Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Electromagnetically induced transparency based on a carbon nanotube film terahertz metasurface

Tao Zhou, Suguo Chen, Xiaoju Zhang, Xiang Zhang, Hui Hu, and Yue Wang

Open Access Open Access

Abstract

In this work, we present a study of bright-bright mode electromagnetically induced transparency based on carbon nanotube films terahertz metasurface consisting of an array of two asymmetric split rings. Under the excitation of terahertz wave, the electromagnetically induced transparency window can be obviously observed. The simulation results agree with the theoretical results. The formation mechanism of the transparent window in bright-bright mode electromagnetically induced transparency is further analyzed. Moreover, the sensing performance of the proposed terahertz metasurface is investigated and the sensitivity can reach to 320 GHz/RIU. To verify the slow light characteristics of the device, the group delay of the terahertz metasurface is calculated and the value is 2.12 ps. The proposed metasurface device and the design strategies provide opportunities for electromagnetically induced transparency applications, such as sensors, optical memories, and flexible terahertz functional devices.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Electromagnetically induced transparency (EIT) originally refers to the appearance of a narrow band of transmission frequencies in a medium that is initially impermeable in its first state by the coherent action of a coupled beam in an atomic system [1–3]. The generation of an EIT analog in metamaterials is achieved by bight-dark mode EIT and bright-bright mode EIT (BB-EIT) [4,5]. A single metal strip can be directly coupled to the incident electromagnetic wave in a dipole resonant state, this metal strip can be called the bright mode. While two parallel metal strips with a small distance apart do not have direct electric dipole coupling to the incident electromagnetic wave due to the presence of asymmetric modes with reverse currents, and can be considered as the dark mode. When the bright mode and the dark mode coupling to produce EIT, which can be called bright-dark mode. When the bright mode and the dark mode are placed at a certain distance from each other, the electromagnetic field is coupled between the two modes. The excited state of the bright mode is suppressed and the electric field becomes weaker, while the dark mode shows a strong electric field, the strength of the coupling depends on the distance between the two modes. Bright-bright mode means that both structures are able to interact strongly with electromagnetic waves, both exhibiting the resonant state of the bright mode. In addition, the BB-EIT coupling has been proved to be the basic method of EIT phenomenon based on metamaterials [6]. The group delay and high-quality factor (Q) accompanying the EIT phenomenon as well as the frequency-selective properties make it highly promising for a number of applications in optical memories [7,8], sensor [9–11], detectors [12], modulators [13], polarization converters [14] and other fields. Since the EIT requires high-intensity laser and extremely low temperature, the practical application of the EIT has been limited to some extent [15]. However, the emergence of metamaterials provides new opportunities for the EIT to work at room temperature.

Metamaterials are artificially constructed on-demand materials that do not exist in nature. They are usually composed of periodically arranged subwavelength structures, which can manipulate electromagnetic waves in unique ways. Metamaterials manipulate electromagnetic waves for extraordinary applications such as the formation of superlens [16], various sensors [17–19]. Therefore, metamaterials have attracted the attentions of researchers in physics, materials science, optics and chemistry [20]. Since the discovery of carbon nanotubes (CNTs) by Iijima in 1991 [19,21], owing to their unique optoelectronic properties, CNTs have gradually become an attractive candidate material for the next generation of photonics and optoelectronic devices in the terahertz (THz) region.

At present, metals [22,23], Dirac semimetals [24,25], graphene [26–31], and superconducting material [32] are the main materials which can be used to generate EIT. The traditional metal-based EIT device can achieve high Q value, however, the applications of the metal-based EIT were limited by the low melting point, high thermal conductivity, and the complicated design and fabrication [33–35]. As a kind of carbon-based material, the Fermi energy level of graphene can be tuned [36], which enriches the application of EIT-like devices even more. Single-walled CNTs, can be seen as rolled-up from graphene and have similar properties to graphene [37], which provides the possibility for the design of EIT based on CNTs. In addition, CNTs with different structures may exhibit metallic or semiconducting priorities, making them more promising in terms of applications. Furthermore, compared to graphene, CNTs are easier to obtain and process, which indicates that the carbon nanotube-based EIT device has higher practical application value. However, the research on an EIT metasurface based on CNTs films has not been reported yet at the THz frequency range.

