Open Access
Add to BibSonomy
Abstract
A hybrid bilayer black phosphorus (BP) and graphene structure with high sensitivity is proposed for obtaining plasmon-induced transparency (PIT). By means of surface plasmon resonance in the rectangular-ring BP structure and ribbon graphene structure, a PIT effect with high refractive index sensitivity is achieved, and the surface plasmon hybridization between graphene and anisotropic BP is analyzed theoretically. Meanwhile, the PIT effect is quantitatively described using the coupled oscillator model and the strong coherent coupling phenomena are analyzed by adjusting the coupling distance between BP and graphene, the Fermi level of graphene, and the crystal orientation of BP, respectively. The simulation results show that the refractive index sensitivity S = 7.343 THz/RIU has been achieved. More importantly, this is the first report of tunable PIT effects that can produce up to quintuple PIT windows by using the BP and graphene hybrid structure. The high refractive index sensitivity of the quintuple PIT system for each peak is 3.467 THz/RIU, 3.467 THz/RIU, 3.600 THz/RIU, 4.267 THz/RIU, 4.733 THz/RIU and 6.133 THz/RIU, respectively, which can be used for multiple refractive index sensing function.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Surface plasmon polaritons (SPPs) are generated by the interaction of free electrons and photons on the metal-dielectric surface [1–5]. SPPs are capable of exhibiting strong field energy near the surface so that high sensitivity can be obtained for the changes in refractive index of adjacent media [6]. Currently, there are many studies based on SPPs, and among them, plasmon-induced transparency (PIT) has attracted a great deal of interest from researchers. As a research focus, PIT is a coherent nonlinear optical effect [7,8] and it is the result of destructive interference between different resonant modes, producing a symmetrical and narrow transparent window in the absorption spectrum. In recent years, the PIT effects have been demonstrated to have potential in a variety of applications, such as optical switches [9,10], slow light devices [1,11,12], and sensors [13,14]. The overall trend in the published work related to PIT is toward multiple PIT effects. In 2019, Gao et al. designed the m-shaped graphene to produce dual PIT. Multi-channel ultra-slow light had been investigated in this paper [15]. In 2020, Xiong et al. reported the triple PIT effects based on quasi-continuous monolayer graphene structure [1], which focused on the slow light effect. In 2021, the same group demonstrated the dynamically adjustable the PIT with quadruple transparency peaks, which could be used for multi-switch and slow light [16]. Optical sensing also is a research focus [17–20]. However, multi-channel sensing functions have been rarely investigated.
Two-dimensional (2D) materials have provided new approaches for improving the sensing performance of PIT devices, such as graphene [21,22], transition metal dichalcogenides (TMDCs) [23] and black phosphorus (BP) [24]. Compared with other 2D materials, the most attractive feature of BP is the different effective electron masses along two crystal axes [25], thus exhibiting the anisotropy of the plasma. Nanostructured BPs have been utilized to excite the PIT effect in the infrared band [26,27]. Beyond BP, the graphene has received widely interest in the PIT field [28,29] because the surface plasmons of graphene have the advantages of strong local electromagnetic field capability and electrically tunable resonant wavelength [30–32]. Through combining the advantages of BP and graphene [27,33–36], it can not only increase the tunable ways of PIT, but also significantly improve the refractive index sensitivity. Therefore, hybridization of plasmonic modes in BP and graphene can further develop the application scopes of PIT in infrared frequency.
In this paper, a hybrid bilayer BP-graphene structure (BPGS) is proposed to obtain multi -PIT effects and the physical properties of PIT are analyzed in planar metamaterials, which helps us to understand specifically the coupling process between the plasmon modes. This work not only has important applications in the field of sensing, but also provides a guidance for the application of infrared BP as well as graphene. In section 2, the parameters of our structure and the theoretical formulation are presented in detail. In section 3, the physical mechanism of bright-dark mode coupling is used to generate the single PIT effect which is further elaborated by observing the electric field diagram. In addition, the transparent window modulation mechanism is discussed from different perspectives. In terms of applications, a high refractive index sensitivity of 7.343 THz/RIU is achieved for the single PIT window. The multi-PIT effects are designed and investigated in section 4. More interestingly, with the introduction of multiple identical dark modes, double PIT, triple PIT, quadruple PIT and quintuple PIT effects are respectively realized, which can be used for multi-channel high-sensitive refractive index sensing. Section 5 provides a summary. In recent years, there have been new developments in the field of sensing [37], and we believe that the proposed structure and the theoretical analysis in this paper can provide guidance for sensing.
2. Structural model and theoretical analysis
According to the published literatures, BP and graphene can produce the bright and dark modes in the infrared band [38], respectively. Also, in previous research work of PIT, the structure of rectangular cavity is also used as the bright mode structure [39–41] and can confine the energy well in the cavity. However, graphene and BP have their own attractive characteristics and properties. Thus, both materials are employed for making full use of their advantages and developing more modulation ways in the proposed BPGS structure, as shown in Fig. 1, which consists of a graphene ribbon (GR) and a BP rectangular ring (BPRR).
