dark mode of Fano resonance on symmetric trimeric metasurfaces,” Opt. Express 28(20), 30141–30149 (2020). [CrossRef]
39. Y. Li, J. Lin, H. J. Guo, W. J. Sun, S. Y. Xiao, and L. Zhou, “A Tunable Metasurface with Switchable Functionalities: From Perfect Transparency to Perfect Absorption,” Adv. Opt. Mater. 8(6), 1901548 (2020). [CrossRef]
40. H. J. Guo, J. Lin, M. Qiu, J. X. Tian, Q. Wang, Y. Li, S. L. Sun, Q. He, S. Y. Xiao, and L. Zhou, “Flat optical transparent window: mechanism and realization based on metasurfaces,” J. Phys. D: Appl. Phys. 51(7), 074001 (2018). [CrossRef]
41. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006). [CrossRef]
42. N. Liu and H. Giessen, “Coupling Effects in Optical Metamaterials,” Chem. Int. Ed. 49(51), 9838–9852 (2010). [CrossRef]
43. H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, Z. W. Liu, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon hybridization and optical activity at optical frequencies in metallic nanostructures,” Phys. Rev. B 76(7), 073101 (2007). [CrossRef]