In this paper, the carbon nanotube-based THz metasurface which can generate BB-EIT has been proposed. The transmission spectrum has been calculated in theoretically. At the same time, the formation mechanism of transparent window in BB-EIT is further analyzed. In addition, the sensing performance and the slow light characteristics of the proposed THz metasurface were investigated. The sensitivity and the group delay of the carbon nanotube-based THz metasurface can achieve 320 GHz/RIU and 2.12 ps, respectively, which provide opportunities for EIT applications, such as sensors, optical memories, and flexible THz functional devices.

2. Structure and design

In order to research the BB-EIT performance of the carbon nanotube-based THz metasurface, a periodic structure has been designed as shown in Fig. 1(a). The structural unit cell is composed of two asymmetric split CNTs film rings deposited on a polyimide substrate, as shown in Fig. 1(b). The CNTs film used in the simulation is a two-dimensional network structure mainly consisted of randomly oriented CNTs, and the parameters of the CNTs are derived from the experimental results which has been reported in our previous work [19,38,39]. The detail structural parameters are shown in Fig. 1(c), The length l = 125 µm and the width p = 65 µm of the unit structure, the polyimide substrate thickness h = 10 µm, the thickness of the CNTs t = 7 µm, and the spacing between the two split rings w = 16 µm. The outer diameter, the width and the opening width of the split of the left ring are Rl = 26 µm, w1 = 10 µm and k = 13 µm, respectively. The outer diameter, the width and the opening width of the right split ring are Rr = 18 µm, w2 = 5 µm and k1 = 8 µm, respectively. A full in-depth analysis of the proposed design has been carried out using the Finite Difference in Time Domain (FDTD) solver in the CST Microwave Studio software. Perfectly matched layer boundary conditions were applied along the x-direction. Transmission spectrum and electric field distributions are recorded by different monitors.

 figure: Fig. 1.

Fig. 1. Schematic diagram of the carbon nanotube-based THz metasurface. (a) The THz metasurface. (b) Side view of the THz metasurface. (c) Unit cell of the THz metasurface.

Download Full Size | PDF

3. Results and discussion

The simulation results of the carbon nanotube-based THz metasurface are shown in Fig. 2, where only the left or right split circular ring generates a separate LC mode resonant peak at frequencies f = 0.826 THz and f = 1.056 THz, respectively. In other words, both the left and right rings of the metasurface can exhibit a bright mode resonant state under the excitation of an electromagnetic wave in the x-direction. Two resonant frequencies are different because the physical dimensions of the two CNTs structures are different. A metasurface which can generate BB-EIT under the excitation of electromagnetic waves, when the two structures are combined. The EIT transmission peak at frequency of 0.942 THz is located between transmission dip 1 (0.826 THz) and dip 2 (1.056 THz). That means, the resonance frequency of the EIT spectrum remains the same as the resonance frequency of the original independent structure.

 figure: Fig. 2.

Fig. 2. The transmission spectrum of the carbon nanotube-based THz metasurface.

Download Full Size | PDF

At the same time, as a contrast, the gold was used to analyze the EIT phenomenon. As shown in Fig. 2, the EIT window shifts to the left by 0.158 THz, and has an increase in amplitude of 4.1%. This means that the difference in EIT amplitude between CNTs and gold is not significant, due to the unique properties of CNTs, it has more advantages and applications than gold.

