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

Two transmission window plasmonically induced transparency with hybrid coupling mechanism

Hai-ming Li and You-yun Xu

Open Access Open Access

Abstract

In this paper, a two transmission window plasmonically-induced transparency (PIT) with hybrid coupling mechanism has been numerically demonstrated. The hybrid coupling mechanism is composed of a bright mode (square ring), bright mode (SRR), and a dark mode (cut wire). Bright-dark coupling is one of the coupling ways; another two of the coupling ways are bright-bright coupling. Only three modes are needed to obtain two transmission window PIT, which can lead to miniaturization of the meta-atom of PIT. In addition, SRR is embedded in a square ring by using an ingenious design, which further leads to miniaturization of the meta-atom of PIT. The miniaturized PIT can enrich PIT research and has potential applications in slow light devices.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

EIT is the quantum interference within three-level atomic system and can make light travelling through an originally opaque media with high Q factor and slow light effect [1–2]. The high Q factor and the slow light characteristics made PIT having potential application in sensors and slow light devices [3–6]. However, EIT needs harsh experiment conditions [7], which has severely hampered the practical applications of EIT. Until 2008, Zhang et al. [8] have proven that EIT within three-level atomic system can be analogy with metamaterials named as PIT without high intensity laser at room temperature. It further promotes the practical application of PIT [9–15]. Henceforth, attentions have been turn to PIT metamaterials [16–24]. A lot of works [25–34] focus on PIT applications at GHz and THz frequency.

PIT metamaterials can be obtained by the coupling between bright mode and dark mode [35–41], bright mode and bright mode [42–47]. The bright mode can be coupled to the incident electromagnetic wave. The dark mode can not be coupled to incident electromagnetic wave. However, the dark mode can be excited by the excited bright mode through the near filed coupling distance. Both of the mutual coupling between bright mode and bright mode, bright mode and dark mode can induced PIT, which is analogy of the quantum interference within three-level atomic system. Zhao et al. [40] have obtained PIT with a graphene patch and SSR pair. The graphene patch can be directly excited by incident electromagnetic wave and SRR pair can not be directly excited by incident electromagnetic wave. Therefore, the graphene patch and SRR pair have been chosen as bright mode and dark mode. The mutual coupling between the graphene patch and SRR pair leads to PIT. Zhang et al. [41] have used parallel-coupled coplanar Dirac semimetal films (DSF) strips to obtain PIT. Two parallel-coupled coplanar DSF strips can be directly excited by incident electromagnetic wave. Therefore, both of them have been chosen as bright mode. The weak coupling between them leads to PIT. In addition, PIT also can be obtained by the hybrid coupling [48–52]. Rivas et al. [49] have used the hybrid coupling dolmen structure to obtain PIT. Most of PIT have only one transmission peak. However, at PIT potential application, two transmission window PIT has a winder range of application. Hua et al. [53] have obtained two transmission window PIT with the mutual coupling of three cut wires. Three cut wire were directly excited by incident electromagnetically wave. Therefore, three cut wire were separately selected as bright mode. The mutual coupling between them is bright mode-bright mode-bright mode. The near field coupling of the three bright mode is weak for the bright mode-bright mode-bright mode. In this paper, the mutual coupling of bright mode-bright mode-dark mode is used to obtain two transmission window PIT. It can enrich PIT research. The square ring and SRR can be directly excited by incident electromagnetically wave. The square ring and SRR are separately selected as bright mode. The cut wire can not be directly excited by incident electromagnetically wave. Therefore, the cut wire is selected as dark mode. Only three modes are needed to obtain two transmission window PIT, which can lead to miniaturization of the meta-atom of PIT. In addition, SRR is embedded in square ring by using the ingenious design, which further leads to miniaturization of the meta-atom of PIT. Thence, two transmission window and miniaturized PIT are obtained with the mutual coupling of bright mode-bright mode-dark mode. The miniaturized PIT has potential application in slow light devices. Compared with the works [54–57], the coupling mechanism in this letter is different, which is based on hybrid coupling mechanism.

2. Results and discussions

Figure 1(a) is schematic view of cut wire. The yellow part is copper and green part is substrate (FR-4 dielectric-slab). The geometrical dimensions are as follows: a = 16 mm, b = 16 mm, l1 = 14 mm, w1 = 1 mm and h = 1 mm. The simulations are carried out with the commercial software CST Studio Suite [58]. The boundary conditions are unite cell. When the electric and magnetic field directions of incident electromagnetic wave are parallel to x and y axis, an obvious transmission valley appears at 3-10 GHz as shown in Fig. 1(b). The field distribution is shown in Fig. 1(c), which is electric resonance. If the electric and magnetic field directions of incident electromagnetic wave are parallel to y and x axis, there is no transmission valley at 3-10 GHz as shown in Fig. 1(b). The field distribution shown in Fig. 1(d) can prove that the cut wire can not be excited by incident y-pol electromagnetic wave. Therefore, the cut wire can be chosen as dark mode when electric and magnetic field directions of incident electromagnetic wave are parallel to y and x axis.

 figure: Fig. 1.

