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Abstract
Dielectric nanostructures reinforcing light-matter interactions by manipulating geometric parameters have a sound momentum in optoelectronic applications. Here, we construct and numerically demonstrate a new platform with multiple dipolar resonant behaviors or impressive switching operation and optical sensing with a high sensitivity and figure of merit (FOM) via the graphene-silicon combined metamaterials. Ultra-sharp resonances are excited by introducing broken symmetry in such all-dielectric metamaterials (ADMs) consisting of two silicon trapezoidal bodies on a silica substrate. By analyzing the distributions of the electromagnetic fields and current densities, we find that two types of multipole modes have been excited to support multiple ultra-narrowband resonances in the near-infrared range. The influence of geometers, such as period, thickness, asymmetry parameters, and polarization angle of the incident light, has also been studied. In addition, by adjusting the Fermi levels of graphene, we realize a 95% amplitude modulation efficiency, which manifests perfect capacity for an optical switch. According to the calculated results, the highest sensitivity can reach 447.5 nm/RIU and a large FOM is also up to 1173 RIU−1. This platform not only introduces new insight onto the achievement of high-quality ultra-sharp resonant responses but also offers a distinct possibility for the further development of high-quality related applications in optical sensors, notch filtering, strong light-matter interactions including the nonlinear optics, and multispectral optoelectronics.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials (MMs), composed of subwavelength scale resonators, manipulate the electromagnetic response via controlling the structure size, material, and shape, ensure the light-matter interaction being stronger, hence having been utilized for high-performance sensing [1–5]. Traditionally, owing to their strong local field enhancement, MMs made of metallic nanostructures have attracted a lot attention and have been widely studied in many promising applications from optical switches [6,7], optical modulators [8–10], solar absorbers [11–13] to multi-band perfect absorbers [14–16], optical sensors [17,18]. However, their drawbacks, the high cost and intrinsic ohmic losses of noble metal [19], and the range of operating wavelength is sacred once determined, led to a low value of FOM, thus hindering their practical applications. Regarding the above problems, dielectric nanostructures have been considered as an alternative due to their low loss responses [20]. As to the latter problem, graphene is a special two-dimensional material comprised of carbon atoms packed in a honeycomb lattice structure. Since its peculiar characteristics in physics and chemistry, graphene became a hot spot in nano-photonics field [21–25]. The outstanding conductivity of graphene can reach up to 200000 cm2 V−1s−1, which means a low non-radiative loss [26]. Most importantly, the Fermi levels would be changed through chemical doping or applied different bias voltage, thereby achieving optical switching and sensing tuning [27–29]. All of these are perfectly suitable for tunable devices that are of great significance in electromagnetic and photonics systems.
In order to enhance the light-mater interaction, highly confined modes and the high-quality resonant behaviors have been widely considered in these years [30–34]. Fano resonance, a special resonance in optics, exists in both plasmonic particles and dielectric particles, is caused by the interference between super-radiant mode (bright mode) and sub-radiant mode (dark mode) [35]. Compared to metal-based metasurfaces, dielectric nanostructures which are accompanied by strong near-field confinement and can be tailored easily at nanoscale. In addition, the dark mode (magnetic responses) that Fano resonance required, which usually existed in more complicated plasmonic geometrics, can be supported by simple all-dielectric nanoparticles like spheres, disks, or cubes [36,37]. It is an interesting phenomenon that occurs in Fano resonance, an asymmetric sharp curve can be generated and converts from absolute transmission to absolute reflection [38]. Therefore, to combine the dielectric nanostructures with narrow spectral lines, optical devices with an enhanced performance can be realized.
In this paper, we design a device to achieve tunable multi-Fano resonances by coupling the bright modes excited directly by the incident light and the dark modes supported by asymmetric dielectric nanostructures, which represent the leading edges in low ohmic losses, compatibility with CMOS (complementary metal oxide semiconductor) preparation technique [39,40]. The device consists of paired silicon-based trapezoid bodies deposited on quartz substrate separated by an unpatterned monolayer graphene sheet. They are all accompanied by non-radiative loss, facilitating to high FOM. Transmission spectra were calculated by the finite-difference time-domain method [41,42]. Then, to give an insight into the nature of resonant modes, we perform multipoles expansion, electromagnetic field, and displacement current distribution analysis, verifying the predominant contribution in the four resonances. It generated two electromagnetic excitation modes (magnetic dipoles (MDs) and electric quadrupoles (EQs). Also, the effect of different geometric parameters was described. Moreover, the modulation depth and resonance position can be tuned by varying the chemical potential of graphene. Interestingly, except achieving high sensitivity and FOM during the optical sensing, we demonstrate that both the polarization angular dependence on the incident light and the modification of bias voltage of graphene can also be applied in optical switching. Therefore, this design and the related results not only get rid of those limitations of traditional sensors but also have potential applications in the fields of nano-photonics and optoelectronic devices including optical switching, detection, modulators.
