Open Access
Add to BibSonomy
Abstract
In this contribution, a tunable plasmonic absorber consisting of periodical elliptical hollow graphene arrays deposited on SiO2 substrate is proposed in the far infrared and terahertz (THz). The simulation calculation results show that the structure supports a variety of effective tuning methods, such as changing the period, geometry parameters, Fermi level, relaxation time, incident angle, to achieve active and passive tuning. When the incident angle is set to 60°, the maximum absorption value (0.31) in our work can be achieved. Meanwhile, the red shift caused by period variations and blue shift phenomenon made of geometry parameters provides an exercisable way to select the resonance range. Therefore, these outcomes undoubtedlyoffer a unique source of inspiration for the diversity of graphene array shapes and the design and fabrication of absorption-related devices, such as filters, spatial light modulators, and sensors.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Exploration on the domain of electromagnetism has always been fascinating. In the process of combining the theory and practice of scientific research, substantial magical and incredible productions have emerged in recent years, such as the invisibility cloaks [1,2]. It takes advantage of super-strong electromagnetic properties of the materials, which are used to manufacture the optical cloaking, to create visual illusions in people or instruments rather than actually concealing objects like witchcraft, so that they disappear from thin air.
The above-mentioned material with magical qualities, called the metamaterial (MM) by the scientific community, is a composite material consisted of artificially designed electromagnetic structures, that purports we can devise the micro-structure to control its macroscopic characteristics. The typical metamaterial is Pendry's earliest metal wire array that can exhibits a negative dielectric constant, and split ring resonator which enables negative magnetic permeability to appear [3,4]. These materials possess abnormal electromagnetic properties that cannot be observed in nature [5,6], such as negative refractive index [7–9], backward wave [10,11]. In recent years, the appearance of a new type of MM has attracted wide attention. Graphene, a single layer of carbon atoms arranged in a two-dimensional plane with a honeycomb lattice [12–17], exhibits the marvelous performance which resembles characters of metal when interacting with incident wave in the infrared and terahertz fields [18–22], and has unique and excellent properties in distrinct fields, embracing that thermal, mechanical, electrical, and optical [23–28]. And apropos of the attraction of graphene, whose surface conductivity can be continuously adjusted with manipulating Fermi level by the application of photo-induced doping or electronic gating [29–33], undoubtedly brings more abundant possibilities for the diversity of MM properties [34–37]. Meanwhile, what pleasantly surprised the researchers is graphene can supports surface plasmon resonance (SPR) [38–42], which allows large amounts of light energy to be concentrated and thus enhances light absorption. Therefore, plasmonic absorbers, based on various properties of graphene metamaterials consisting of diverse arrays shapes, have recently appeared, for instance, nanodisks, ribbons, crosses, etc [24,43–48]. Without exception, all of which have been shown to provide better absorption data than the absorption of light energy (2.3%) by a single sheet of graphene [49]. Thus, we propose an elliptical hollow graphene array that has been rarely studied. Compared with elliptical and double elliptical hollow, our proposed structure has more flexible and variable geometric parameters (long and short axes of inner and outer diameters), which contribute much to the diversity of graphene-based metamaterial resonance absorber designs.
In this work, we designed and theoretically studied a plasmonic absorber consisting of periodical elliptical hollow graphene arrays deposited on SiO2 substrate. Change its period, geometric parameters, Fermi level, relaxation time and incident light angle, so that the optical absorption can be expressly modulated. In addition, the elliptical hollow, elliptical and double elliptical hollow graphene arrays were simply compared under the same parameters. The above simulation results can provide new inspiration for the design and manufacture of photoelectric sensors, photon detectors and modulators in the near-infrared and terahertz bands.
2. Geometric structure of model and method
The important theoretical research measure relies on the finite-difference time-domain (FDTD) method. Figure 1 shows the structural representation and geometric parameters of periodic elliptical hollow graphene arrays deposited on silicon dioxide. The thickness of silica is 300 nm while the substrate is semi-infinite. With regard to the fundamental model of our research, L1 = 600 nm and W1 = 200 nm are long axis and short axis of inner diameter of elliptical hollow, whose long axis and short axis of outer diameter are L2 = 800 nm and W2 = 400 nm. And a systematic arrangement of graphene arrays is achieved in accordance with periodic a = 2.5 μm. The accuracy of mesh in the graphene layer along the x (y) and z axes are set to 25 and 0.2 nm. The above-mentioned geometric parameters of the array transform with specific circumstance in our research procedure, and in the simulation system, light travels in the direction of negative Z axis to irradiate the whole graphene arrays, and its polarization is along the X axis. Therefore, we can obtain the spectral responses of elliptical hollow, elliptical, and double-elliptical of graphene arrays under various parameters.