Fig. 1. (a) The schematic view of cut wire. (b) The transmission spectra of cut wire under incident x-pol and y-pol electromagnetic wave. (c) The electric field distribution of cut wire under incident x-pol electromagnetic wave. (d) The electric field distribution of cut wire under the incident y-pol electromagnetic wave. The geometrical parameters are as follows: a = 16 mm, b = 16 mm, l1 = 14 mm, w1 = 1 mm, h = 1 mm.

Download Full Size | PDF

Figure 2(a) is schematic view of square ring. The geometrical dimensions are as follows: a = 16 mm, b = 16 mm, l2 = 10.9 mm, w2 = 0.2 mm. The electric and magnetic field of incident electromagnetic wave is parallel to y and x axis. An obvious transmission valley appears at 3-10 GHz as shown in Fig. 2(b). The field distribution is shown in Fig. 2(c), which is electric resonance. The square ring can be chosen as bright mode when electric and magnetic field directions of incident electromagnetic wave are parallel to y and x axis.

 figure: Fig. 2.

Fig. 2. (a) The schematic view of square ring. (b) The transmission spectra of square ring under incident y-pol electromagnetic wave. (c) The electric field distribution of square ring under incident y-pol electromagnetic wave. The geometrical parameters are as follows: a = 16 mm, b = 16 mm, l2 = 10.9 mm, w2 = 0.2 mm, h = 1 mm.

Download Full Size | PDF

Figure 3(a) is schematic view of SRR. The geometrical dimensions are as follows: a = 16 mm, b = 16 mm, l3 = 10 mm, w3 = 0.2 mm, g = 0.6 mm, h = 1 mm. The electric and magnetic field directions of incident electromagnetic wave are parallel to y and x axis. An obvious transmission valley appears at 3-10 GHz as shown in Fig. 3(b). The field distribution is shown in Fig. 3(c), which is electric resonance. SRR can also be chosen as bright mode when electric and magnetic field directions of incident electromagnetic wave are parallel to y and x axis.

 figure: Fig. 3.

Fig. 3. (a) The schematic view of SRR. (b) The transmission spectra of SRR under incident y-pol electromagnetic wave. (c) The electric field distribution of SRR under incident y-pol electromagnetic wave. The geometrical parameters are as follows: a = 16 mm, b = 16 mm, l3 = 10 mm, w3 = 0.2 mm, g = 0.6 mm, h = 1 mm.

Download Full Size | PDF

Figure 4(a) is the schematic view of two transmission window PIT. The electric and magnetic field directions of incident electromagnetic wave are parallel to y and x axis. Both of SRR and square ring have been chosen as bright mode and cut wire has been chosen as dark mode. The mutual coupling of cut wire, square ring and SRR leads to two transmission window PIT as shown in Fig. 4(b).

 figure: Fig. 4.

Fig. 4. (a) The schematic view of two transmission window PIT. (b) The transmission spectra of two transmission window PIT.

Download Full Size | PDF

In order to vividly see the mutual coupling process between cut wire, square ring and SRR. Figure 5 is electric field distributions of two transmission window PIT at three transmission valleys and two transmission peaks frequencies. Figure 5(a) is electric field distribution of two transmission window PIT at low transmission valley frequency (5.40 GHz). At the beginning, square ring and SRR are excited by incident y-pol electromagnetic wave and cut wire can not be excited by incident y-pol electromagnetic wave as shown in Fig. 5(a). Figure 5(b) is electric field distribution of two transmission window PIT at low transmission peak frequency (6.05 GHz). The electric distributions of square ring and cut wire are out of phase as shown in Fig. 5(b), which leads to transmission peak at low frequency. Figure 5(c) is the electric field distribution of two transmission window PIT at middle transmission valley frequency (6.72 GHz). The electric field of square ring and SRR have been coupled to cut wire through near field coupling distance (d1) as shown in Fig. 5(c). The cut wire, square ring and SRR have been excited, which leads to transmission valley at 6.72 GHz. Figure 5(d) is electric field distribution of two transmission window PIT at high transmission peak frequency (7.05 GHz). The electric distributions of square ring, SRR and cut wire are out of phase as shown in Fig. 5(d), which leads to transmission peak at high frequency at 7.05 GHz. Figure 5(e) is electric field distribution of two transmission window PIT at high transmission valley frequency (7.60 GHz). The filed of cut wire has been coupled back to square ring and SRR through near field coupling distance (d2) as shown in Fig. 5(e). The cut wire, square ring and SRR have been excited, which leads to transmission valley at 7.05 GHz.

 figure: Fig. 5.