2. Structural design and results
Structural simulation and analyses of spectral pattern were based on the technique of three-dimensional FDTD. The simulation conditions of the z direction are set as perfectly matched layers (PMLs). Meanwhile, periodic boundary conditions (PBC) are set in the x and y directions. The incident beam propagates along the z direction with the linearly polarized electric field along x direction. A 3 × 3 array is shown schematically in Fig. 1(a). we can see that paired Si trapezoid bodies with the thickness of t1 = t2 = 310 nm are deposited on the silica (SiO2) substrate with the thickness of 200 nm. The Si resonators array and the SiO2 substrate are separated by a single graphene sheet. The Si material we prefer for the pairs is based on the feature that its high refractive index in optical band is with high feasibility for strong electromagnetic resonances [43,44]. Both the dielectric constants of Si and SiO2 are adopted from Palik handbook [45]. The refractive index of the initial surrounding medium we assume is 1.33. We place two dielectric structures of varying sizes to provide asymmetry in a unit cell. The dark mode can be excited by the interaction between the double structures of un-uniform size, realizing Fano resonances. Top view of the unit cell is illustrated in Fig. 1(b) and the geometric parameters are described briefly below: the periodic length along x and y directions is selected as P = 680 nm; the lengths of the top side (lt) and bottom side (lb) are 220 nm and 450 nm, respectively. The width of the top structure is w1 = 230 nm and the bottom one is w2 = 180 nm to yield an asymmetry that exists on y-axis. Besides, the distance from center to center is 335 nm. For simplicity's sake, the thickness of graphene is regarded as 0.34 nm. The surface conductivity (${\sigma _{gra}}$) can be calculated by the following Kubo formula [46,47]:
Here, j is the unit of imaginary part, e denotes the charge of a unit electron, $\omega $ is the angular frequency, $\hbar $ is the reduced Planck’s constant, scattering rate $\Gamma = 2{\tau ^{^{ - 1}}}$ ($\tau $ is relaxation time), ${f_d}(\zeta ,{\mu _c},{\rm T}) = {({{e^{{{^{({\zeta - {\mu_c}} )}} / {{k_B}\textrm{T}}}}} + 1} )^{ - 1}}$ is Fermi-Dirac distribution where kB is Boltzmann’s constant, Τ is the Kelvin temperature (unit: K), and µc is the chemical potential of graphene, which would change when chemical doping or bias voltage is employed. Due to the flexible tunability of the Fermi level of graphene, many workers used it to tailor nano resonant frequency to cater to different needs [48–50]. In the modeling and simulation, the corresponding values are listed as follows: T = 300 K, $\tau $ = 1 ps, and µc = 1.0 eV.
Fig. 1. (a) Structure diagram of the periodic asymmetry trapezoidal bodies nanostructures on a silica substrate. The t, t1, and t2 are the thicknesses of the substrate, the top trapezoidal body, and the bottom trapezoidal body, respectively. (b) Top view of the unit cell and the geometric parameters. P is the periodic length along x and y directions. lt and lb are the top and bottom lengths of the trapezoidal bodies. w1 and w2 are the widths of the trapezoidal bodies, respectively.
The transmission behavior for graphene-all dielectric metamaterials (GADMs) structure is provided in Fig. 2(a). Four asymmetric line shapes can be observed around the wavelength of 1312 nm, 1222 nm, 1175 nm, and 1129 nm, respectively. Herein, we named them orderly as Res1, Res2, Res3, and Res4, respectively. One should note that all the four resonances can produce unity modulation amplitude. More importantly, our structure proposed is not limited to the simulation level, but also with the feasibility for experiments. First, a single graphene sheet is produced on copper by chemical vapor deposition (CVD) and transferred to the SiO2 substrate by wet transfer. Then spin-coating and baking the ZEP520A, a photoresist, on the Si film which can be deposited onto the sample by low pressure physical vapor deposition (LPCVD). Finally, employing electron beam lithography (EBL) and inductively coupled plasma etching (ICP etching) to pattern the trapezium-like array. The process ends up with the removal of positive resist [51,52]. For the convenience of manipulating the Fermi energy by external voltage, we need to cover an ion-gel film on the graphene, and employ metal as a gate electrode [53–55].