Fig. 1 The structural representation and geometric parameters of periodic elliptical hollow graphene arrays deposited on SiO2, and the geometric parameters are marked as shown in the figure. The electric field direction is parallel to X direction.
In the case of local confinement, the surface conductivity σg of graphene is represented by random phase approximation (RPA) [50–52], which includes the interband term σinter and the intraband term σintra
where angular frequency is expressed in ω, e represents the electron charge, kB is the Boltzmann constant, EF is Fermi level, ћ = һ/2π is reduced Planck constant, τ refers to relaxation time, T is the temperature in Kelvin, setting to 300 K in our simulation.And the equivalent permittivity of graphene can be described as follows [53]:
where ε0 is the permittivity in a vacuum, tg, setting to 1 nm in our work, refers to the thickness of graphene sheet. In terms of the relative permittivity of SiO2, we choose 3.9 [54]. And the paramount importance in our whole study proceeding is consistently the light absorption that can be calculated by A = 1-T-R expression, where T = |S21(ω)|2 refers to the transmission and R = |S11(ω)|2 is the reflection [55–57]. It is worth mentioning that the perfectly matched layer (PML) boundary condition is applied to the z-direction while the x/y-direction boundary has the application of periodic boundary condition (PBC) [58].3. Results and discussion
In this simulation, the essential parameters of elliptical hollow graphene arrays are set as L1 = 600 nm, W1 = 200 nm, L2 = 800 nm, W2 = 400 nm, EF = 0.6 ev, τ = 0.8 ps, θ = 0°. When we consider the effect of one of parameters on absorption, the others remain unchanged.
Firstly, we change the graphene arrays period a and the variation of absorption can be shown in Fig. 2. With the increase of period a, absorption gradually decreases where accompanied by the blue shift of resonance peak wavelength in the Fig. 2(A). The particular movement in the numbers can be analyzed in detail from Fig. 2(B), and red line represents an approximate linear relationship between absorption and period a. When a = 2.5 μm, absorption is the maximum, 0.224, while the minimum value is 0.06, at a = 5 μm. However, the smallest absorption is stronger than that of monolayer continuous graphene sheet. The cause of this phenomenon can be found from the electric field diagram of Fig. 2(A). In the far infrared and terahertz bands, local surface plasmon resonance (LSPR) is excited in graphene arrays, which requires more energy to excite a strong electric dipole at both ends of the elliptical hollow long axis to enhance the local electromagnetic field, thus effectively capturing the light energy and enhancing absorption [59]. As for the peak wavelength, it moves to the short wavelength direction, and when the period a increases to a certain extent, the resonance peak wavelength tends to be the same according to the data fitting, just like the black line depicted in the Fig. 2(B).
Fig. 2 (A) The absorption spectrum of different elliptical hollow graphene arrays under conditions of varying period a and an electric field schematic of the basic model is in the upper left corner. (B) the specific data fitting diagrams about absorption maximum and resonance wavelength.
Then, we explore the influence of the geometric structure on absorption by applying the control variable method with other parameters keeping constant. Figure 3 indicates the absorption of the graphene arrays when changing the long axis (L1, L2) of the inner and outer diameter. As shown in Fig. 3(A), the inner diameter long axis L1 rises from 200 nm to 700 nm, while the absorption varies inversely on an extremely pimping scale, from 0.195 to 0.179. We can seek reason from the electric field diagrams of Fig. 3(B). Obviously, the consuming electric field, whose strength remains practically invariable, primarily concentrates on both ends of two long axis of outer diameter. As the inner diameter of the long axis becomes longer, the electric field around the inner diameter enhances almost negligibly, and the graphene that can be irradiated by the incident light declines, resulting in the absorption reduction. Therefore, the reduction of light-absorbing area of graphene is more significant than the absorption enhancement caused by the new SPR at the inner diameter long axis. On the contrary, absorption increases in turn with the enhancement of the outer diameter of long axis in Fig. 3(C), and incremental quantity per time is larger, about 0.02. As a result of the diploid positive impacts of above factors (incremental light area and broadening of SPR), as shown in Fig. 3(D). In addition, the red shift of resonance wavelength exists in both cases. Therefore, in practical application, the appropriate geometric parameters can be selected according to the wavelength of incident light source to maximize absorption of the array.