Fig. 5. (a) The electric field distribution of two transmission window PIT at low transmission valley frequency (5.40 GHz). (b) The electric field distribution of two transmission window PIT at low transmission peak (6.05 GHz). (c) The electric field distribution of two transmission window PIT at middle transmission valley frequency (6.72 GHz). (d) The electric field distribution of two transmission window PIT at high transmission peak (7.05 GHz). (e) The electric field distribution of two transmission window PIT at high transmission valley frequency (7.60 GHz).

Download Full Size | PDF

In order to better understand the mutual coupling process between cut wire, square ring and SRR. The coupling between SRR + SR + CW (SRR, square ring, cut wire), SRR + SR (SRR, square ring), SRR + CW (SRR, cut wire), and SR + CW (square ring, cut wire) have been investigated. Figure 6 is the transmission spectra of SRR + SR + CW, SRR + SR, SRR + CW, and SR + CW. From Fig. 6, we can see that the low transmission peak of two transmission window PIT is mainly due to coupling between square ring and CW, and the high transmission peak of two transmission window EIT is mainly due to the coupling between SRR and cut wire. In addition, we can also see that coupling between SRR and square ring has been suppressed.

 figure: Fig. 6.

Fig. 6. The transmission spectra of SRR + SR + CW (SRR, square ring, cut wire), SRR + SR (SRR, square ring), SRR + CW (SRR, cut wire), and SR + CW (square ring, cut wire).

Download Full Size | PDF

The near field coupling distance plays key role in PIT. d2 is coupling distance between square ring and cut wire. When d2 increases from 0.2 to 0.6, only low frequency transmission peak moves as shown in Fig. 7(a). When d2 changes, the coupling distance between square ring and cut wire changes, the coupling distance between square ring and SRR do not changes, both of which lead to the changed of low frequency transmission peak and the unchanged of high frequency transmission peak. we can conclusion that low frequency transmission peak can be affected by the coupling distance between square ring and cut wire. When d1 increases from 0.15 to 0.35, both of low and high frequency transmission peak moves as shown in Fig. 7(b). When d1 changes, the coupling distance between square ring and SRR changes, the coupling distance between SRR and cut wire changes, l2 changes, all of which lead to the changed of both of low and high frequency transmission peak.

 figure: Fig. 7.

Fig. 7. (a) The transmission spectra of two transmission window PIT with different d2. (b) The transmission spectra of two transmission window PIT with different d1.

Download Full Size | PDF

In order to thoroughly study the coupling process between SRR, square wire and cut wire, the linearly coupled Lorentz oscillator model has been used.

$$\begin{array}{l} {{\ddot{Q}}_1}(t) + {\gamma _1}{{\dot{Q}}_1}(t) + \omega _a^2{Q_1}(t) + {\kappa _{12}}{Q_2}(t) + {\kappa _{13}}{Q_3}(t) = {g_1}{E_0}(t)\\ {{\ddot{Q}}_2}(t) + {\gamma _2}{{\dot{Q}}_2}(t) + \omega _b^\textrm{2}{Q_2}(t) + {\kappa _{21}}Q{}_1(t) + {\kappa _{2\textrm{3}}}{Q_3}(t) = {g_2}{E_0}(t)\\ {{\ddot{Q}}_3}(t) + {\gamma _3}{{\dot{Q}}_3}(t) + \omega _c^\textrm{2}{Q_3}(t) + {\kappa _{31}}Q{}_1(t) + {\kappa _{32}}Q{}_2(t) = 0 \end{array}$$
${Q_1}$, ${Q_2}$, ${Q_3}$ are amplitudes of SRR, square ring and cut wire. ${\omega _a}$, ${\omega _b}$ and ${\omega _c}$ are the resonance frequencies of SRR, square wire and cut wire. ${\gamma _1}$ is damping coefficient of SRR. ${\gamma _2}$ is damping coefficient of square ring. ${\gamma _3}$ is damping coefficient of cut wire. ${\kappa _{12}}$ is coupling coefficient between SRR and square ring. ${\kappa _{21}}$ is coupling coefficient between square ring and SRR. ${\kappa _{13}}$ is coupling coefficient between SRR and cut wire. ${\kappa _{31}}$ is coupling coefficient between cut wire and SRR. ${\kappa _{23}}$ is coupling coefficients between square ring and cut wire. ${\kappa _{32}}$ is coupling coefficients between cut wire and square ring. g1 and g2 are coupling strength of SRR and square ring with incident electric field E0. Consider they have the time-harmonic form:
$${E_0}(t) = {E_0}{e^{i\omega t}}$$
$${Q_1}(t) = {Q_1}{e^{i\omega t}}$$
$${Q_2}(t) = {Q_2}{e^{i\omega t}}$$
Let ${a_1} = - {\omega ^2} + i{\gamma _1}\omega + \omega _a^2, \ {a_2} = - {\omega ^2} + i{\gamma _2}\omega + \omega _b^2, \ {a_3} = - {\omega ^2} + i{\gamma _3}\omega + \omega _c^2$