Fig. 2. (a) Transmission spectra of our proposed structure under the illumination of an x-polarized plane wave at normal incidence. (b) The contributions of different electromagnetic excitations in four resonances. The insets are large versions of Res1, Res2, and Res3.
To have a better understanding of the mechanism of each resonance, we utilized multipole decomposition under Cartesian coordinate, getting the scattered powers of various electromagnetic excitations [56]. Due to the difference in the simulation software, there is a certain deviation in the resonance positions, but it does not affect the analysis and discussion. The corresponding multipole moments can be given by [57,58]:
Here, $\vec{P},\vec{M},\vec{T}$ are the symbols of electric, magnetic, and toroidal dipole (namely ED, MD, TD), respectively. $Q_{\alpha \beta }^{(e)},Q_{\alpha \beta }^{(m)}(\alpha ,\beta = x,y,z)$ denote electric, magnetic quadrupole (namely EQ, MQ). $\vec{j} $ is the displacement current, $\vec{r} $ is a vector of distance, c and $\omega $ are the light speed and angular frequency. Then, the scattering intensities we calculated can be derived:
Based on the equations and theories above, we can definitely know how the four Fano resonances are realized. As shown in Fig. 2(b), we can obtain that the main contributions of the resonances. The electromagnetic field distributions are plotted in Figs. 3(a)–3(d), which agree well with the simulations above except for Res2. It will be explained in following. The magnetic field component Hz in the x-y plane of Res1 is shown in Fig. 3(a). We note that the field is nearly confined in the bottom structure and formed an anticlockwise current loop, which brings forth MD mode [59]. Figure 2(b) seems to give us a direct assumption that MQ is the dominant contribution of Res2 excitation. But in fact, from the electric field profile Ez and displacement current in the x-z plane at Res2 (Fig. 3(b)), we can observe that it is a pair of MD moments that are at work, and the reverse direction leads to their offset cancellation, which causes them to be no effort on far-field. Thus, it may have been neglected in multipole decomposition analysis. Res3 is similar to Res1, except that, the generated position is the opposite of Res1, as illustrated in Fig. 3(c). Figure 3(d) confirms that the EQ contribution to Res3 is dominant. The EQ is created by the four corners, where current loops formed on the same side have inverse orientations. And we can also figure them as two antiparallel EDs [60].
Fig. 3. The distribution of electric magnetic field and displacement current. (a) Magnetic field component (Hz) distribution in x-y plane at Res1. (b) Electric field profile Ez and displacement current in the x-z plane at Res2. (c) Magnetic field component (Hz) distribution in x-y plane at Res3. (d) Electric field component (Ez) distribution and displacement current direction in x-y plane at Res4. The blank arrows in (a)-(d) denote the displacement current vectors.
3. Discussion
For the proposed structure, taking into account modulator amplitude and narrow line width, we derived the ideal structure by optimizing various geometrical parameters. Firstly, as shown in Fig. 4(a), increasing the period P of the structure and other parameter values are fixed, it will be accompanied by the attenuated collective oscillations, thus yielding red shift on all resonances. Moreover, apart from red shift, with the P close to 720 nm, we get narrower line-widths on Res1 and Res3, which mean higher Q-factors. Q factor, namely the ratio between the operating wavelength at the resonant dip and the line width of the half-transmission peak value [61]. Thus, the simulation results reflect an effectiveness way in respect to pursued high Q factor. But one could notice that the resonance amplitudes have fallen. The balance between the strong modulation depth and high Q-factor, however, leaves something to be desired. In Fig. 4(b), similarly, clear red shifts can be spotted resulting from the increased effective refractive index of Si metasurface with the gradual t1 = t2. Moreover, Fig. 4(c) is the linear fitting shift of operating wavelength as a function of P in a certain error range. And a steeper slope of Res2 can be observed in Fig. 4(d), meaning Res2 has more sensitivity to the change of the thickness of Si relative to other resonances.
Fig. 4. (a),(b) Transmission spectra of the GADMs structure with different periods (P) and the thickness of Si (t1 and t2). (c) The linearly fitted of resonance positions as a function of P. (d) The line chart between resonance positions and the thickness of Si.