Fig. 3 (A) and (B) the absorption spectrum of different elliptical hollow graphene arrays under conditions of the long axis (L1, L2) of the inner and outer diameter. (B) and (D) are corresponding electric field diagrams with distinct long axis (L1, L2).
Next, the dependence of absorption spectrum on the short axis of elliptical hollow graphene inside and outside the diameter is explored through Fig. 4. Similar to which has been discussed above, merely the inner and outer diameters are transformed separately in this section, while the other parameters remain the original setting. As shown in Fig. 4 (A), with increasing the short axis of the inner diameter, the absorption spectrum has analogous change regulation to that of Fig. 3(A), where the absorption maximum decreases. When the short axis runs up from 100 nm to 300 nm, the absorption drops to 0.21. Combining with the electric field diagram in Fig. 4(B), the primary reason is that the filling factor of elliptical hollow graphene array decreases, which leads to absorption reduction. Simultaneously, it is noteworthy that the width of the resonance wavelength is obviously broadened because of the increment of real part in graphene surface conductivity expression with wavelength elongates [60], leading to additional loss of SPP. The influence of short axis on absorption is exceedingly fascinating yet. On the one hand, the gap between periodically arranged elliptical hollow graphene arrays narrows with the increase of the short axis, which leads to coupling enhancement between arrays [61]. On the other hand, the filling factor of graphene increases. The aforementioned reasons cause the absorption enhancement in common, where the absorption reaches the maximum (0.225) at 600 nm of the short axis. Figure 4(B) can provide us practical assistance with comprehension for physical mechanism. Accidentally, the blue shift phenomenon in the resonance band has emerged.
Fig. 4 (A) and (B) the absorption spectrum of different elliptical hollow graphene arrays under conditions of the short axis (W1, W2) of the inner and outer diameter, and (B) and (D) are corresponding electric field diagrams with distinct short axis (W1, W2).
The absorption of elliptical hollow, elliptical and double elliptical hollow graphene arrays is compared when the parameters are set to initial values. As shown in Fig. 5(A), resonance wavelength ranges of the three modes are different. As conjectured, the double elliptical hollow graphene arrays have two resonance bands, one approaches 27 μm and the other close to 66 μm. In terms of absorption, the elliptical hollow array absorption (0.237) is the largest. Compared with the elliptical array, elliptical hollow arrays still has obvious advantages of absorption, where so stronger SPR leads to higher absorption. The electric field diagram shown in Figs. 5(B) and 5(C) shows that the electric field intensity inside the elliptical hollow is obviously stronger than that of inside the elliptical while both the external electric field intensity is little difference. And the absorption of double elliptical hollow arrays is the smallest which is 0.175 at the resonance peak wavelength of 66 μm, while absorption of 27 μm is merely 0.06 that is higher than that of the single continuous graphene. Comparing Fig. 5(C) with 5(D), representing the electric field at 27 μm and 66 μm respectively, we found that more charges are accumulated at both ends of long axis of the outer diameter which produces the much stronger electric field, although the intensity of inner diameter of electric field at 27 μm is slightly stronger than that of 66 μm. In general, the absorption peak at 66 μm is higher in both resonance bands.
Fig. 5 (A) The absorption spectrum of elliptical hollow, elliptical and double elliptical hollow graphene arrays, and (B), (C) are homologous electric field diagrams. (D) and (E) represents the electric field distribution at the two distinct absorption peaks of adouble elliptical hollow graphene arrays, respectively.
We will discuss the effect on absorption of elliptical hollow, elliptical and double-elliptical graphene arrays with the variation of Fermi level. All other parameter settings are kept as their original values. As shown in Fig. 6, when the Fermi level increases from 0.4 ev to 0.8 ev, the absorption of three models achieves their several maximum values of 0.24, 0.23 and 0.17 respectively, which conforms to the identical trend shown in Fig. 5. Therefore, the elliptical hollow array we proposed has much tunability in geometric structure and higher absorption at the identical Fermi level. Double elliptical hollow graphene arrays unexpectedly have two resonance bands, one with weak resonance intensity and the other with strong resonance intensity, indicating that Fermi levels have a positive effect on the three models. Increasing the Fermi level can enhance the SPR resonance intensity, which results in the array interacting with more proportions of light. Moreover, the wavelength of homologous graphene plasma polaritons is lengthened due to Fermi level enhancement, and the resonance wavelength is blue-shifted when Fermi level level runs up. In the actual preparation of raw materials, the surface conductivity of graphene can be continuously tuned by manipulation of Fermi level with electronic gating and chemical doping, so it can achieve dynamic tunable resonance and amplify the light response of incident light at a selected wavelength.