To further explain the mechanism of the EIT, a three-stage system have been used to analyze the transmission spectrum [40,41]. Here, the incident electric field is $E = E_0{e^{j\omega t}}$. Then, two equations can describe our model:

$${\ddot{x}_1}(t) + {\gamma _a}{\dot{x}_1}(t) + \omega _1^2{x_1}(t) + {\kappa ^2}{x_2}(t) = {q_1}{E_0}$$
$${\ddot{x}_2}(t) + {\gamma _b}{\dot{x}_2}(t) + \omega _2^2{x_2}(t) + {\kappa ^2}{x_2}(t) = {q_2}{E_0}$$
where, $({x_1},{x_2})$, (${\omega _1},{\omega _2}$), and (${q _1},{q _2}$) are the displacements, resonant frequencies, and coupling strength coefficients with THz waves, respectively. (${\gamma _a},{\gamma _b}$) are the loss terms of metasurface structures which are closely to ${\gamma _1}$ and ${\gamma _2}$ for each single metasurface structure as shown in Fig. 3 (a) and (b). In addition, and ${\gamma _b} = ({\gamma _2} - {\gamma _1})/2$. To better fit our model, phase information $\phi $ has been introduced [42]. the $\kappa $ represents the coupling strength with loss, and the loss of transferring energy from one separate ring to another. can be calculated by formula:
$$\kappa = g - i\sqrt {{\gamma _a}{\gamma _b}} {e^{i\phi }}$$
where, $g$ is the coupling strength between two bright modes, and $\phi $ can be expressed as:
$$\phi = ({\phi _1} - {\phi _2})({\omega _1} + {\omega _2})/2$$

By solving Eqs. (1) and (2), combined with (3) and (4), The effective electric susceptibility of the modes can be obtained as:

$$\displaystyle{\chi _{eff}} = \frac{K}{{P_1^2{P_2}}}(\frac{{{P_1}({P_2} + 1){\kappa ^2} + P_1^2({\omega ^2} - \omega _2^2) + {P_2}({\omega ^2} - \omega _1^2)}}{{{\kappa ^4} - ({\omega ^2} - \omega _1^2 + i\omega {\gamma _a})({\omega ^2} - \omega _2^2 + i\omega {\gamma _b})}} + i\omega \frac{{P_1^2{\gamma _b} + {P_2}{\gamma _a}}}{{{\kappa ^4} - ({\omega ^2} - \omega _1^2 + i\omega {\gamma _a})({\omega ^2} - \omega _2^2 + i\omega {\gamma _b})}})$$
where, the K is the proportionality factor of the carbon nanotube-based THz metasurface, P1 is the ratio of coupling strength coefficients with incident waves in single structure, and P2 is the ratio of effective mass of two structures. Moreover, the transmission T is:
$$T = 1 - {\mathop{\rm Im}\nolimits} ({\chi _{eff}})$$

Combined with (5) and (6), the transmission spectrum of the carbon nanotube-based THz metasurface has been obtained. Figure 3(c) shows the simulation and theoretical calculation results. It can be seen that the position of the transmission peak is consistent with the simulation results, which explains the mechanism of using CNTs to generate EIT.

 figure: Fig. 3.

Fig. 3. (a)Transmission spectrum and phase of single left structure. (b)Transmission spectrum and phase of single right structure. (c)Transmission and theory spectrum of the carbon nanotube-based THz metasurface.

Download Full Size | PDF

To investigate the physical mechanism of the EIT phenomenon in the carbon nanotube-based THz metasurface, the electric field and surface current distribution of the CNTs at the resonance points were calculated, as shown in Fig. 4. The left split ring can generate strong coupling with the electromagnetic wave at f = 0.828 THz in Fig. 4 (a), while the right split ring is weakly excited. On the contrary, at f = 1.056 THz, the right split ring generates strong coupling with the electromagnetic wave, while the left split ring is weakly excited as shown in Fig. 4 (c). Figure 4(d) and 4(f) show that isotropic currents appear inside the circular ring and in the opposite direction to the split ones, indicating that the transmission dip is the LC mode resonant excitation. Furthermore, comparing the currents on the surface of the left and right split rings reveals that the currents inside the rings are in the opposite direction. Thus, in the unit structure, the LC mode resonance is generated at different resonant frequencies because two split rings of different dimensions and excite opposite surface currents. At suitable intervals, the radiated field of the LC mode generates an interference phase extinction due to the adjacent reverse currents. Then the structure generates a LC-mode resonance with a distinct peak and rises to EIT, the electric field and surface currents at the peak shown in Fig. 4(b) and Fig. 4 (e). It is worth noting that a weak reverse current is also observed at the two transmission valleys, just because the difference of the reverse current is too great, the EIT phenomenon cannot be generated.

 figure: Fig. 4.