The introduction of symmetry breaking in the structure, generating new Fano resonant modes. Therefore, asymmetry parameter is crucial to our research. Here, two different asymmetric parameters (thickness gap Δt = t2 – t1 and width gap δ = w1 – w2) are reported. For the symmetric condition (t1 = t2 = 310 nm, w1 = w2 = 230 nm), there is only one resonance can be observed and a relative wide line width between the transmission peak and the transmission dip, and we distinguish it as MD. As shown in Fig. 5(a), we discuss the effect of asymmetry parameter Δt formed by increasing t2. As soon as the Δt ≠ 0, three new resonances possessed ultra-narrow line widths are excited. But what is noteworthy is that, the shifts and intensities of other resonant wavelengths are insensitive to the increasing Δt apart from that Res1 has a growing modulation amplitude. This is because there is no remarkable influence on the resonances’ excitation energies altered by the symmetry breaking along the z direction of the nanostructure. Then, we consider decreasing w2 in order to increase asymmetry parameter δ, as illustrated in Fig. 5(b). It means reducing the proportion of Si, the interaction between light and matter becomes weaker, which results in blue shifts in resonances. Until δ is stepped up to 50 nm, the optimization on strength and quantity is realized at our chosen operating wavelength. Interestingly, Res3 vanishes when δ goes up to over 75 nm and the Q-factor of that is meanwhile infinitely high. But while further increasing δ, Res3 emerges gradually again and presents pronounced Fano resonance. Essentially, we attributed this phenomenon to the symmetry protected-BICs which is unstable in a state of disturbed symmetry. All up, altering the symmetry properties of proposed structure enables adjusting the transmission characteristics, including linewidth, number, and intensity. The results will help us affirm the introduction of asymmetry in ADMs opening a pathway to design excellent performance optical devices further.
Fig. 5. Transmission evolution for the sensor under the adjustment of various structure elements. (a) Asymmetric parameter Δt = t2 – t1, t1 = 310 nm. (b) asymmetric parameter δ = w1 - w2, w1 = 230 nm. (c) Polarization angle of the incident light (θ). The green shade areas portray the disappearance of the initial resonances. The orange shade areas portray the appearance of three new resonance modes.
We further study the effect of polarization angle of incident light (θ) on resonance positions when other structural elements are fixed. Figure 5(c) illustrates the calculated spectral features at different polarization angles (from 0° to 90°). Interestingly, we discover that the initial four resonances fade gradually until they vanish with increasing θ. Whereas three new resonances arise and the intensities reinforce to maximum at TM mode. The ultra-sharp resonances at Res1, Res2, Res3, and Res4 can be turned on or off by tuning the polarization direction of the incident light. Thereby, controlling the resonance numbers and operating wavelengths by the polarization angle actively may indicate the possibility to apply in multispectral optical switching.
Following, to explore the chemical potential of graphene effect, we investigate the transmission spectra in Fig. 6. The chemical potentials are modified through bias voltage. We can see that resonance amplitudes become prominent with µc varying from 0.5 eV to 0.6 eV, especially in Res1, Res3, and Res4. Then there is a slight change just on Res1 when µc increases to 1 eV. It doesn’t keep increasing and just adjusts optical wavelength shift if µc is higher than 1 eV. However, the most noteworthy feature of the change is that the modulation depth occurs in Res1. We take the spectrum condition at Res1 under µc = 0.5 eV as Ton state and take the spectrum condition under µc = 1 eV as Toff state. The spectral intensity of Ton state is 0.61, whereas Toff state is only 0.03. According to the equation of modulation depth [62]: (Ton - Toff)/ Ton ×100%, the modulation degree can be calculated as 95%, which manifests perfect capacity for an optical switch.
Fig. 6. Spectrum responses of the sensor under a tuning of the chemical potential of graphene. The red short lines are the label of Toff and Ton, respectively.