Fig. 1. (a) A 3D diagram of the proposed structure. (b) Top view of BP rectangular ring. (c) Top view of graphene ribbon. (d) The cross-section of structure.
The corresponding geometric parameters in Fig. 1 are given as follows: Px = 255 nm, Py = 400 nm, S1 = 255 nm, S2 = 250 nm, S3 = 67.5 nm, S4 = 57.5 nm, S5 = 215 nm, w = 45 nm, h1 = 60 nm and h2 = 1.34 µm. The dielectric is assumed a constant refractive index of n = 1.70 [27,38]. Here, the finite difference time domain (FDTD) method is used to investigate numerically. The incident wave is the x- polarized planar wave in the negative direction of the z- axis, and the periodic boundary conditions are used in the x- and y- directions, while the z- direction is adopted as the perfectly matched layer. The mesh size is 10 nm.
According the Kubo model, the conductivity of graphene is as follows [16,33]:
The conductivity ${\sigma _{x,y}}$ of monolayer BP are given as [24,33,46]:
where ${\sigma _{x,y}}$ are defined as the armchair (AC) and zigzag (ZZ) direction conductivities of BP, respectively. $\eta$ = 10 meV is the scattering rate. ${D_{x,y}} = \pi {e^2}n/{m_{x,y}}$ are the drude weight along the AC and ZZ directions, respectively. n is the carrier density of monolayer BP. ${m_x} = {\hbar ^2}/(2{\gamma ^2}/\Delta + {\eta _c})$ and ${m_y} = {\hbar ^2}/(2{\upsilon _c})$ are the electron mass along the AC and ZZ directions, respectively. The four conduction band parameters are $\gamma = 4a/\pi eVm$, $\Delta = 2eV$, ${\upsilon _c} = {\hbar ^2}/1.4{m_0}$, and $a = 0.223nm$, respectively. ${m_0} = 9.10938 \times {10^{ - 31}}kg$ is the standard electron rest mass.The coupled Lorentz oscillator model is explained, where the incident wavelength is indicated by ${E_0}{e^{i\omega t}}$, while the two modes are defined as $\textrm{|}{A_1}\rangle \textrm{ = }{\tilde{A}_1}(\omega ){e^{i\omega t}}$ and $\textrm{|}{A_2}\rangle \textrm{ = }{\tilde{A}_2}(\omega ){e^{i\omega t}}$, respectively, so the field amplitudes can be summarized as [47,48]:
The following relationship exists by solving Eq. (3):
The theoretical absorption $A(\omega )$ is calculated as [47–49]:
The graphene metamaterial shown in the Fig. 1 can be obtained by the following process: graphene can be controllably grown on copper foils by chemical vapor deposition and then transferred to the substrate by dry transfer technique. The bias voltage can be applied between the graphene and the dielectric layer by using an applied ionic gel. The Fermi level of graphene is modulated by adding an applied voltage, allowing the response characteristics of the entire composite structure to be tuned [50,51]. In addition, various methods, such as mechanical stripping and liquid phase stripping, have been developed to prepare BP materials of different sizes [52,53].
3. Simulation results and applications
Figure 2(a) illustrates the absorption spectrum of each structure, where the x- direction crystal axis of BP is along the AC direction and the electric field distributions corresponding to points “a”, “b” and “c” are shown in Figs. 2(b) – 2(d), respectively. In this simulation, the carrier density of BP is set to $n = 1.2 \times {10^{14}}c{m^{ - 2}}$ and the Fermi level of graphene is set to ${E_f} = 0.7eV$. As shown in Fig. 2(a), a PIT peak is generated at f = 34.84 THz.
Fig. 2. (a) Simulation results and analytical fitting of absorption spectrum. (b) – (d) Electric field distribution diagram corresponding to the points “a”, “b” and “c”, respectively.
The PIT effect is caused by the coupling between the bright and dark modes [1,33]. The bright mode can be excited by the incident wave, such as dipole plasmon mode. In contrast, the dark mode cannot be excited by the incident wave and do not radiate to the external environment, such as quadrupolar plasmon mode. The BPRR and the GR structure can excite the bright mode and the dark mode, respectively. The strong interaction occurs between the BPRR and the incident light at f = 34.84 THz, as shown in the blue curve. On the contrary, the GR structure is not directly excited, and the absorption spectrum does not change significantly. Consequently, as shown in the black curve, the PIT is caused by the interaction between BPRR and GR.
Through analysis and fitting of Eq. (5), Fig. 2(a) illustrates the Lorentz coupling mode curve. The fitting spectra between FDTD and the Lorentz coupling mode are displayed in Fig. 2(a), which shows that the simulation results are consistent with the analysis ones. The values are given as: ${\omega _1}$ is 34.99 THz, ${\omega _2}$ is 35.19 THz, $\kappa $ is 2.6, ${g_1}$ is 1.49, $\varphi $ is $\pi $. ${\gamma _1}$ is 1.65 and ${\gamma _2}$ is 0.54, respectively.