Fig. 4. Electric field and surface current distribution at different resonance frequencies of the carbon nanotube-based THz metasurface.

Download Full Size | PDF

In order to study the effect of structural parameters on the BB-EIT of the carbon nanotube-based THz metasurface. The parameters of the left and right split rings were changed respectively, and the results are shown in Fig. 5. It can be observed that when the outer diameter of the left ring increases in Fig. 5 (a), that is, the width of the ring increases, the LC resonance of the left split ring enhanced and the Q value of the transparent peak of BB-EIT decreases. This is because the resonance of the left ring enhanced, which reduces the energy of the transparent peak of BB-EIT and leads to Q value decreased. However, when the outer diameter of the right split ring decreases, that is, the ring width decreases, as shown in Fig. 5 (b), the LC resonance of the right split ring decreases, resulting the energy of the BB-EIT transparent peak and the Q value decreased. All the above conclusions can be obtained by combining Fig. 4 (b) and (e). The decrease in the energy of the BB-EIT transparent peak will decrease the Q value of the transparent peak as shown in Fig. 5(c) and Fig. 5(d). The larger the distance between the two split rings, the higher the Q value of the transparent peak as shown in Fig. 5(e). The Q value is increase, and the amplitude of the BB-EIT transparent peak is increase as shown in Fig. 5 (f), with the increase of the distance between the two split rings. The change of EIT transparent peak caused by the above parameters proves that the obvious EIT window comes from the weak coupling effect, which is consistent with the relevant reports [43].

 figure: Fig. 5.

Fig. 5. The influence of the parameters of the left and right split ring on the transmission spectrum. (a) The influence of outer diameter of left split ring on the transmission spectrum. (b) The influence of outer diameter of right split ring on the transmission spectrum. (c) The relationship between the width changes of left split ring split and the change of EIT transparent peak. (d) The relationship between the width changes of right split ring on the EIT transparent peak. (e) Influence of distance between two split rings on EIT transparent peak. (f) Relationship of the Q value and amplitude of EIT transparency peak caused by distance change between two split rings.

Download Full Size | PDF

4. Application of the carbon nanotube-based THz metasurface

When the surface of the carbon nanotube-based THz metasurface is covered by the analyte, the resonance frequency and amplitude have changed, which can be used for sensing detection [19,39]. In order to expand the application of the device, we studied the refractive index of the analyte. The analyses are measured when the analyte covered the device surface, where d is the thickness of the analyte. Firstly, the refractive index has been fixed and the thickness has been scanned, and the results are shown in Fig. 6 (a). As the thickness of the analyte increases, the frequency and amplitude of the BB-EIT transmission peak change significantly. Figure 6 (b) shows that the frequency and amplitude change slowly after reaching a certain thickness. Sensitivity represents the frequency shift caused by the change in the refractive index per unit of the object to be measured and can be calculated as:

$$S = \frac{{|df|}}{{|dn|}}$$

 figure: Fig. 6.

Fig. 6. The sensing analysis of the carbon nanotube-based THz metasurface. (a) Results of different thicknesses of the analyte to be measured. (b) Frequency shifts and amplitude changes of different thicknesses. (c) The results of different refractive index. (d) Results analysis of frequency shifts and amplitude changes.

Download Full Size | PDF

In order to further study the sensing sensitivity of the carbon nanotube-based THz metasurface, the transmission of the analyte with refractive index of 1, 1.1, 1.2, 1.3, 1.4, 1.5 is studied. The frequency shift and amplitude change caused by different refractive indexes are shown in Fig. 6 (c). The sensitivity of the device has been calculated which is S = 320 GHz/RIU, as shown in Fig. 6 (d). We also research the changes of the amplitude, and the results show that the sensitivity of amplitude about 13.04%/RIU. These results indicate that both the amplitude shift and the frequency shift can be used for sensing applications during the detection process.