The magnitude of electric dipole ${Q_1}$, ${Q_2}$ and ${Q_3}$ can be obtained:

$${Q_1} = \frac{{{g_1}({a_2}{a_3} - {k_{23}}{k_{32}}){E_0} + {g_2}({k_{32}}{k_{13}} - {k_{12}}{a_3}){E_0}}}{{{a_1}{a_2}{a_3} + {k_{12}}{k_{23}}{k_{31}} + {k_{13}}{k_{21}}{k_{32}} - {k_{23}}{k_{32}}{a_1} - {k_{13}}{k_{31}}{a_2} - {k_{21}}{k_{12}}{a_3}}}$$
$${Q_2} = \frac{{{g_1}({k_{23}}{k_{31}} - {k_{21}}{a_3}){E_0} + {g_2}({a_1}{a_3} - {k_{12}}{k_{31}}){E_0}}}{{{a_1}{a_2}{a_3} + {k_{12}}{k_{23}}{k_{31}} + {k_{13}}{k_{21}}{k_{32}} - {k_{23}}{k_{32}}{a_1} - {k_{13}}{k_{31}}{a_2} - {k_{21}}{k_{12}}{a_3}}}$$
$${Q_3} = \frac{{{g_1}({k_{21}}{k_{32}} - {k_{31}}{a_2}){E_0} + {g_2}({k_{31}}{k_{12}} - {k_{32}}{a_1}){E_0}}}{{{a_1}{a_2}{a_3} + {k_{12}}{k_{23}}{k_{31}} + {k_{13}}{k_{21}}{k_{32}} - {k_{23}}{k_{32}}{a_1} - {k_{13}}{k_{31}}{a_2} - {k_{21}}{k_{12}}{a_3}}}$$
The susceptibility of PIT metamaterials can be determined:
$$\chi = \frac{{{g_1}({a_2}{a_3} + {k_{23}}{k_{31}} - {k_{32}}{k_{23}} - {k_{21}}{a_3}) + {g_2}({a_1}{a_3} + {k_{32}}{k_{13}} - {k_{13}}{k_{31}} - {k_{12}}{a_3})}}{{{a_1}{a_2}{a_3} + {k_{12}}{k_{23}}{k_{31}} + {k_{13}}{k_{21}}{k_{32}} - {k_{23}}{k_{32}}{a_1} - {k_{13}}{k_{31}}{a_2} - {k_{21}}{k_{12}}{a_3}}}$$
The transmission spectrum of PIT metamaterials can be obtained:
$$|t |= |{{{c(1 + n)} \mathord{\left/ {\vphantom {{c(1 + n)} {[{c(1 + n) - i\omega x} ]}}} \right.} {[{c(1 + n) - i\omega x} ]}}} |$$
Figure 8 is the transmission spectra of PIT based on simulated and mode. The unit of modeling parameters is GHz. ${\kappa _{12}} = 14,\ {\kappa _{21}} = 5.6,\ {\kappa _{13}} = - 14,\ {\kappa _{31}} = 6,\ {\kappa _{23}} = - 4.5,\ {\kappa _{32}} = - 28$ ${g_1} = - 5.3,\ {g_2} = - 3.7,\ {r_1} = 0.25,\ {r_2} = - 0.01,\ {r_3} = 0.17.$ The transmission window based on mole is similar to the transmission window based on simulated as shown in Fig. 8, the difference between them is frequency shift, which is caused by the difference of substrate (FR-4 dielectric-slab) in simulated and model. In model, the dissipation factor of substrate has not been considered, which leads to frequency shift. From Fig. 8, We can conclude that the linearly coupled Lorentz oscillator mode can be used to analyse coupling process between SRR, square wire and cut wire.

 figure: Fig. 8.

Fig. 8. The transmission spectra of two transmission window PIT based on simulated and model.

Download Full Size | PDF

3. Conclusion

In summary, two transmission window PIT with bright-bright coupling and bright-dark coupling has been implemented. only three modes are needed to obtain two transmission window PIT, which can lead to miniaturization of the meta-atom of PIT. In addition, SRR is embedded in square ring by using the ingenious design, which further leads to miniaturization of the meta-atom of PIT. At last, the linearly coupled Lorentz oscillator model has been used to analyse coupling process between SRR, square wire and cut wire.