Lastly, let us consider spectral sensitivity and FOM, the two important characteristic performances of sensing. The shift in the resonant wavelength becomes well-pronounced when the refractive index of surrounding medium has changed slightly, enabling excellent performance, as demonstrated in Figs. 7(a)–7(d). Notably, the operating wavelengths appear to red-shift as the refractive index increases at a rate of 0.01. The linear relationships between them are provided in Fig. 7(e). The sensitivity can be defined as S = Δλ/Δn where Δλ and Δn define as the wavelength shift of resonance position and the variation of refractive index, while FOM = S/Δλ′, Δλ′ is the resonance linewidth difference between transmission peak and transmission dip [63]. Therefore, linear fittings to these data reveal the sensitivities of Res1, Res2, Res3, and Res4 of 351.8, 90, 219.5, 447.5 nm/RIU, and the corresponding FOM are equal to 1172.7, 44, 378.4, and 552.5 RIU−1. The optimal results are superior to some previous works [64–68], promoting a further practical application in optical sensing.
Fig. 7. (a)-(d) Transmission responses for Res1, Res2, Res3, and Res4 under different refractive indices of surrounding environment medium. (e) The linearly fitted relationship between resonance positions and refractive indices.
4. Conclusion
In this paper, artificial all-dielectric nano-scale metamaterials are used for high performance optical switching and sensing applications considering their advantages in strong multi-polar resonant and ultra-narrowband lineshape. We represent asymmetrical silicon nanostructures that can excite magnetic responses, thus leading to multiple sharp Fano resonances. Coupled with the low-loss dielectric materials and tunable Fermi levels of graphene, excellent performance on the device is realized. We obtain a modulation depth of 95% owing to the tunability of conductivity through adjusting the bias voltage, which manifests perfect capacity for an optical switch. Moreover, artificially controlling the resonance numbers and operating wavelengths is also realized by the polarization angle actively, which may indicate the possibility to apply in multispectral optical switching and the further operations. Based on the multiple dipolar resonant silicon-based metamaterials, high quality optical sensing capability is numerically demonstrated with the optimal sensitivity up to 447.5 nm/RIU and a maximal FOM surpassing 1170. These results boost the development of GADMs-based nanostructure with desirable resonances at demanding optical frequencies and offer a platform to construct multispectral optical switching and sensing devices.
Funding
National Natural Science Foundation of China (62275112, 62065007, 11804134); Natural Science Foundation of Jiangxi Province (20202BAB201009, JXSQ2019201058).
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. W. Tang, L. Wang, X. Chen, C. Liu, A. Yu, and W. Lu, “Dynamic metamaterial based on the graphene split ring high-Q Fano-resonator for sensing applications,” Nanoscale 8(33), 15196–15204 (2016). [CrossRef]
2. M. Yang, X. Song, H. Zhang, Y. Ye, Y. Ren, X. Ren, and J. Yao, “Position-guided Fano resonance and amended Gauss Amp model for the control of slow light in hybrid graphene-silicon metamaterials,” Opt. Express 28(8), 11933–11945 (2020). [CrossRef]
3. Y. L. Liao and Y. Zhao, “Ultra-narrowband dielectric metamaterial absorber with ultra-sparse nanowire grids for sensing applications,” Sci. Rep. 10(1), 1–7 (2020). [CrossRef]
4. D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef]