The electric field energy indicates the excited extent of the structure, and both are positively correlated. As shown in Figs. 2(b) – 2(c), the electric field energy of BPRR structure shows a strong electric field distribution, which indicates a strong interaction with the incident wave. However, the GR structure is the opposite. Figure 2(c) shows the electric field diagram of only the graphene structure for generating the dark mode. The light almost directly passes through the whole structure. In this case, there is no energy localized in the structure. So, the energy distribution is hardly seen in Fig. 2(c). On the contrary, when BPGR are presented, as shown in Fig. 2(d), it can be seen that the energy is confined in the GR structure. The absorption spectrum and the electric field intensity are consistent. In the absorption spectrum in Fig. 2(a), a PIT window is generated at f = 34.84 THz. Therefore, the mode produced by graphene is analyzed at this frequency. Combining the absorption spectrum and the electric field distribution diagram, the dark-mode frequency is at f = 34.84 THz. As can be observed in Fig. 2(d), when both structure units exist, the electric field energy is transferred from BPRR structure to GR structure. According to the above discussion, the incident wave is firstly coupled into the bright mode. Then the electromagnetic energy will oscillate back and forth between the bright mode and the dark mode, resulting in a destructive interference. Finally, the bright mode is suppressed to generate the PIT phenomenon.
Next, the factors that influence the PIT phenomenon are further analyzed. The PIT coupling strength can be changed by adjusting the coupling distance. The effect of different coupling distances h1 on the absorption spectrum is investigated by the simulation and the results of different h1 are shown in Fig. 3. When h1 gradually decreases, the resonance peak is gradually wider and deeper, resulting in a transparent window at f = 34.84 THz. Obviously, the coupling strength can be adjusted by designing the coupling distance. The smaller coupling distance is, the stronger coupling between the BPRR and the GR is.
Fig. 3. Simulation results of absorption spectrum at different coupling distance h1. The purple curve, blue curve, red curve, green curve and black correspond to h1 = 60 nm, 90 nm, 120 nm,150 nm and 180 nm, respectively.
The PIT can also be dynamically tuned by adjusting the Fermi level of GR structure. In Fig. 4(a), two specific PIT effects are activated in the same structure. The transparent window can be observed when ${E_f}$ of graphene is 0.7 eV or 1.4 eV. In Fig. 4(a), the distinct peaks and dips are named as “a1”, “a2”, “a3”, “b1”, “b2”, and “b3” in the order from left to right. It can be seen from Fig. 4(b), as the Fermi level of graphene increases, the first PIT gradually disappears and the second PIT slowly forms. The yellow position represents the movement of peaks with high absorption. From previous research work, the Fermi level can be modulated by voltage [54,55], so the PIT effect based on the BPGS structure can also be flexibly and dynamically modulated.
Fig. 4. (a) Simulation results of absorption spectrum. The green curve, blue curve and red curve correspond to BPGS with ${E_f}$ = 0.7 eV, 1.4 eV and only BPRR, respectively. (b) The visual evolution of the whole structure at different ${E_f}$. (c) – (h) Electric field distribution diagram corresponding to the points “ai” and “bi” (i = 1, 2, 3), respectively.
To further investigate the cause of splitting, the electric field distribution corresponding to the GR is shown in Figs. 4(c)–4(h). It can be seen that when the Fermi levels are 0.7 eV and 1.4 eV, the excitation modes of graphene are different. It is worth noting that the phases of electric fields in Figs. 4(c) and 4(e), or Figs. 4(f) and 4(h), have opposite distributions at the two inclination angles. Therefore, due to the coupling of two different dark modes and the same bright mode, two PIT windows are produced.
Furthermore, the absorption performance under changing the crystal orientation of BP is analyzed. An important property of BP is the anisotropy, i.e., the electron mass m of BP along the y- direction is larger than that in the x- direction. Using the above property, the PIT window can be regulated.
The absorption spectra are shown in Fig. 5, where the x- direction crystal axis of BP is along the ZZ direction. The corresponding geometric parameters are consistent with Fig. 1 mentioned above. A new PIT phenomenon can be seen. The resonant frequencies are different owing to the anisotropic conductivity of the metamaterial. Since the electron mass of BP along the ZZ direction is larger than that of the AC direction, the resonant peak of BP structure moves toward the lower frequency. As shown in Fig. 5, the bright mode generated by BP and the dark mode generated by graphene, produce bright-dark mode coupling at f = 25.93 THz, and then two bright modes of BP and graphene lead to a new PIT window at f = 21.04 THz. The electric field distributions corresponding to points “I”, “II”, “III” and “IV” are shown in Figs. 5(b)–5(e). According to Figs. 5(b) and 5(c), if it’s just only the BPRR or GR structure, the electric field energy is weak. However, when the BPRR and GR structures interact with each other, corresponding to the Figs. 5(d) and 5(e), the energy is much higher than that in Figs. 5(b) and 5(c), indicating that strong coupling occurs. In general, two PIT windows are generated at f = 21.04 THz and f = 25.93 THz.