Funding

National Natural Science Foundation of China (NSFC) (61701253 and 61601243); National Key Research and Development Program of China (2016YFE0200200); Natural Science Foundation of Jiangsu Province(BK20170907); Open Research Program in China’s State Key Laboratory of Millimeter Waves (K201809); Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education; NUPTSF (NY217122).

References

1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997). [CrossRef]  

2. S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990). [CrossRef]  

3. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999). [CrossRef]  

4. G. Shvets and J. S. Wurtele, “Transparency of magnetized plasma at the cyclotron frequency,” Phys. Rev. Lett. 89(11), 115003 (2002). [CrossRef]  

5. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001). [CrossRef]  

6. M. D. Lukin and A. Imamoglu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001). [CrossRef]  

7. X. Q. Lu, J. H. Shi, R. Liu, and C. Y. Guan, “Highly-dispersive electromagnetically induced transparency in planar symmetric metamaterials,” Opt. Express 20(16), 17581–17590 (2012). [CrossRef]  

8. 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]  

9. S. X. Xia, X. Zhai, L. L. Wang, and S. C. Wen, “Plasmonically induced transparency in double-layered graphene nanoribbons,” Photonics Res. 6(7), 692–702 (2018). [CrossRef]  

10. Z. Vafapour and M. R. Forouzeshfard, “Disappearance of plasmonically induced reflectance by breaking symmetry in metamaterials,” Plasmonics 12(5), 1331–1342 (2017). [CrossRef]  

11. Y. L. Xiang, L. L. Wang, Q. Lin, S. X. Xia, M. Qin, and X. Zhai, “Tunable dual-band perfect absorber based on L-shaped graphene resonator,” IEEE Photonics Technol. Lett. 31(6), 483–486 (2019). [CrossRef]  

12. M. Amin, M. Farhat, and H. Baǧcı, “A dynamically reconfigurable Fano metamaterial through graphene tuning for switching and sensing applications,” Sci. Rep. 3(1), 2105 (2013). [CrossRef]  

13. Y. L. Xiang, X. Zhai, Q. Lin, S. X. Xia, M. Qin, and L. L. Wang, “Dynamically tunable plasmon-induced transparency based on an H-shaped graphene resonator,” IEEE Photonics Technol. Lett. 30(7), 622–625 (2018). [CrossRef]  

14. Z. Vafapour, “Slow light modulator using semiconductor metamaterial,” in Integrated Optics: Devices, Materials, and Technologies XXII. International Society for Optics and Photonics, San Francisco, CA, ed. (Academic, 2018), pp. 105352A.

15. Z. Vafapour and H. Ghahraloud, “Semiconductor-based far-infrared biosensor by optical control of light propagation using THz metamaterial,” J. Opt. Soc. Am. B 35(5), 1192–1199 (2018). [CrossRef]  

16. Y. Zhao, C. K. Wu, B. S. Ham, M. K. Kim, and E. Awad, “Microwave induced transparency in ruby,” Phys. Rev. Lett. 79(4), 641–644 (1997). [CrossRef]  

17. Y. B. Luo, X. Yan, Q. S. Zeng, J. N. Zhang, X. Zhang, B. Li, Q. C. Lu, and X. M. Ren, “Graphene-based dual-band antenna in the millimeter-wave band,” Microw. Opt. Technol. Lett. 60(12), 3014–3019 (2018). [CrossRef]  

18. Z. Vafapour, “Large group delay in a microwave metamaterial analog of electromagnetically induced reflectance,” J. Opt. Soc. Am. A 35(3), 417–422 (2018). [CrossRef]  

19. C. Zhang, Q. Cheng, J. Yang, J. Zhao, and T. J. Cui, “Broadband metamaterial for optical transparency and microwave absorption,” Appl. Phys. Lett. 110(14), 143511 (2017). [CrossRef]  

20. L. J. Liang, Z. Zhang, X. Yan, X. Ding, D. Q. Wei, Q. L. Yang, Z. H. Li, and J. Q. Yao, “Broadband Terahertz Transmission Modulation Based on Hybrid Graphene-Metal Metamaterial,” J. Electron. Sci. Technol. 16(2), 98–104 (2018). [CrossRef]  

21. A. Jabber, F. A. Tahir, R. Ramzan, O. Siddiqui, and M. Amin, “A Lumped Element Analog of Dual-Stub Microwave Electromagnetically Induced Transparency Resonator,” in 2018 18th Mediterranean Microwave Symposium (MMS). IEEE, Istanbul, Turkey, ed. (Academic, 2018), pp. 168-170.