5. X. Chen, W. Fan, and C. Song, “Multiple plasmonic resonance excitations on graphene metamaterials for ultrasensitive terahertz sensing,” Carbon 133, 416–422 (2018). [CrossRef]
6. H. Zhong, Z. Liu, X. Liu, G. Fu, G. Liu, J. Chen, and C. Tang, “Ultra-high quality graphene perfect absorbers for high performance switching manipulation,” Opt. Express 28(25), 37294–37306 (2020). [CrossRef]
7. K. Moon and S. Park, “Graphene-based plasmonic switch using resonant coupling to the local plasmon resonance,” Phys. Rev. Appl. 11(3), 034074 (2019). [CrossRef]
8. W. Zhao, H. Jiang, B. Liu, Y. Jiang, C. Tang, and J. Li, “Fano resonance based optical modulator reaching 85% modulation depth,” Appl. Phys. Lett. 107(17), 171109 (2015). [CrossRef]
9. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, and M. Paniccia, “A high-speed silicon optical modulator based on a metal–oxide–semiconductor capacitor,” Nature 427(6975), 615–618 (2004). [CrossRef]
10. J. Chen, M. Zhang, P. Gu, Z. Yan, C. Tang, B. Lv, and M. Zhu, “Broadband, wide-incident-angle, and polarization-insensitive high-efficiency absorption of monolayer graphene with nearly 100% modulation depth at communication wavelength,” Results Phys. 40, 105833 (2022). [CrossRef]
11. T. Putnin, C. Lertvachirapaiboon, R. Ishikawa, K. Shinbo, K. Kato, S. Ekgasit, K. Ounnunkad, and A. Baba, “Enhanced organic solar cell performance: Multiple surface plasmon resonance and incorporation of silver nanodisks into a grating-structure electrode,” Opto-Electron. Adv. 2(7), 19001001 (2019). [CrossRef]
12. H. Xiong, Y. B. Wu, J. Dong, M. C. Tang, Y. N. Jiang, and X. P. Zeng, “Ultra-thin and broadband tunable metamaterial graphene absorber,” Opt. Express 26(2), 1681–1688 (2018). [CrossRef]
13. Y. Chen, X. Li, X. Luo, S. Maier, and M. Hong, “Tunable near-infrared plasmonic perfect absorber based on phase-change materials,” Photonics Res. 3(3), 54–57 (2015). [CrossRef]
14. S. X. Xia, X. Zhai, Y. Huang, J. Q. Liu, L. L. Wang, and S. C. Wen, “Multi-band perfect plasmonic absorptions using rectangular graphene gratings,” Opt. Lett. 42(15), 3052–3055 (2017). [CrossRef]
15. B. Tang, N. Yang, X. Song, G. Jin, and J. Su, “Triple-band anisotropic perfect absorbers based on alpha-phase MoO3 metamaterials in visible frequencies,” Nanomaterials 11(8), 2061 (2021). [CrossRef]
16. Z. Yan, X. Lu, K. Chen, Z. Lv, X. Pu, C. Tang, and P. Cai, “Ultranarrow dual-band perfect absorption in visible and near-infrared regimes based on three-dimensional metamaterials for ultrahigh-sensitivity sensing,” J. Lightwave Technol. 39(22), 7217–7222 (2021). [CrossRef]
17. X. Liu, G. Fu, X. Zhan, and Z. Liu, “All-metal resonant metamaterials for one-, two-, three-band perfect light absorbers and sensors,” Plasmonics 14(4), 967–971 (2019). [CrossRef]
18. Y. Zhu, H. Zhang, D. Li, Z. Zhang, S. Zhang, J. Yi, and W. Wang, “Magnetic plasmons in a simple metallic nanogroove array for refractive index sensing,” Opt. Express 26(7), 9148–9154 (2018). [CrossRef]
19. DÖ Güney, T. Koschny, and C. M. Soukoulis, “Reducing ohmic losses in metamaterials by geometric tailoring,” Phys. Rev. B 80(12), 125129 (2009). [CrossRef]
20. B. I. Popa and S. A. Cummer, “Compact dielectric particles as a building block for low-loss magnetic metamaterials,” Phys. Rev. Lett. 100(20), 207401 (2008). [CrossRef]
21. E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent nonlinear optical response of graphene,” Phys. Rev. Lett. 105(9), 097401 (2010). [CrossRef]
22. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010). [CrossRef]
23. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]
24. S. Huang, C. Song, G. Zhang, and H. Yan, “Graphene plasmonics: physics and potential applications,” Nat. Photonics 6(6), 1191–1204 (2016). [CrossRef]