Fig. 5. (a) The absorption spectra of PIT metamaterial structure. (b)-(e) Electric field distribution diagram corresponding to the points “I”, “II”, “III” and “IV”. The polarization of incident wave is along AC direction.
Moreover, the PIT sensing function of the structure is analyzed. The change in local refractive index produces a perturbation of the electric field, which eventually leads to a change in the resonant frequency. Refractive index sensor is one of the sensing research highlights [56]. The relations between the refractive index of surrounding environment and the absorption peaks are investigated. As shown in Fig. 6, under the conditions of different refractive index changing from 1.00 to 1.30 with a step of 0.05, the absorption peak 1 and peak 2 show a red shift with the refractive index increasing.
Fig. 6. (a) Absorption spectrum at different refractive index. (b) Spectrum drifts of the peak 1 with the change of RI. (c) Spectrum drifts of the peak 2 with the change of RI.
The resonant frequency of the BPRR structure can be expressed as [57,58]:
The resonant frequency of the GR structure can be expressed as [57]:
Therefore, the resonant frequency of the BPGS structure can be expressed as [33,57]:
Surface plasmon can be excited when the momentum between light and SPPs is matched. The photon momentums of BP and graphene are $\hbar k_d$ (where $k_d = 2\pi n_d/\lambda$), and $\hbar k_d$ (where $k_d = 2\pi n_d/\lambda$) [3], respectively. ${n_{d(g)}}$ represent refractive index. The dispersion relation represents the relationship between the effective refractive index and wavelength. When the dispersion relation exists at the intersection point, ${n_d}$ is equal to ${n_g}$, leading to the same photon momentums. Consequently, the wave vector matching condition is satisfied, and strong coupling occurs between the two resonant modes [57,59].
The sensitivity of the refractive index sensor is specified as [31,38,60]:
here, $\Delta f$ and $\Delta n$ are the changes of the resonant frequency and the refractive index, respectively. The ${S_{peak1}}$ is 5.314 THz/RIU and ${S_{peak2}}$ is 7.343 THz/RIU. The sensing-comparison is presented in Table 1. Compared with other structures, our proposed structure has advantages in refractive index sensing. The S values are larger than other PIT-based devices. Based on the single PIT effect of this paper, the function of high-sensitivity sensing can be achieved.
Table 1. Sensing – comparison of PIT devices
4. Multiple PIT structure design
From the above analysis, combining BP and graphene materials have been investigated to improve the refractive index sensitivity of PIT devices. Multiple PITs are further extended to achieve multiple high-sensitivity sensing function by using the BP-multiple graphene structure. As described in the previous section, the graphene structure can generate the dark mode. In this way, multiple PIT effects are achieved by introducing additional graphene structures. The specific schematic diagram is shown in Fig. 7, in which the size parameters of graphene and BP are the same as those in section 2. The corresponding geometric parameters are given in Table 2.
Fig. 7. (a)–(d) The cross-section of the BP-multiple graphene structure. “A”, “B”, “C” and “D” are named for the four structures, respectively.
Table 2. Geometric parameters of BP-graphene structure in Fig. 7
Figure 8 shows that multiple PIT windows are achieved. These new graphene structures are considered as the new dark modes. The independent graphene structures cannot directly be interacted with the incident wave. As described in section 2, the transmission peak in Fig. 8(a) has been shown to be a PIT phenomenon due to the bright and dark mode coupling. A BP – graphene-graphene structure (“A”) with dual PIT phenomenon is constructed by adding a single layer of graphene structure below the GR structure. In Figs. 8(a)–8(b), a new PIT peak appears at the original dip at f = 34.84 THz. In fact, since the newly added graphene structures have exactly the same size parameters as the GR, the same mode is produced, resulting in the bright-dark coupling with the BPRR. It indicates that dual PIT peaks originate from the same physical mechanism as before. Dual PIT, triple PIT, quadruple PIT and quintuple PIT effects can be achieved with the same procedure by adding extra graphene layers. Since the newly added graphene structures have exactly the same size parameters as the graphene ribbon, each graphene structure generates an identical mode. For the whole structure, BP and graphene produce the bright mode and the dark mode, respectively. That is, the dual PIT is generated by one bright mode of BP and two dark modes of graphene. The triple PIT is produced by one bright mode of BP and three dark modes of graphene. Analogously, the quadruple PIT and the quintuple PIT are obtained according to the same mechanism. Consequently, tunability of the number of PIT windows is successfully achieved. The electric field distribution of each structure is given at f = 34.84 THz which reflects the variation of the absorption spectrum. From Figs. 8(f)–8(j), when a new graphene layer is added, the value of absorption spectrum varies from trough to peak, corresponding to the electric field distribution of the BPRR structure cycling sequentially from low-high energy. Low absorption at the centre frequency corresponds to a weak electric field, because the light passes through the structure and will not be captured within the BPRR. That is, the original mode is disrupted when the newly graphene structure is added. In addition, the maximum distance between graphene and BP to produce coupling reaction is much increased. According to the analysis of the coupling distance in section 2, the maximum value of h1 is 180 nm. While in the “D” structure, the coupling distance between the lowermost graphene structure and BP has reached 335 nm. It is because that the upper graphene structures are excited, enhancing the energy transferred to the lowermost graphene layer.