22. X. Yan, M. S. Yang, Z. Zhang, L. J. Liang, D. Q. Wei, M. Wang, M. J. Zhang, T. Wang, L. H. Liu, J. H. Xie, and J. Q. Yao, “The terahertz electromagnetically induced transparency-like metamaterials for sensitive biosensors in the detection of cancer cells,” Biosens. Bioelectron. 126, 485–492 (2019). [CrossRef]  

23. A. Keshavarz and Z. Vafapour, “Thermo-optical applications of a novel terahertz semiconductor metamaterial design,” J. Opt. Soc. Am. B 36(1), 35–41 (2019). [CrossRef]  

24. W. Pan, Y. J. Yan, Y. Ma, and D. J. Shen, “A terahertz metamaterial based on electromagnetically induced transparency effect and its sensing performance,” Opt. Commun. 431, 115–119 (2019). [CrossRef]  

25. A. Keshavarz and Z. Vafapour, “Water-Based Terahertz Metamaterial for Skin Cancer Detection Application,” IEEE Sens. J. 19(4), 1519–1524 (2019). [CrossRef]  

26. C.-K. Chen, Y.-C. Lai, Y.-H. Yang, C.-Y. Chen, and T.-J. Yen, “Inducing transparency with large magnetic response and group indices by hybrid dielectric metamaterials,” Opt. Express 20(7), 6952–6960 (2012). [CrossRef]  

27. S. Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. L. Zhang, and A. A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80(15), 153103 (2009). [CrossRef]  

28. H.-M. Li, S.-B. Liu, S.-Y. Liu, S.-Y. Wang, H. F. Zhang, B.-R. Bian, and X.-K. Kong, “Electromagnetically induced transparency with large delay-bandwidth product induced by magnetic resonance near field coupling to electric resonance,” Appl. Phys. Lett. 106(11), 114101 (2015). [CrossRef]  

29. X. J. Liu, J. Q. Gu, R. Singh, Y. F. Ma, J. Zhu, Z. Tian, M. X. He, J. G. Han, and W. L. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett. 100(13), 131101 (2012). [CrossRef]  

30. J. Q. Gu, R. Singh, X. J. Liu, X. Q. Zhang, Y. F. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. G. Han, and W. L. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012). [CrossRef]  

31. 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]  

32. F. L. Zhang, X. He, X. Zhou, Y. L. Zhou, S. An, G. Y. Yu, and L. N. Pang, “Large group index induced by asymmetric split ring resonator dimmer,” Appl. Phys. Lett. 103(22), 221904 (2013). [CrossRef]  

33. L. Zhu, F. Y. Meng, J. H. Fu, Q. Wu, and J. Hua, “An approach to configure low-loss and full transmission metamaterial based on electromagnetically induced transparency,” IEEE Trans. Magn. 48(11), 4285–4288 (2012). [CrossRef]  

34. H.-M. Li, S.-B. Liu, S.-Y. Liu, and H.-F. Zhang, “Electromagnetically induced transparency with large group index induced by simultaneously exciting the electric and the magnetic resonance,” Appl. Phys. Lett. 105(13), 133514 (2014). [CrossRef]  

35. F. L. Zhang, Q. Zhao, C. W. Lan, X. He, W. H. Zhang, J. Zhou, and K. P. Qiu, “Magnetically coupled electromagnetically induced transparency analogy of dielectric metamaterial,” Appl. Phys. Lett. 104(13), 131907 (2014). [CrossRef]  

36. S. Y. Xiao, T. Wang, T. T. Liu, X. C. Yan, Z. Li, and C. Xu, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018). [CrossRef]  

37. H.-M. Li, S. B. Liu, S.-Y. Liu, S.-Y. Wang, G.-W. Ding, H. Yang, Z.-Y. Yu, and H.-F. Zhang, “Low-loss metamaterial electromagnetically induced transparency based on electric toroidal dipolar response,” Appl. Phys. Lett. 106(8), 083511 (2015). [CrossRef]  

38. R. Singh, I. Al-Naib, D. R. Chowdhury, L. Q. Cong, C. Rockstuhl, and W. L. Zhang, “Probing the transition from an uncoupled to a strong near-field coupled regime between bright and dark mode resonators in metasurfaces,” Appl. Phys. Lett. 105(8), 081108 (2014). [CrossRef]  

39. X.-J. Shang, X. Zhai, X.-F. Li, L.-L. Wang, B.-X. Wang, and G.-D. Liu, “Realization of graphene-based tunable plasmon-induced transparency by the dipole-dipole coupling,” Plasmonics 11(2), 419–423 (2016). [CrossRef]  