Fig. 6 (A)-(C) represent the absorption spectrum of elliptical hollow, elliptical and double elliptical hollow graphene arrays with the alterable Fermi level, respectively.
The absorption of elliptical hollow graphene arrays has a complicated relationship with the relaxation time of electrons which can be expressed in τ = μμc / (eυ2F) [62], where υF = 106 m/s refer to the Fermi velocity and e is the charge. In practice operation, the relaxation time τ can be directly controlled by manipulating the chemical potential with chemical doping and electrostatic [63]. Figure 7(A) shows the absorption spectra under different relaxation times. Obviously, absorption increases by enhancing the relaxation time τ. When the relaxation time comes to 1.0 ps or more, the maximum absorption is very close and has a little dissimilarity. The maximum absorption is 0.25 at τ = 2.0 ps. We make the relaxation time continues to increase, absorption tends to declines but width of peak resonance wavelength narrows. The reason is that the contribution of charge carriers to plasma oscillation enhances with the increase of relaxation time, resulting in higher absorption, however, when the number of charge carriers is large enough, most of the energy will be reflected so that a downward trend has emerged. Figure 7(B) shows the electric field of elliptical hollow graphene arrays at different relaxation times. With the increase of relaxation time, the strong electric field intensity at both ends of the long axis (along the X axis) decreases slightly, while the electric field at the short axis (along the Y axis) increases gradually, which can be seen evidently by comparing the four diagrams in Fig. 7(B). As the electric field of τ = 2.5 ps shows that although the SPP of the short axis part is enhanced, the contribution of charge carriers in the long axis part to the resonance intensity is reduced. Therefore, the absorption enhances to almost constant before decreasing because the reflected energy is also improving. Generally speaking, the absorption of the array shows a downward trend, which also conforms to the data of Fig. 7(A).
Fig. 7 (A) The absorption spectrum under different relaxation times, and (B) includes four schematic diagrams of the elliptical hollow graphene arrays electric field at different relaxation times (τ = 0.5 ps, τ = 1.0 ps, τ = 1.5 ps, τ = 2.5 ps).
Ultimately, the absorption spectra at different incident angles, under the TM polarization mode and TE polarization mode, are shown in Figs. 8(A) and 8(C) respectively. Figures 8(B) and 8(D) are the corresponding specific data fitting diagrams about absorption maximum and resonance wavelength. In this section, other parameters maintain original settings. Obviously, the absorption peak has inseparable connection with the incident angle, resembled as multitudinous arrays [64,65]. Despite the distinct polarization modes, the absorption comes to their maximum values of 0.31 under TM polarization and 0.17 under TE polarization at 60° respectively, when the incident angle increases from 0° to 60°. The fitting curve shown by the black line in Fig. 8(B), it can be concluded that the array will have a high absorption of 0.42 at θ = 70°, where the similar trend that the estimated absorption maximum of 0.23 in Fig. 8(D) has emerged. On the contrary, the peak wavelength of resonance are impervious to the variation of angle. It can be evidently seen from the black line in Fig. 8(B), the peak wavelength of resonance hardly shifts, all of which are 57 μm while the peak resonance wavelength in Fig. 8(D) are 60.8 μm. Observing the electric field distribution (shown in Fig. 8(A)) around the elliptical hollow graphene array, with the attenuation of reflected light caused by the deviation of incident angle θ, the strong electric field around the resonator, especially at both ends of the long and short axis, accumulates a large number of charges, indicating that the SPR excited here is the strongest. Similar to the above-mentioned (shown in Fig. 8(C)), the strong electric field is mainly distributed at both ends of the short axis with outer diameter. Compared with the absorption of elliptical hollow graphene arrays under TM and TE polarization, the arrays capture light more intensely in TM polarization mode, which can be confirmed by the electric field schematic. Although the graphene element receives less and less light in the unit area of the long and short axis when the angle increases, the SPR attenuates to a certain extent. Moreover, the influence of the former is better than that of the latter. In total, the overall absorption performance is enhanced.