Fig. 8. (a)–(e) The absorption spectrum of the “BPGS”, “A”, “B”, “C” and “D” structures. (f)–(j) Corresponding to the electric field distribution of the BPRR in (a)–(e) at f = 34.84 THz
When the surrounding refractive index changes from 1.00 to 1.15 with a step of 0.05, ${S_{f1}}$, ${S_{f2}}$, ${S_{f3}}$, ${S_{f4}}$, ${S_{f5}}$ and ${S_{f6}}$ are 3.467 THz/RIU, 3.467 THz/RIU, 3.600 THz/RIU, 4.267 THz/RIU, 4.733 THz/RIU and 6.133 THz/RIU, as shown in Fig. 9. With these sensitivity advantages, our proposed structure holds promise for the development of a new high-sensitivity multi-channel sensor.
According to Fig. 3, the strong coupling distance between the two structures is about 60 nm–90 nm. Parameters like L1, L2, L3, L4, L5 …… follow the distances range from 50 nm to 70 nm. The distance between the two lowermost graphene layers is the largest, up to 90 nm. In our proposed structure, the range of frequency band for generating multiple PIT is almost from 30 THz to 41 THz, which leads to a large change of refractive index sensitivity. In general, for higher frequency band, the refractive index sensitivity increases accordingly. At the same time, complex interferences occur between multiple structures, so the refractive index sensitivity is difficult to be improved over a single PIT. This is also a problem encountered in multi-channel optical sensing.
5. Conclusions
In this work, a dynamically controllable PIT has been proposed and investigated by using the BP and graphene hybrid structure. Strong and anisotropic plasmon resonance is excited in this structure, which opens a new door for PIT devices with high sensitivity. The physical mechanisms generating PIT are analyzed in focus. Then, the Lorentz coupling mode is applied to numerically investigate the simulation results. The Fermi level of graphene, the anisotropy of BP, and the coupling distance are the important factors to manipulate the PIT window in our work. Remarkably, the sensitivity S value is 5.314 THz/RIU and 7.343 THz/RIU, which are higher than the same type of PIT structures. In addition, single, double, triple, quadruple and quintuple PIT effects have also been achieved for the first time in the BP and graphene hybrid structure. What’s more, the S of the quintuple PIT system for each peak is 3.467 THz/RIU, 3.467 THz/RIU, 3.600 THz/RIU, 4.267 THz/RIU, 4.733 THz/RIU and 6.133 THz/RIU, respectively. It is believed that the proposed structure can find importance applications in the sensing area.
Funding
National Key Research and Development Program of China (2019YFB1803505); National Natural Science Foundation of China (61975037, 62175039, U2001601); Major Special Projects in Guangdong Province (2018B010114002); Natural Science Foundation of Guangdong Province (2019A1515011471); Guangdong Introducing Innovative and Entrepreneurial Teams of “The Pearl River Talent Recruitment Program” (2019ZT08X340); the Program of Marine Economy Development Special Fund (Six Marine Industries) under Department of Natural Resources of Guangdong Province (GDNRC [2021]33); the Engineering Research Center of Digital Imaging and Display, Ministry of Education, Soochow University (Grant No. SDGC2133); 2021 Characteristic Innovation Research Project for University Teachers (Grant No. 2021DZXX21).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. C. X. Xiong, H. Xu, M. Z. Zhao, B. H. Zhang, C. Liu, B. Zeng, K. Wu, B. X. Ruan, M. Li, and H. J. Li, “Triple plasmon-induced transparency and outstanding slow-light in quasi-continuous monolayer graphene structure,” Sci. China Phys. Mech. Astron. 64(2), 224211 (2021). [CrossRef]
2. T. B. Wang, X. W. Wen, C. P. Yin, and H. Z. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17(26), 24096–24101 (2009). [CrossRef]
3. J. X. Zhang, L. D. Zhang, and W. Xu, “Surface plasmon polaritons: physics and applications,” J. Phys. D: Appl. Phys. 45(11), 113001 (2012). [CrossRef]
4. L. W. Zhang, Q. Wang, and W. W. Meng, “Dual-band absorption enhancement of monolayer transition-metal dichalcogenides in metamaterials,” Optoelectron. Lett. 17(7), 412–417 (2021). [CrossRef]
5. X. M. Wen, Y. G. Bi, F. S. Yi, X. L. Zhang, Y. F. Liu, W. Q. Wang, J. Feng, and H. B. Sun, “Tunable surface plasmon-polariton resonance in organic light-emitting devices based on corrugated alloy electrodes,” Opto-Electron. Adv. 4(8), 200024 (2021). [CrossRef]
6. L. Chen, L. Zhang, X. F. Xu, and L. Lu, “Tuning of the graphene surface plasmon by the monolayer MoS2,” Optoelectron. Lett. 17(11), 646–650 (2021). [CrossRef]
7. 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]
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. M. Li, H. J. Li, H. Xu, C. X. Xiong, M. Z. Zhao, C. Liu, B. X. Ruan, B. H. Zhang, and K. Wu, “Dual-frequency on-off modulation and slow light analysis based on dual plasmon-induced transparency in terahertz patterned graphene metamaterial,” New J. Phys. 22(10), 103030 (2020). [CrossRef]
10. X. Zhang, Z. M. Liu, Z. B. Zhang, E. D. Gao, F. Q. Zhou, X. Luo, J. W. Wang, and Q. Wang, “Photoelectric switch and triple-mode frequency modulator based on dual-PIT in the multilayer patterned graphene metamaterial,” J. Opt. Soc. Am. A 37(6), 1002–1007 (2020). [CrossRef]
11. P. Pitchappa, M. Manjappa, C. P. Ho, R. Singh, N. Singh, C. Lee, and Ieee, “Active Control of Electromagnetically Induced Transparency analogue and Slow Light Phenomena via MEMS Based Terahertz Metamaterials,” in International Conference on Optical MEMS and Nanophotonics (OMN), Singapore, 2016.