25. Z. Yan, L. Gao, C. Tang, B. Lv, P. Gu, J. Chen, and M. Zhu, “Simultaneously achieving narrowband and broadband light absorption enhancement in monolayer graphene,” Diamond Relat. Mater. 126, 109122 (2022). [CrossRef]
26. S. K. Vashist, “Advances in graphene-based sensors and devices,” J. Nanomed. Nanotechnol. 04(01), e127 (2012). [CrossRef]
27. H. Li, L. Wang, and X. Zhai, “Tunable graphene-based mid-infrared plasmonic wide-angle narrowband perfect absorber,” Sci. Rep. 6(1), 36651 (2016). [CrossRef]
28. D. B. Farmer, R. Golizadeh-Mojarad, V. Perebeinos, Y. M. Lin, G. S. Tulevski, J. C. Tsang, and P. Avouris, “Chemical doping and electron-hole conduction asymmetry in graphene devices,” Nano Lett. 9(1), 388–392 (2009). [CrossRef]
29. X. Jiang, J. Bao, and X. Sun, “Multiwavelength optical switch based on controlling the Fermi energy of graphene,” Phys. Rev. Appl. 9(4), 044026 (2018). [CrossRef]
30. J. Li, R. Yu, and Y. Wu, “Actively tunable double-Fano and Ramsey-Fano resonances in photonic molecules and improved sensing performance,” Phys. Rev. A 94(6), 063822 (2016). [CrossRef]
31. N. Acharyya and G. Kozyreff, “Multiple critical couplings and sensing in a microresonator-waveguide system,” Phys. Rev. Appl. 8(3), 034029 (2017). [CrossRef]
32. Z. Liu, Y. Xu, Y. Lin, J. Xiang, T. Feng, Q. Cao, J. Li, S. Lan, and J. Liu, “High-Q quasibound states in the continuum for nonlinear metasurfaces,” Phys. Rev. Lett. 123(25), 253901 (2019). [CrossRef]
33. Y. Y. Li, Q. T. Cao, J. H. Chen, X. C. Yu, and Y. F. Xiao, “Microcavity sensor enhanced by spontaneous chiral symmetry breaking,” Phys. Rev. Appl. 16(4), 044016 (2021). [CrossRef]
34. D. V. Nesterenko, S. Hayashi, and V. Soifer, “Ab initio spatial coupled-mode theory of Fano resonances in optical responses of multilayer interference resonators,” Phys. Rev. A 106(2), 023507 (2022). [CrossRef]
35. M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017). [CrossRef]
36. J. C. Yan, Y. Zhang, X. G. Yin, and C. P. Huang, “Excitation and dynamic tuning of high-Q resonances with electromagnetic coupling asymmetry,” Phys. Rev. Appl. 14(5), 054003 (2020). [CrossRef]
37. K. E. Chong, B. Hopkins, I. Staude, A. E. Miroshnichenko, J. Dominguez, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Observation of Fano resonances in all-dielectric nanoparticle oligomers,” Small 10(10), 1985–1990 (2014). [CrossRef]
38. C.Y. Ji, Y. Zhang, B. Zou, and Y. Yao, “Robust Fano resonance in the photonic valley Hall states,” Phys. Rev. A 103(2), 023512 (2021). [CrossRef]
39. X. Zhang, Q. T. Cao, Z. Wang, Y. X. Liu, C. W. Qiu, L. Yang, Q. Gong, and Y. F. Xiao, “Symmetry-breaking-induced nonlinear optics at a microcavity surface,” Nat. Photonics 13(1), 21–24 (2019). [CrossRef]
40. S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016). [CrossRef]
41. S. D. Gedney, “Introduction to the finite-difference time-domain (FDTD) method for electromagnetics,” Synthesis Lectures on Computational Electromagnetics 6(1), 1–250 (2011). [CrossRef]
42. D. M. Sullivan, “Electromagnetic Simulation Using the FDTD Method,” (John Wiley & Sons, 2013).
43. P. Moitra, B. A. Slovick, W. li, I. I. Kravchencko, D. P. Briggs, S. Krishnamurthy, and J. Valentine, “Large-scale all-dielectric metamaterial perfect reflectors,” ACS Photonics 2(6), 692–698 (2015). [CrossRef]
44. M. Panmai, J. Xiang, S. Li, X. He, Y. Ren, M. Zeng, J. She, J. Li, and S. Lan, “Highly efficient nonlinear optical emission from a subwavelength crystalline silicon cuboid mediated by supercavity mode,” Nat. Commun. 13(1), 2749 (2022). [CrossRef]