Fig. 8 (A) and (C) represent the absorption spectra of different incident angles under the TM and TE polarization configurations, respectively. (B) and (D) are the corresponding specific data fitting diagrams about absorption maximum and resonance wavelength. The upper left-hand corner of (A) and (C) is a schematic of the electric field in the TM polarization mode and TE polarization.
4. Conclusion
In conclusion, tunable absorbers depositing periodic elliptical hollow graphene arrays on SiO2 are investigated, which makes the graphene arrays more diverse. The passive tuning of absorption is achieved by adjusting the geometric parameters of the graphene array. Under the basic conditions and the Fermi level changes, the absorption variations of elliptical hollow, elliptical and double-elliptical graphene arrays in different resonance bands are compared. By increasing the Fermi level, the resonance intensity of SPR is strengthened to enhance the local electric field, realizing the active tuning of absorption and the ideal effect of absorption enhancement is acquired. Due to the decrease of reflected light, increasing the incidence angle θ can promote absorption. Among the six parameters proposed by us, changing the angle is the most effective way to achieve high absorption. In order to achieve high efficiency of design process, we can first determine the wavelength range of selected wave source to find the appropriate parameters to maximize the absorption of the entire elliptical hollow graphene array. Therefore, the proposed hollow graphene arrays have practical applications (such as photoelectric sensors, photon detectors and modulators, etc.) in terahertz field, and their prospects are immeasurable due to their high efficiency and tunable spectral selectivity.
Funding
National Natural Science Foundation of China (NNSFC) (51606158, 11604311, 61705204, 21506257); Longshan academic talent research supporting program of SWUST (17LZX452); the Postgraduate Innovation Fund Project by Southwest University of Science and Technology (18ycx034).
References
1. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical Cloaking with Non-Magnetic Metamaterials,” Nat. Photonics 1(4), 224–227 (2007). [CrossRef]
2. D. Shin, Y. Urzhumov, Y. Jung, G. Kang, S. Baek, M. Choi, H. Park, K. Kim, and D. R. Smith, “Broadband electromagnetic cloaking with smart metamaterials,” Nat. Commun. 3(1), 1213 (2012). [CrossRef] [PubMed]
3. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]
4. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE T Microw Theory 47(11), 2075–2084 (1999). [CrossRef]
5. H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006). [CrossRef] [PubMed]
6. J. Chen, T. Zhang, C. Tang, P. Mao, Y. Liu, Y. Yu, and Z. Liu, “Optical Magnetic Field Enhancement via Coupling Magnetic Plasmons to Optical Cavity Modes,” IEEE Photonic Tech L. 28(14), 1529–1532 (2016). [CrossRef]
7. P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: always positive and very inhomogeneous,” Phys. Rev. Lett. 88(18), 187401 (2002). [CrossRef] [PubMed]
8. Z. Liu, G. Liu, S. Huang, X. Liu, P. Pan, Y. Wang, and G. Gu, “Multispectral spatial and frequency selective sensing with ultra-compact cross-shaped antenna plasmonic crystals,” Sensor Actuat. Biol. Chem. 215, 480–488 (2015).