12. Q. F. Chen, F. Y. Li, D. Zhang, and H. F. Zhang, “Tunable electromagnetically induced transparency metamaterial based on solid-state plasma: from a narrow band to a broad one,” J. Opt. Soc. Am. B 38(5), 1571–1578 (2021). [CrossRef]
13. 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]
14. A. Alipour, A. Farmani, and A. Mir, “High Sensitivity and Tunable Nanoscale Sensor Based on Plasmon-Induced Transparency in Plasmonic Metasurface,” IEEE Sensors J. 18(17), 7047–7054 (2018). [CrossRef]
15. E. D. Gao, Z. M. Liu, H. J. Li, H. Xu, Z. B. Zhang, X. Zhang, X. Luo, and F. Q. Zhou, “Dual plasmonically induced transparency and ultra-slow light effect in m-shaped graphene-based terahertz metasurfaces,” Appl. Phys. Express 12(12), 126001 (2019). [CrossRef]
16. C. X. Xiong, L. Chao, B. Zeng, K. Wu, M. Li, B. X. Ruan, B. H. Zhang, E. D. Gao, and H. J. Li, “Dynamically controllable multi-switch and slow light based on a pyramid-shaped monolayer graphene metamaterial,” Phys. Chem. Chem. Phys. 23(6), 3949–3962 (2021). [CrossRef]
17. J. P. Nong, L. L. Tang, G. L. Lan, P. Luo, Z. C. Li, D. P. Huang, J. M. Yi, H. F. Shi, and W. Wei, “Enhanced Graphene Plasmonic Mode Energy for Highly Sensitive Molecular Fingerprint Retrieval,” Laser Photonics Rev. 15(1), 2000300 (2021). [CrossRef]
18. J. P. Nong, L. L. Tang, G. L. Lan, P. Luo, Z. C. Li, D. P. Huang, J. Shen, and W. Wei, “Combined Visible Plasmons of Ag Nanoparticles and Infrared Plasmons of Graphene Nanoribbons for High-Performance Surface-Enhanced Raman and Infrared Spectroscopies,” Small 17(1), 2004640 (2021). [CrossRef]
19. G. L. Lan, W. Wei, P. Luo, J. M. Yi, Z. G. Shang, and T. Xu, “Dynamically tunable coherent perfect absorption in topological insulators at oblique incidence,” Opt. Express 29(18), 28652–28663 (2021). [CrossRef]
20. P. Luo, G. Lan, J. Nong, X. Zhang, T. Xu, and W. Wei, “Broadband coherent perfect absorption employing an inverse-designed metasurface via genetic algorithm,” Opt. Express 30(19), 34429–34440 (2022). [CrossRef]
21. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]
22. X. Shi, D. Z. Han, Y. Y. Dai, Z. F. Yu, Y. Sun, H. Chen, X. H. Liu, and J. Zi, “Plasmonic analog of electromagnetically induced transparency in nanostructure graphene,” Opt. Express 21(23), 28438–28443 (2013). [CrossRef]
23. S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev, and A. Kis, “2D transition metal dichalcogenides,” Nat. Rev. Mater. 2(8), 17033 (2017). [CrossRef]
24. K. Wu, H. J. Li, C. Liu, C. X. Xiong, B. X. Ruan, M. Li, E. D. Gao, and B. H. Zhang, “Slow-light analysis based on tunable plasmon-induced transparency in patterned black phosphorus metamaterial,” J. Opt. Soc. Am. A 38(3), 412–418 (2021). [CrossRef]
25. F. N. Xia, H. Wang, and Y. C. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014). [CrossRef]
26. Z. P. Jia, L. Huang, J. B. Su, and B. Tang, “Tunable plasmon-induced transparency based on monolayer black phosphorus by bright-dark mode coupling,” Appl. Phys. Express 13(7), 072006 (2020). [CrossRef]
27. L. Han, L. Wang, H. Z. Xing, and X. S. Chen, “Active control of plasmon-induced transparency with large tunability and high Q-factor in graphene-black phosphorus hybrid system,” J. Phys. D: Appl. Phys. 54(22), 225103 (2021). [CrossRef]
28. D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349(6244), 165–168 (2015). [CrossRef]
29. B. Sensale-Rodriguez, “Graphene-insulator-graphene active plasmonic terahertz devices,” Appl. Phys. Lett. 103(12), 123109 (2013). [CrossRef]