It is well known that a prominent feature of EIT-like response is the strong phase dispersion in the transparent window region, which can reduce the group velocity [44]. In order to verify the slow light characteristics of the structure, the group delay is calculated by formula:

$$t ={-} d\varphi /d\omega $$
where $\varphi $ and $\omega $ represent the phase difference and frequency of the transmission spectrum, respectively [45]. Figure 7 shows the phase difference and group delay characteristics of the incident THz wave. From the phase curve in Fig. 7, it can be seen that the phase mutation occurs and the phase dispersion occurs at the position of the transparent window, which resulting in a significantly enhanced group delay. At the transparent peak frequency, the group delay can reach 2.12 ps. This provides a new direction for slow-light storage devices.

 figure: Fig. 7.

Fig. 7. Phase difference and group delay in transmission spectra of the carbon nanotube-based THz metasurface.

Download Full Size | PDF

5. Conclusion

In summary, a THz metasurface based on CNTs films that can generate BB-EIT is proposed and verified. The unit structure of the device is composed of polyimide substrate and two asymmetric split rings. We demonstrate that asymmetric CNTs film structure can generate BB-EIT window under the excitation of incident THz wave. The spectrum has been calculated in theoretically which have a good agreement with simulation results. The carbon nanotube-based THz metasurface can be applied detecting analyte with different thicknesses and refractive indices. The metasurface can be used for slow light storage because of its good slow light characteristics. Moreover, the sensing performance and group delay of the metasurface can reach to 320 GHz/RIU, 2.12 ps, respectively. This provides significance for the research of new CNTs terahertz functional devices and the wide application of EIT.

Funding

Youth Innovation Team of Shaanxi Universities (21JP084); National Natural Science Foundation of China (11704310, 61975163); Natural Science Foundation of Shaanxi Province (2020JZ-48).

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 maybe obtained from the authors upon reasonable request.

References

1. N. Papasimakis, Y. Fu, V. Fedotov, S. Prosvirnin, D. Tsai, and N. Zheludev, “Metamaterial with polarization and direction insensitive resonant transmission response mimicking electromagnetically induced transparency,” Appl. Phys. Lett. 94(21), 211902 (2009). [CrossRef]  

2. C. Liu, P. Liu, L. Bian, Q. Zhou, G. Li, and H. Liu, “Dynamically tunable electromagnetically induced transparency analogy in terahertz metamaterial,” Opt. Commun. 410(1), 17–24 (2018). [CrossRef]  

3. C. Lao, Y. Liang, X. Wang, H. Fan, F. Wang, H. Meng, J. Guo, H. Liu, and Z. Wei, “Dynamically Tunable Resonant Strength in Electromagnetically Induced Transparency (EIT) Analogue by Hybrid Metal-Graphene Metamaterials,” Nanomaterials 9(2), 171 (2019). [CrossRef]  

4. J. J. Zhang, S. S. Xiao, C. Jeppesen, A. Kristensen, and N. A. Mortensen, “Electromagnetically induced transparency in metamaterials at near-infrared frequency,” Opt. Express 18(16), 17187–17192 (2010). [CrossRef]  

5. M. Chen, Z. Xiao, X. Lu, F. Lv, and Y. Zhou, “Simulation of dynamically tunable and switchable electromagnetically induced transparency analogue based on metal-graphene hybrid metamaterial,” Carbon 159, 273–282 (2020). [CrossRef]  

6. X. R. Jin, J. Park, H. Zheng, S. Lee, Y. Lee, R. J. Y. hee, K. W. Kim, H. S. Cheong, and W. H. Jang, “Highly-dispersive transparency at optical frequencies in planar metamaterials based on two-bright-mode coupling,” Opt. Express 19(22), 21652–21657 (2011). [CrossRef]  

7. L. Qin, K. Zhang, R. W. Peng, X. Xiong, W. Zhang, X. R. Huang, and M. Wang, “Optical-magnetism-induced transparency in a metamaterial,” Phys. Rev. B 87(12), 125136 (2013). [CrossRef]  

8. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001). [CrossRef]  