9. X. Wang, X. Wu, Y. Chen, X. Bai, Z. Pang, H. Yang, Y. Qi, and X. Wen, “Investigation of wide-range refractive index sensor based on asymmetric metal-cladding dielectric waveguide structure,” AIP Adv. 8(10), 105029 (2018). [CrossRef]
10. C. R. Simovski, P. A. Belov, and S. He, “Backward wave region and negative material parameters of a structure formed by lattices of wires and split-ring resonators,” IEEE Trans. Antenn. Propag. 51(10), 2582–2591 (2003). [CrossRef]
11. Z. Xiong and L. Cao, “Interparticle spacing dependence of magnetic anisotropy and dipolar interaction of Ni nanocrystals embedded in epitaxial BaTiO3 matrix,” Ceram. Int. 44(7), 8155–8160 (2018). [CrossRef]
12. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005). [CrossRef] [PubMed]
13. C. Cen, H. Lin, J. Huang, C. Liang, X. Chen, Y. Tang, Z. Yi, X. Ye, J. Liu, Y. Yi, and S. Xiao, “A Tunable Plasmonic Refractive Index Sensor with Nanoring-Strip Graphene Arrays,” Sensors (Basel) 18(12), 4489 (2018). [CrossRef] [PubMed]
14. X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8(19), 10388–10397 (2016). [CrossRef] [PubMed]
15. X. He, G. Xiao, F. Liu, F. Lin, and W. Shi, “Flexible properties of THz graphene bowtie metamaterials structures,” Opt. Mater. Express 9(1), 44–55 (2019). [CrossRef]
16. J. Wang, C. Song, J. Hang, Z. D. Hu, and F. Zhang, “Tunable Fano resonance based on grating-coupled and graphene-based Otto configuration,” Opt. Express 25(20), 23880–23892 (2017). [CrossRef] [PubMed]
17. X. Wang, C. Chen, L. Pan, and J. Wang, “A graphene-based Fabry-Pérot spectrometer in mid-infrared region,” Sci. Rep. 6(1), 32616 (2016). [CrossRef] [PubMed]
18. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]
19. F. J. García de Abajo, “Graphene Plasmonics: Challenges and Opportunities,” ACS Photonics 1(3), 135–152 (2014). [CrossRef]
20. X. Luo, Z. Liu, Z. Cheng, J. Liu, Q. Lin, and L. Wang, “Polarization-insensitive and wide-angle broadband absorption enhancement of molybdenum disulfide in visible regime,” Opt. Express 26(26), 33918–33929 (2018). [CrossRef]
21. W. Wang, C. Kang, X. Liu, and S. Qu, “Spin-selected and spin-independent dielectric metalenses,” J. Opt. 20(9), 095102 (2018). [CrossRef]
22. J. Fu, B. Lv, R. Li, R. Ma, W. Chen, and Z. Wang, “Excitation of Surface Plasmon Polaritons in an Inhomogeneous Graphene-Covered Grating,” Plasmonics 12(1), 209–213 (2017). [CrossRef]
23. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science 306(5696), 666–669 (2004). [CrossRef] [PubMed]
24. H. Lin, X. Ye, X. F. Chen, Z. G. Zhou, Z. Yi, G. Niu, Y. G. Yi, Y. T. Hua, J. J. Hua, and S. Y. Xiao, “Plasmonic absorption enhancement in graphene circular and elliptical disk arrays,” Mater. Res. Express 2019, aafc3e (2019), doi:. [CrossRef]
25. C. X. Zheng and H. Yang, “Assembly of Ag3PO4 nanoparticles on rose flower-like Bi2WO6 hierarchical architectures for achieving high photocatalytic performance,” J Mater Sci-Mater EL 29(11), 9291–9300 (2018). [CrossRef]
26. W. Liu, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Electrically Tunable Absorption Enhancement with Spectral and Polarization Selectivity through Graphene Plasmonic Light Trapping,” Nanomaterials (Basel) 6(9), 155 (2016). [CrossRef] [PubMed]
27. Y. Yang, G. Kolesov, L. Kocia, and E. J. Heller, “Reassessing Graphene Absorption and Emission Spectroscopy,” Nano Lett. 17(10), 6077–6082 (2017). [CrossRef] [PubMed]
28. X. Luo, X. Zhai, L. Wang, and Q. Lin, “Enhanced dual-band absorption of molybdenum disulfide using a plasmonic perfect absorber,” Opt. Express 26(9), 11658–11666 (2018). [CrossRef] [PubMed]