30. X. J. Wang, H. Y. Meng, S. Y. Deng, C. D. Lao, Z. C. Wei, F. H. Wang, C. G. Tan, and X. Huang, “Hybrid Metal Graphene-Based Tunable Plasmon-Induced Transparency in Terahertz Metasurface,” Nanomaterials 9(3), 385 (2019). [CrossRef]
31. H. Y. Shen, C. Y. Liu, F. X. Liu, Y. Q. Jin, B. H. Guo, Z. C. Wei, F. Q. Wang, C. H. Tan, X. G. Huang, and H. Y. Meng, “Multi-band plasmonic absorber based on hybrid metal-graphene metasurface for refractive index sensing application,” Results Phys. 23, 104020 (2021). [CrossRef]
32. C. Zeng, H. Lu, D. Mao, Y. Q. Du, H. Hua, W. Zhao, and J. L. Zhao, “Graphene-empowered dynamic metasurfaces and metadevices,” Opto-Electron. Adv. 5(4), 200098 (2022). [CrossRef]
33. P. Luo, W. Wei, G. L. Lan, X. Z. Wei, L. Y. Meng, Y. Liu, J. M. Yi, and G. Q. Han, “Dynamical manipulation of a dual-polarization plasmon-induced transparency employing an anisotropic graphene-black phosphorus heterostructure,” Opt. Express 29(19), 29690–29703 (2021). [CrossRef]
34. Y. J. Cai, S. L. Li, Y. G. Zhou, K. D. Xu, Y. Wang, S. K. Zuo, and W. T. Joines, “Investigation of multi-resonant and anisotropic plasmonic resonances in the stacked graphene-black phosphorus bilayers,” J. Phys. D: Appl. Phys. 53(2), 025107 (2020). [CrossRef]
35. J. M. Liang, J. T. Lei, Y. Wang, Y. Ding, Y. Shen, and X. H. Deng, “High performance terahertz anisotropic absorption in graphene-black phosphorus heterostructure,” Chin. Phys. B 29(8), 087805 (2020). [CrossRef]
36. Y. J. Cai, K. D. Xu, N. X. Feng, R. R. Guo, H. J. Lin, and J. F. Zhu, “Anisotropic infrared plasmonic broadband absorber based on graphene-black phosphorus multilayers,” Opt. Express 27(3), 3101–3112 (2019). [CrossRef]
37. P. B. Xu, C. Pang, X. Y. Dong, Y. W. Qin, and Y. K. Dong, “Fast Acquirable Brillouin Optical Time-Domain Reflectometry Based on Bipolar-Chirped Pulse Pair,” J. Lightwave Technol. 39(12), 3941–3949 (2021). [CrossRef]
38. C. Liu, H. J. Li, H. Xu, M. Z. Zhao, C. X. Xiong, M. Li, B. X. Ruan, B. H. Zhang, and K. Wu, “Plasmonic biosensor based on excellently absorbable adjustable plasmon-induced transparency in black phosphorus and graphene metamaterials,” New J. Phys. 22(7), 073049 (2020). [CrossRef]
39. B. Tang, Z. P. Jia, L. Huang, J. B. Su, and C. Jiang, “Polarization-Controlled Dynamically Tunable Electromagnetically Induced Transparency-Like Effect Based on Graphene Metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 27(1), 1–6 (2021). [CrossRef]
40. F. Q. Zhou, Y. Q. Wang, X. Zhang, J. W. Wang, Z. M. Liu, X. Luo, Z. B. Zhang, and E. D. Gao, “Dynamically adjustable plasmon-induced transparency and switching application based on bilayer graphene metamaterials,” J. Phys. D: Appl. Phys. 54(5), 054002 (2021). [CrossRef]
41. Z. M. Liu, X. Zhang, F. Q. Zhou, X. Luo, Z. B. Zhang, Y. P. Qin, S. S. Zhuo, E. D. Gao, H. J. Li, and Z. Yi, “Triple plasmon-induced transparency and optical switch desensitized to polarized light based on a mono-layer metamaterial,” Opt. Express 29(9), 13949–13959 (2021). [CrossRef]
42. J. H. Chen, C. Jang, S. D. Xiao, M. Ishigami, and M. S. Fuhrer, “Intrinsic and extrinsic performance limits of graphene devices on SiO2,” Nat. Nanotechnol. 3(4), 206–209 (2008). [CrossRef]
43. S. Y. Xiao, T. T. Liu, C. B. Zhou, X. Y. Jiang, L. Cheng, Y. B. Liu, and Z. Li, “Strong interaction between graphene and localized hot spots in all-dielectric metasurfaces,” J. Phys. D: Appl. Phys. 52(38), 385102 (2019). [CrossRef]
44. M. Li, C. X. Xiong, C. Liu, B. A. Zeng, B. X. Ruan, B. H. Zhang, E. D. Gao, and H. J. Li, “Terahertz plasmonic sensing based on tunable multispectral plasmon-induced transparency and absorption in graphene metamaterials,” J. Phys. D: Appl. Phys. 54(24), 245201 (2021). [CrossRef]