9. J. Zhang, N. Mu, L. Liu, J. Xie, H. Feng, J. Yao, T. Chen, and W. Zhu, “Highly sensitive detection of malignant glioma cells using metamaterial-inspired THz biosensor based on electromagnetically induced transparency,” Biosens. Bioelectron. 185, 113241 (2021). [CrossRef]  

10. X. He, Q. Zhang, G. Lu, G. Ying, F. Wu, and J. Jiang, “Tunable ultrasensitive terahertz sensor based on complementary graphene metamaterials,” RSC Adv. 6(57), 52212–52218 (2016). [CrossRef]  

11. X. Gan, R. J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, and D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7(11), 883–887 (2013). [CrossRef]  

12. Z. G. Dong, H. Liu, J. X. Cao, T. Li, S. M. Wang, S. N. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett. 97(11), 114101 (2010). [CrossRef]  

13. M. Liu, X. Yin, E. UlinAvila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011). [CrossRef]  

14. F. Ling, G. Yao, and J. Yao, “Active tunable plasmonically induced polarization conversion in the THz regime,” Sci. Rep. 6(1), 34994 (2016). [CrossRef]  

15. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008). [CrossRef]  

16. C. M. Soukoulis, S. Linden, and M. Wegener, “Negative Refractive Index at Optical Wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef]  

17. L. Zheng, X. Sun, H. Xu, Y. Lu, Y. Lee, J. Y. Rhee, and W. Song, “Strain Sensitivity of Electric-Magnetic Coupling in Flexible Terahertz Metamaterials,” Plasmonics 10(6), 1331–1335 (2015). [CrossRef]  

18. J. J. Bai, W. Shen, S. S. Wang, M. L. Ge, T. T. Chen, P. Y. Shen, and S. J. Chang, “An ultra-thin multiband terahertz metamaterial absorber and sensing applications,” Opt Quant Electron 53(9), 506 (2021). [CrossRef]  

19. Y. Wang, Z. J. Cui, X. J. Zhang, X. Zhang, Y. Q. Zhu, S. G. Chen, and H. Hu, “Excitation of Surface Plasmon Resonance on Multiwalled Carbon Nanotube Metasurfaces for Pesticide Sensors,” ACS Appl. Mater. Interfaces 12(46), 52082–52088 (2020). [CrossRef]  

20. V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photon 1(1), 41–48 (2007). [CrossRef]  

21. Sumio Iijima, “Helical microtubules of graphitic carbon,” Nature 354(6348), 56–58 (1991). [CrossRef]  

22. B. Sun, F. F. Xie, S. Kang, Y. C. Yang, and J. Q. Liu, “A Novel Method for PIT Effects Based on Plasmonic Decoupling,” Chinese Phys. Lett. 36(1), 017801 (2019). [CrossRef]  

23. T. Zheng, Z. Xiao, M. Chen, X. Miao, and X. Wang, “Ultra-Broadband Electromagnetically Induced Transparency in Metamaterial Based on Conductive Coupling,” Plasmonics 17(2), 717–723 (2022). [CrossRef]  

24. H. Chen, H. Zhang, M. Liu, Y. Zhao, X. Guo, and Y. Zhang, “Realization of tunable plasmon-induced transparency by bright-bright mode coupling in Dirac semimetals,” Opt. Mater. Express 7(9), 3397–3407 (2017). [CrossRef]  

25. J. Zhao, J. Song, Y. Zhou, R. Zhao, and J. Zhou, “Dual-Polarization, Tunable Breaking Window in the Polarization Conversion Pass Band in a Terahertz Dirac Semimetal-Based Metamaterial,” IEEE Photonics J. 11(6), 1–9 (2019). [CrossRef]  

26. L. Zhu, X. Zhao, F. Miao, B. K. Ghosh, L. Dong, B. Tao, F. Meng, and W. Li, “Dual-band polarization convertor based on electromagnetically induced transparency (EIT) effect in all-dielectric metamaterial,” Opt. Express 27(9), 12163–12170 (2019). [CrossRef]  