40. X. L. Zhao, C. Yuan, W. H. Lv, S. L. Xu, and J. Q. Yao, “Plasmon-induced transparency in metamaterial based on graphene and split-ring resonators,” IEEE Photonics Technol. Lett. 27(12), 1321–1324 (2015). [CrossRef]  

41. S. Han, R. Singh, L. Q. Cong, and H. L. Yang, “Engineering the fano resonance and electromagnetically induced transparency in near-field coupled bright and dark metamaterial,” J. Phys. D: Appl. Phys. 48(3), 035104 (2015). [CrossRef]  

42. J. Malik, S. K. Oruganti, S. Song, N. Y. Ko, and F. Bien, “Electromagnetically induced transparency in sinusoidal modulated ring resonator,” Appl. Phys. Lett. 112(23), 234102 (2018). [CrossRef]  

43. L. Zhu, L. Dong, F.-Y. Meng, J.-H. Fu, and Q. Wu, “Influence of symmetry breaking in a planar metamaterial on transparency effect and sensing application,” Appl. Opt. 51(32), 7794 (2012). [CrossRef]  

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

45. 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]  

46. H. Y. Zhang, Y. Y. Cao, Y. Z. Liu, Y. Li, and Y. P. Zhang, “A novel graphene metamaterial design for tunable terahertz plasmon induced transparency by two bright mode coupling,” Opt. Commun. 391, 9–15 (2017). [CrossRef]  

47. R. Yahiaoui, J. A. Burrow, S. M. Mekonen, A. Sarangan, J. Mathews, I. Agha, and T. A. Searles, “Electromagnetically induced transparency control in terahertz metasurfaces based on bright-bright mode coupling,” Phys. Rev. B 97(15), 155403 (2018). [CrossRef]  

48. M. C. Schaafsma, A. Bhattacharya, and J. G. Rivas, “Diffraction enhanced transparency and slow thz light in periodic arrays of detuned and displaced dipoles,” ACS Photonics 3(9), 1596–1603 (2016). [CrossRef]  

49. A. Halpin, N. Hoof, A. Bhattacharya, M. Christiaan, and J. G. Rivas, “Terahertz diffraction enhanced transparency probed in the near field,” Phys. Rev. B 96(8), 085110 (2017). [CrossRef]  

50. A. D. Humphrey, N. Meinzer, T. A. Starkey, and W. L. Barnes, “Surface lattice resonances in plasmonic arrays of asymmetric disc dimers,” ACS Photonics 3(4), 634–639 (2016). [CrossRef]  

51. A. Bhattacharya and J. G. Rivas, “Full vectorial mapping of the complex electric near-fields of THz resonators,” APL Photonics 1(8), 086103 (2016). [CrossRef]  

52. M. Manjappa, Y. K. Srivastava, and R. Singh, “Lattice-induced transparency in planar metamaterials,” Phys. Rev. B 94(16), 161103 (2016). [CrossRef]  

53. L. Zhu, F.-Y. Meng, J.-H. Fu, Q. Wu, and J. Hua, “Multi-band slow light metamaterial,” Opt. Express 20(4), 4494–4512 (2012). [CrossRef]  

54. I. M. Mirza, W. Ge, and H. Jing, “On the optical nonreciprocity and slow light propagation in coupled spinning optomechanical resonators,” arXiv preprint arXiv,1810.03709 (2018).

55. M. Amin, R. Ramzan, and O. Siddiqui, “Slow wave applications of electromagnetically induced transparency in microstrip resonator,” Sci. Rep. 8(1), 2357 (2018). [CrossRef]  

56. Z. J. Zhang, J. B. Yang, X. He, Y. X. Han, J. J. Zhang, J. Huang, D. B. Chen, and S. Y. Xu, “Active Enhancement of Slow Light Based on Plasmon-Induced Transparency with Gain Materials,” Materials 11(6), 941 (2018). [CrossRef]  

57. Z. Vafapour, “Slowing down light using terahertz semiconductor metamaterial for dual-band thermally tunable modulator applications,” Appl. Opt. 57(4), 722–729 (2018). [CrossRef]  

58. https://www.cst.com/products/csts2.

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 (8)
Fig. 1.
Fig. 1. (a) The schematic view of cut wire. (b) The transmission spectra of cut wire under incident x-pol and y-pol electromagnetic wave. (c) The electric field distribution of cut wire under incident x-pol electromagnetic wave. (d) The electric field distribution of cut wire under the incident y-pol electromagnetic wave. The geometrical parameters are as follows: a = 16 mm, b = 16 mm, l1 = 14 mm, w1 = 1 mm, h = 1 mm.