45. B. H. Zhang, H. J. Li, H. Xu, M. Z. Zhao, C. X. Xiong, C. Liu, and K. Wu, “Absorption and slow-light analysis based on tunable plasmon-induced transparency in patterned graphene metamaterial,” Opt. Express 27(3), 3598–3608 (2019). [CrossRef]
46. Y. M. Qing, H. F. Ma, and T. J. Cui, “Tailoring anisotropic perfect absorption in monolayer black phosphorus by critical coupling at terahertz frequencies,” Opt. Express 26(25), 32442–32450 (2018). [CrossRef]
47. C. Hu, Q. Lin, X. Zhai, M. T. Wen, and L. L. Wang, “Plasmonically induced perfect absorption in graphene/metal system,” Nanoscale Res. Lett. 14(1), 1–8 (2019). [CrossRef]
48. Q. Lin, X. Zhai, L. L. Wang, X. Luo, G. D. Liu, J. P. Liu, and S. X. Xia, “A novel design of plasmon-induced absorption sensor,” Appl. Phys. Express 9(6), 062002 (2016). [CrossRef]
49. R. Taubert, M. Hentschel, and H. Giessen, “Plasmonic analog of electromagnetically induced absorption: simulations, experiments, and coupled oscillator analysis,” J. Opt. Soc. Am. B 30(12), 3123–3134 (2013). [CrossRef]
50. J. W. Suk, A. Kitt, C. W. Magnuson, Y. F. Hao, S. Ahmed, J. H. An, A. K. Swan, B. B. Goldberg, and R. S. Ruoff, “Transfer of CVD-Grown Monolayer Graphene onto Arbitrary Substrates,” ACS Nano 5(9), 6916–6924 (2011). [CrossRef]
51. M. Liu, X. B. Yin, E. Ulin-Avila, B. S. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011). [CrossRef]
52. A. Castellanos-Gomez, L. Vicarelli, E. Prada, J. O. Island, K. L. Narasimha-Acharya, S. I. Blanter, D. J. Groenendijk, M. Buscema, G. A. Steele, J. V. Alvarez, H. W. Zandbergen, J. J. Palacios, and H. S. J. van der Zant, “Isolation and characterization of few-layer black phosphorus,” 2D Mater. 1(2), 025001 (2014). [CrossRef]
53. J. Kang, J. D. Wood, S. A. Wells, J. H. Lee, X. L. Liu, K. S. Chen, and M. C. Hersam, “Solvent Exfoliation of Electronic-Grade, Two-Dimensional Black Phosphorus,” ACS Nano 9(4), 3596–3604 (2015). [CrossRef]
54. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012). [CrossRef]
55. Y. X. Wang, W. Cui, H. Q. Ma, H. Xu, Z. Yi, X. L. Cao, X. C. Ren, and Z. H. He, “Outstanding slow-light effect for graphene metasurface in terahertz,” Results Phys. 23, 104002 (2021). [CrossRef]
56. P. B. Xu, X. F. Yu, Z. J. Chen, L. W. Sheng, J. Q. Liu, S. Zhou, K. H. Wen, O. Xu, X. Y. Dong, J. Yang, and Y. W. Qin, “Distributed refractive index sensing based on bending-induced multimodal interference and Rayleigh backscattering spectrum,” Opt. Express 29(14), 21530–21538 (2021). [CrossRef]
57. J. P. Nong, W. Wei, W. Wang, G. L. Lan, Z. G. Shang, J. M. Yi, and L. L. Tang, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express 26(2), 1633–1644 (2018). [CrossRef]
58. T. Low, R. Roldan, H. Wang, F. N. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and Screening in Monolayer and Multilayer Black Phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014). [CrossRef]
59. W. L. Gao, J. Shu, C. Y. Qiu, and Q. F. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012). [CrossRef]
60. 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]
61. V. Ercaglar, H. Hajian, and E. Ozbay, “VO2-graphene-integrated hBN-based metasurface for bi-tunable phonon-induced transparency and nearly perfect resonant absorption,” J. Phys. D: Appl. Phys. 54(24), 245101 (2021). [CrossRef]
62. 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]
63. B. G. Xiao, S. J. Tong, A. Fyffe, and Z. M. Shi, “Tunable electromagnetically induced transparency based on graphene metamaterials,” Opt. Express 28(3), 4048–4057 (2020). [CrossRef]