27. B. Tang, Z. Jia, L. Huang, J. Su, and C. Jiang, “Polarization-Controlled Dynamically Tunable Electromagnetically Induced Transparency-Like Effect Based on Graphene Metasurfaces,” IEEE J. Select. Topics Quantum Electron. 27(1), 1–6 (2021). [CrossRef]  

28. M. Chen, Z. Xiao, F. Lv, Z. Cui, and Q. Xu, “Dynamically Tunable Electromagnetically Induced Transparency-Like Effect in Terahertz Metamaterial Based on Graphene Cross Structures,” IEEE J. Select. Topics Quantum Electron. 28(1), 1–9 (2022). [CrossRef]  

29. J. Chen, S. Xie, L. Wu, R. Zhou, Q. Liu, D. Liu, M. Wu, and L. Zeng, “Tuneable paired nanoribbons with graphene for single and multiple transparency windows,” Optik 127(20), 9683–9690 (2016). [CrossRef]  

30. Y. Wang, M. Tao, Z. Pei, X. Yu, B. Wang, J. Jiang, and X. He, “Tunable bandwidth of double electromagnetic induced transparency windows in terahertz graphene metamaterial,” RSC Adv. 8(65), 37057–37063 (2018). [CrossRef]  

31. X. Zhou, T. Zhang, X. Yin, L. Chen, and X. Li, “Dynamically Tunable Electromagnetically Induced Transparency in Graphene-Based Coupled Micro-Ring Resonators,” IEEE Photonics J. 9(2), 1–9 (2017). [CrossRef]  

32. C. Zhang, J. Wu, B. Jin, X. Jia, L. Kang, W. Xu, H. Wang, J. Chen, M. Tonouchi, and P. Wu, “Tunable electromagnetically induced transparency from a superconducting terahertz metamaterial,” >Appl. Phys. Lett. 110(24), 241105 (2017). [CrossRef]  

33. M. Seo and H. R. Park, “Terahertz Biochemical Molecule-Specific Sensors,” Adv. Opt. Mater. 8(3), 1900662 (2020). [CrossRef]  

34. B. H. Ng, J. F. Wu, S. M. Hanham, A. I. Fernandez-Dominguez, N. Klein, Y. F. Liew, M. B. H. Breese, M. H. Hong, and S. A. Maier, “Spoof Plasmon Surfaces: A Novel Platform for THz Sensing,” Adv. Opt. Mater. 1(8), 543–548 (2013). [CrossRef]  

35. 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]  

36. Y. Cui, X. S. Wang, H. Jiang, and Y. Y. Jiang, “High-efficiency and tunable circular dichroism in chiral graphene metasurface,” J. Phys. D: Appl. Phys. 55(13), 135102 (2022). [CrossRef]  

37. M. C. Hersam, “Progress towards monodisperse single-walled carbon nanotubes,” Nat. Nanotechnol. 3(7), 387–394 (2008). [CrossRef]  

38. X. Zhang, Y. Wang, Z. Cui, X. Zhang, S. Chen, K. Zhang, and X. Wang, “Carbon nanotube-based flexible metamaterials for THz sensing,” Opt. Mater. Express 11(5), 1470–1483 (2021). [CrossRef]  

39. Y. Wang, Z. J. Cui, D. Y. Zhu, X. B. Zhang, and L. Qian, “Tailoring terahertz surface plasmon wave through free-standing multi-walled carbon nanotubes metasurface,” Opt. Express 26(12), 15343–15352 (2018). [CrossRef]  

40. C. Mcab, C. Zxab, C. Xlab, L. Fei, C. Zcab, and C. Qxab, “Dynamically tunable multi-resonance and polarization-insensitive electromagnetically induced transparency-like based on vanadium dioxide film,” Opt. Mater. 102, 109811 (2020). [CrossRef]  

41. X. He, C. Sun, Y. Wang, G. Lu, J. Jiang, Y. Yang, and Y. Gao, “Graphene-Modulated Terahertz Metasurfaces for Selective and Active Control of Dual-Band Electromagnetic Induced Reflection (EIR) Windows,” Nanomaterials 11(9), 2420 (2021). [CrossRef]  