View in Article | Download Full Size | PDF

Fig. 2.
Fig. 2. (a) The schematic view of square ring. (b) The transmission spectra of square ring under incident y-pol electromagnetic wave. (c) The electric field distribution of square ring under incident y-pol electromagnetic wave. The geometrical parameters are as follows: a = 16 mm, b = 16 mm, l2 = 10.9 mm, w2 = 0.2 mm, h = 1 mm.

View in Article | Download Full Size | PDF

Fig. 3.
Fig. 3. (a) The schematic view of SRR. (b) The transmission spectra of SRR under incident y-pol electromagnetic wave. (c) The electric field distribution of SRR under incident y-pol electromagnetic wave. The geometrical parameters are as follows: a = 16 mm, b = 16 mm, l3 = 10 mm, w3 = 0.2 mm, g = 0.6 mm, h = 1 mm.

View in Article | Download Full Size | PDF

Fig. 4.
Fig. 4. (a) The schematic view of two transmission window PIT. (b) The transmission spectra of two transmission window PIT.

View in Article | Download Full Size | PDF

Fig. 5.
Fig. 5. (a) The electric field distribution of two transmission window PIT at low transmission valley frequency (5.40 GHz). (b) The electric field distribution of two transmission window PIT at low transmission peak (6.05 GHz). (c) The electric field distribution of two transmission window PIT at middle transmission valley frequency (6.72 GHz). (d) The electric field distribution of two transmission window PIT at high transmission peak (7.05 GHz). (e) The electric field distribution of two transmission window PIT at high transmission valley frequency (7.60 GHz).

View in Article | Download Full Size | PDF

Fig. 6.
Fig. 6. The transmission spectra of SRR + SR + CW (SRR, square ring, cut wire), SRR + SR (SRR, square ring), SRR + CW (SRR, cut wire), and SR + CW (square ring, cut wire).

View in Article | Download Full Size | PDF

Fig. 7.
Fig. 7. (a) The transmission spectra of two transmission window PIT with different d2. (b) The transmission spectra of two transmission window PIT with different d1.

View in Article | Download Full Size | PDF

Fig. 8.
Fig. 8. The transmission spectra of two transmission window PIT based on simulated and model.

View in Article | Download Full Size | PDF

Equations (9)

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

Q ¨ 1 ( t ) + γ 1 Q ˙ 1 ( t ) + ω a 2 Q 1 ( t ) + κ 12 Q 2 ( t ) + κ 13 Q 3 ( t ) = g 1 E 0 ( t ) Q ¨ 2 ( t ) + γ 2 Q ˙ 2 ( t ) + ω b 2 Q 2 ( t ) + κ 21 Q 1 ( t ) + κ 2 3 Q 3 ( t ) = g 2 E 0 ( t ) Q ¨ 3 ( t ) + γ 3 Q ˙ 3 ( t ) + ω c 2 Q 3 ( t ) + κ 31 Q 1 ( t ) + κ 32 Q 2 ( t ) = 0
E 0 ( t ) = E 0 e i ω t
Q 1 ( t ) = Q 1 e i ω t
Q 2 ( t ) = Q 2 e i ω t
Q 1 = g 1 ( a 2 a 3 − k 23 k 32 ) E 0 + g 2 ( k 32 k 13 − k 12 a 3 ) E 0 a 1 a 2 a 3 + k 12 k 23 k 31 + k 13 k 21 k 32 − k 23 k 32 a 1 − k 13 k 31 a 2 − k 21 k 12 a 3
Q 2 = g 1 ( k 23 k 31 − k 21 a 3 ) E 0 + g 2 ( a 1 a 3 − k 12 k 31 ) E 0 a 1 a 2 a 3 + k 12 k 23 k 31 + k 13 k 21 k 32 − k 23 k 32 a 1 − k 13 k 31 a 2 − k 21 k 12 a 3
Q 3 = g 1 ( k 21 k 32 − k 31 a 2 ) E 0 + g 2 ( k 31 k 12 − k 32 a 1 ) E 0 a 1 a 2 a 3 + k 12 k 23 k 31 + k 13 k 21 k 32 − k 23 k 32 a 1 − k 13 k 31 a 2 − k 21 k 12 a 3
χ = g 1 ( a 2 a 3 + k 23 k 31 − k 32 k 23 − k 21 a 3 ) + g 2 ( a 1 a 3 + k 32 k 13 − k 13 k 31 − k 12 a 3 ) a 1 a 2 a 3 + k 12 k 23 k 31 + k 13 k 21 k 32 − k 23 k 32 a 1 − k 13 k 31 a 2 − k 21 k 12 a 3
| t | = | c ( 1 + n ) / c ( 1 + n ) [ c ( 1 + n ) − i ω x ] [ c ( 1 + n ) − i ω x ] |
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