45. E. D. Palik, “Electromagnetic Simulation Using the FDTD Method,” (Academic Press, 1998).
46. B. Wang, X. Zhang, F. J. Garcia-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012). [CrossRef]
47. A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B 86(19), 195408 (2012). [CrossRef]
48. S. Xiao, T. Liu, X. Wang, X. Liu, and C. Zhou, “Tailoring the absorption bandwidth of graphene at critical coupling,” Phys. Rev. B 102(8), 085410 (2020). [CrossRef]
49. Y. Fan, N. H. Shen, F. Zhang, Q. Zhao, Z. Wei, P. Zhang, J. Dong, Q. Fu, H. Li, and C. M. Soukoulis, “Photoexcited graphene metasurfaces: significantly enhanced and tunable magnetic resonances,” ACS Photonics 5(4), 1612–1618 (2018). [CrossRef]
50. K. N. Shushama, M. M. Rana, R. Inum, and M. B. Hossain, “Graphene coated fiber optic surface plasmon resonance biosensor for the DNA hybridization detection: Simulation analysis,” Opt. Commun. 383, 186–190 (2017). [CrossRef]
51. B. Xiao, S. Tong, A. Fyffe, and Z. Shi, “Tunable electromagnetically induced transparency based on graphene metamaterials,” Opt. Express 28(3), 4048–4057 (2020). [CrossRef]
52. Z. Yan, L. Kong, C. Tang, J. Deng, P. Gu, J. Chen, and M. Zhu, “Ultra-broadband and completely modulated absorption enhancement of monolayer graphene in a near-infrared region,” Opt. Express 30(19), 34787–34796 (2022). [CrossRef]
53. M. Chen and Z. Xiao, “Metal-graphene hybrid terahertz metamaterial based on dynamically switchable electromagnetically induced transparency effect and its sensing performance,” Diamond Relat. Mater. 124, 108935 (2022). [CrossRef]
54. E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, and D. I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015). [CrossRef]
55. B. Xiao, Y. Wang, W. Cai, and L. Xiao, “Design and prediction of PIT devices through deep learning,” Opt. Express 30(9), 14985–14997 (2022). [CrossRef]
56. A. E. Miroshnichenko, A. B. Evlyukhin, Y. F. Yu, R. M. Bakker, A. Chipouline, A. I. Kuznetsov, B. Luk’yanchuk, B. N. Chichkov, and Y. S. Kivshar, “Nonradiating anapole modes in dielectric nanoparticles,” Nat. Commun. 6(1), 8069 (2015). [CrossRef]
57. C. Zhou, S. Li, Y. Wang, and M. Zhan, “Multiple toroidal dipole Fano resonances of asymmetric dielectric nanohole arrays,” Phys. Rev. B 100(19), 195306 (2019). [CrossRef]
58. Y. Wang, S. Yu, Z. Gao, S. Song, H. Li, T. Zhao, and Z. Hu, “Excitations of multiple Fano resonances based on permittivity-asymmetric dielectric meta-Surfaces for nano-sensors,” IEEE Photonics J. 14(1), 1–7 (2022). [CrossRef]
59. V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014). [CrossRef]
60. R. Xu and J. Takahara, “All-dielectric perfect absorber based on quadrupole modes,” Opt. Lett. 46(15), 3596–3599 (2021). [CrossRef]
61. H. Liu, L. Zheng, P. Ma, Y. Zhong, B. Liu, X. Chen, and H. Liu, “Metasurface generated polarization insensitive Fano resonance for high-performance refractive index sensing,” Opt. Express 27(9), 13252–13262 (2019). [CrossRef]
62. L. Huang, J. Liu, H. Deng, and S. Wu, “Phonon-like plasmonic resonances in a finite number of graphene nanoribbons,” Adv. Optical Mater. 6(11), 1701378 (2018). [CrossRef]
63. G. D. Liu, X. Zhai, L. L. Wang, Q. Lin, S. X. Xia, X. Luo, and C. J. Zhao, “A high-performance refractive index sensor based on Fano resonance in Si split-ring metasurface,” Plasmonics 13(1), 15–19 (2018). [CrossRef]
64. S. Sahu, J. Ali, P. P. Yupapin, and G. Singh, “Porous silicon based Bragg-grating resonator for refractive index biosensor,” Photonic Sens 8(3), 248–254 (2018). [CrossRef]
65. N. Wang, M. Zeisberger, U. Huebner, V. Giannini, and M. A. Schmidt, “Symmetry-breaking induced magnetic Fano resonances in densely packed arrays of symmetric nanotrimers,” Sci. Rep. 9(1), 1–9 (2019). [CrossRef]
66. M. Qin, C. Pan, Y. Chen, Q. Ma, S. Liu, E. Wu, and B. Wu, “Electromagnetically induced transparency in all-dielectric U-shaped silicon metamaterials,” Appl. Sci. 8(10), 1799 (2018). [CrossRef]
67. Y. Chen, X. Zhou, Y. Xu, C. Xiao, and Q. Zhu, “Fano resonance sensing based on coupling of a sub-wavelength grating and an all-dielectric multilayer film under angle modulation,” Appl. Opt. 60(10), 2902–2906 (2021). [CrossRef]
68. Z. Yan, X. Lu, W. Du, Z. Lv, C. Tang, P. Cai, and Z. Yu, “Ultraviolet graphene ultranarrow absorption engineered by lattice plasmon resonance,” Nanotechnology 32(46), 465202 (2021). [CrossRef]