42. W. Huang, S. Y. Liu, Y. Cheng, J. G. Han, S. Yin, and W. T. Zhang, “Universal coupled theory for metamaterial bound states in the continuum,” New J. Phys. 23(9), 093017 (2021). [CrossRef]  

43. G. L. Fu, X. Zhai, H. J. Li, S. X. Xia, and L. L. Wang, “Tunable plasmon-induced transparency based on bright-bright mode coupling between two parallel graphene nanostrips,” Plasmonics 11(6), 1597–1602 (2016). [CrossRef]  

44. W. Cai, B. Xiao, J. Yu, and L. Xiao, “A compact graphene metamaterial based on electromagnetically induced transparency effect,” Opt. Commun. 475(22), 126266 (2020). [CrossRef]  

45. J. Mei, C. Song, and C. Shu, “Active manipulation of dual transparency windows in dark–bright–dark mode coupling graphene metamaterial,” Opt. Commun. 488(10), 126851 (2021). [CrossRef]  

Data availability

Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)
Fig. 1.
Fig. 1. Schematic diagram of the carbon nanotube-based THz metasurface. (a) The THz metasurface. (b) Side view of the THz metasurface. (c) Unit cell of the THz metasurface.

View in Article | Download Full Size | PDF

Fig. 2.
Fig. 2. The transmission spectrum of the carbon nanotube-based THz metasurface.

View in Article | Download Full Size | PDF

Fig. 3.
Fig. 3. (a)Transmission spectrum and phase of single left structure. (b)Transmission spectrum and phase of single right structure. (c)Transmission and theory spectrum of the carbon nanotube-based THz metasurface.

View in Article | Download Full Size | PDF

Fig. 4.
Fig. 4. Electric field and surface current distribution at different resonance frequencies of the carbon nanotube-based THz metasurface.

View in Article | Download Full Size | PDF

Fig. 5.
Fig. 5. The influence of the parameters of the left and right split ring on the transmission spectrum. (a) The influence of outer diameter of left split ring on the transmission spectrum. (b) The influence of outer diameter of right split ring on the transmission spectrum. (c) The relationship between the width changes of left split ring split and the change of EIT transparent peak. (d) The relationship between the width changes of right split ring on the EIT transparent peak. (e) Influence of distance between two split rings on EIT transparent peak. (f) Relationship of the Q value and amplitude of EIT transparency peak caused by distance change between two split rings.

View in Article | Download Full Size | PDF

Fig. 6.
Fig. 6. The sensing analysis of the carbon nanotube-based THz metasurface. (a) Results of different thicknesses of the analyte to be measured. (b) Frequency shifts and amplitude changes of different thicknesses. (c) The results of different refractive index. (d) Results analysis of frequency shifts and amplitude changes.

View in Article | Download Full Size | PDF

Fig. 7.
Fig. 7. Phase difference and group delay in transmission spectra of the carbon nanotube-based THz metasurface.

View in Article | Download Full Size | PDF

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

x ¨ 1 ( t ) + γ a x ˙ 1 ( t ) + ω 1 2 x 1 ( t ) + κ 2 x 2 ( t ) = q 1 E 0
x ¨ 2 ( t ) + γ b x ˙ 2 ( t ) + ω 2 2 x 2 ( t ) + κ 2 x 2 ( t ) = q 2 E 0
κ = g − i γ a γ b e i ϕ
ϕ = ( ϕ 1 − ϕ 2 ) ( ω 1 + ω 2 ) / 2
χ e f f = K P 1 2 P 2 ( P 1 ( P 2 + 1 ) κ 2 + P 1 2 ( ω 2 − ω 2 2 ) + P 2 ( ω 2 − ω 1 2 ) κ 4 − ( ω 2 − ω 1 2 + i ω γ a ) ( ω 2 − ω 2 2 + i ω γ b ) + i ω P 1 2 γ b + P 2 γ a κ 4 − ( ω 2 − ω 1 2 + i ω γ a ) ( ω 2 − ω 2 2 + i ω γ b ) )
T = 1 − Im ( χ e f f )
S = | d f | | d n |
t = − d φ / d ω
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use