29. X. X. Zhao, H. Yang, S. H. Li, Z. M. Cui, and C. R. Zhang, “Synthesis and theoretical study of large-sized Bi4Ti3O12 square nanosheets with high photocatalytic activity,” Mater. Res. Bull. 107, 180–188 (2018). [CrossRef]
30. X. He, “Tunable terahertz graphene metamaterials,” Carbon 82, 229–237 (2015). [CrossRef]
31. Y. Fan, N. H. Shen, T. Koschny, and C. M. Soukoulis, “Tunable Terahertz Meta-Surface with Graphene Cut-Wires,” ACS Photonics 2(1), 151–156 (2015). [CrossRef]
32. J. Linder and K. Halterman, “Graphene-based extremely wide-angle tunable metamaterial absorber,” Sci. Rep. 6(1), 31225 (2016). [CrossRef] [PubMed]
33. Y. Zeng, X. F. Chen, Z. Yi, Y. G. Yi, and X. B. Xu, “Fabrication of p-n heterostructure ZnO/Si moth-eye structures: Antireflection, enhanced charge separation and photocatalytic properties,” Appl. Surf. Sci. 441, 40–48 (2018). [CrossRef]
34. Y. Zhang, Y. Kuang, Z. Zhang, Y. Tang, J. Han, R. Wang, J. Cui, Y. Hou, and W. Liu, “High-sensitivity refractive index sensors based on Fano resonance in the plasmonic system of splitting ring cavity-coupled MIM waveguide with tooth cavity,” Appl. Phys., A Mater. Sci. Process. 125(1), 13 (2019). [CrossRef]
35. Z. W. Xiong and L. H. Cao, “Red-ultraviolet photoluminescence tuning by Ni nanocrystals in epitaxial SrTiO3 matrix,” Appl. Surf. Sci. 445, 65–70 (2018). [CrossRef]
36. X. He, Z. Y. Zhao, and W. Shi, “Graphene-supported tunable near-IR metamaterials,” Opt. Lett. 40(2), 178–181 (2015). [CrossRef] [PubMed]
37. L. Di, H. Yang, T. Xian, and X. Chen, “Construction of Z-scheme g-C3N4/CNT/Bi2Fe4O9 composites with improved simulated-sunlight photocatalytic activity for the dye degradation,” Micromachines (Basel) 9(12), 613 (2018). [CrossRef] [PubMed]
38. C. Liu, W. Su, Q. Liu, X. Lu, F. Wang, T. Sun, and P. K. Chu, “Symmetrical dual D-shape photonic crystal fibers for surface plasmon resonance sensing,” Opt. Express 26(7), 9039–9049 (2018). [CrossRef] [PubMed]
39. Z. Pang, H. Tong, X. Wu, J. Zhu, X. Wang, H. Yang, and Y. Qi, “Theoretical study of multiexposure zeroth-order waveguide mode interference lithography,” Opt. Quantum Electron. 50(9), 335 (2018). [CrossRef]
40. X. Wang, Z. Pang, H. Tong, X. Wu, X. Bai, H. Yang, X. Wen, and Y. Qi, “Theoretical investigation of subwavelength structure fabrication based onmulti-exposure surface plasmon interference lithography,” Results Phys. 12, 732–737 (2019). [CrossRef]
41. X. Zhang, Y. Qi, P. Zhou, H. Gong, B. Hu, and C. Yan, “Refractive Index Sensor Based on Fano Resonances in Plasmonic Waveguide With Dual Side-Coupled Ring Resonators,” Photonic Sens. 8(4), 367–374 (2018). [CrossRef]
42. B. Zheng, S. Xu, L. Lin, Z. Wang, Z. Feng, and Z. Zheng, “Plasmon enhanced near-infrared quantum cutting of KYF4: Tb3+, Yb3+ doped with Ag nanoparticles,” Opt. Lett. 40(11), 2630–2633 (2015). [CrossRef] [PubMed]
43. R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012). [CrossRef] [PubMed]
44. Z. Xiong and L. Cao, “Tailoring morphology, enhancing magnetization and photocatalytic activity via Cr doping in Bi25FeO40,” J. Alloys Compd. 773, 828–837 (2019). [CrossRef]
45. X. Shi, L. Ma, Z. Zhang, Y. Tang, Y. Zhang, J. Han, and Y. Sun, “Dual Fano resonance control and refractive index sensors based on a plasmonic waveguide-coupled resonator system,” Opt. Commun. 427(25), 326–330 (2018). [CrossRef]
46. S. Ke, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Plasmonic absorption enhancement in periodic cross-shaped graphene arrays,” Opt. Express 23(7), 8888–8900 (2015). [CrossRef] [PubMed]
47. Y. X. Yan, H. Yang, X. X. Zhao, R. S. Li, and X. X. Wang, “Enhanced photocatalytic activity of surface disorder-engineered CaTiO3,” Mater. Res. Bull. 105, 286–290 (2018). [CrossRef]
48. T. Liu, H. Wang, Y. Liu, L. Xiao, Z. Yi, C. Zhou, and S. Xiao, “Active manipulation of electromagnetically induced transparency in a terahertz hybrid metamaterial,” Opt. Commun. 426(1), 629–634 (2018). [CrossRef]
49. K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008). [CrossRef] [PubMed]
50. B. Zhu, G. Ren, S. Zheng, Z. Lin, and S. Jian, “Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices,” Opt. Express 21(14), 17089–17096 (2013). [CrossRef] [PubMed]
51. Z. Yi, X. B. Xu, X. L. Kang, Y. L. Zhao, S. L. Zhang, W. T. Yao, Y. G. Yi, J. S. Luo, C. Y. Wang, Y. Yi, and Y. J. Tang, “Fabrication of well-aligned ZnO@Ag nanorod arrayswith effective charge transfer for surface-enhanced Raman scattering,” Surf. Coat. Tech. 324, 257–263 (2017). [CrossRef]
52. X. He, F. Liu, F. Lin, and W. Shi, “Graphene patterns supported terahertz tunable plasmon induced transparency,” Opt. Express 26(8), 9931–9944 (2018). [CrossRef] [PubMed]
53. C. Cen, H. Lin, C. Liang, J. Huang, X. Chen, Z. Yi, Y. Tang, T. Duan, X. Xu, S. Xiao, and Y. Yi, “Tunable plasmonic resonance absorption characteries-tics in periodic H-shaped graphene arrays,” Superlattices Microstruct. 120, 427–435 (2018). [CrossRef]
54. P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011). [CrossRef] [PubMed]
55. C. Liang, G. Niu, X. Chen, Z. Zhou, Z. Yi, X. Ye, T. Duan, Y. Yi, and S. Xiao, “Tunable triple-band graphene refractive index sensor with good angle-polarization tolerance,” Opt. Commun. 436(1), 57–62 (2019). [CrossRef]
56. C. Cen, J. Chen, C. Liang, J. Huang, X. Chen, Y. Tang, Z. Yi, X. Xu, Y. Yi, and S. Xiao, “Plasmonic absorption characteristics based on dumbbell-shaped graphene metamaterial arrays,” Physica E 103, 93–98 (2018). [CrossRef]
57. J. Chen, Z. Yi, S. Xiao, and X. Xu, “Absorption enhancement in double-layer cross-shaped graphene arrays,” Mater. Res. Express 5(1), 015605 (2018). [CrossRef]
58. S. X. Xia, X. Zhai, L. L. Wang, and S. C. Wen, “Plasmonically induced transparency in double-layered graphene nanoribbons,” Photon. Res. 6(7), 692–702 (2018). [CrossRef]
59. Z. Yi, X. Li, X. Xu, X. Chen, X. Ye, Y. Yi, T. Duan, Y. Tang, J. Liu, and Y. Yi, “Nanostrip-Induced High Tunability Multipolar Fano Resonances in a Au Ring-Strip Nanosystem,” Nanomaterials (Basel) 8(8), 568 (2018). [CrossRef] [PubMed]
60. W. Xiao, Z. Wang, Y. Zhang, R. Fang, Z. Yuan, C. Miao, X. M. Yan, and Y. Jiang, “Enhanced performance of P (VDF-HFP)-based composite polymer electrolytes doped with organic-inorganic hybrid particles PMMA-ZrO2 for lithium ion batteries,” J. Power Sources 382, 128–134 (2018). [CrossRef]
61. J. Chen, Y. Zeng, X. Xu, X. Chen, Z. Zhou, P. Shi, Z. Yi, X. Ye, S. Xiao, and Y. Yi, “Plasmonic Absorption Enhancement in Elliptical Graphene Arrays,” Nanomaterials (Basel) 8(3), 175 (2018). [CrossRef] [PubMed]
62. X. Liu, G. Liu, P. Tang, G. Fu, G. Du, Q. Chen, and Z. Liu, “Quantitatively optical and electrical-adjusting high-performance switch by graphene plasmonic perfect absorbers,” Carbon 140, 362–367 (2018). [CrossRef]
63. D. Wang, X. Liu, L. He, Y. Yin, D. Wu, and J. Shi, “Manipulating Graphene Mobility and Charge Neutral Point with Ligand-Bound Nanoparticles as Charge Reservoir,” Nano Lett. 10(12), 4989–4993 (2010). [CrossRef] [PubMed]
64. J. Y. Dai, J. J. Li, Q. B. Zhang, M. Liao, T. Duan, and W. T. Yao, “Co3S4@C@MoS2 microstructures fabricated from MOF template as advanced lithium-ion battery anode,” Mater. Lett. 236, 483–486 (2019). [CrossRef]
65. L. Liu, J. Chen, Z. Zhou, Y. Zao, and X. Ye, “Tunable absorption enhancement in electric split-ring resonators-shaped graphene arrays,” Mater. Res. Express 5(4), 045802 (2018). [CrossRef]
