Open Access
Add to BibSonomy
Abstract
In this paper, a bi-functional tunable reflector/absorber device using an assembly of graphene-coated cylindrical wires, backed by a thermally controlled phase change material, is proposed. The reflection coefficient of the graphene-coated wire-grating manifests multiple resonances, originating from the hybridized excitation of localized surface plasmons in the graphene shells. The first plasmonic resonance (with the order of two), in the free-standing configuration, shows tunable near-perfect reflection while the second plasmonic resonance (with the order of three), in the reflector-backed array, exhibits near-perfect absorption. Because of the metal-insulator transition in the phase change material, it is feasible to switch between these two functionalities using a VO2 back layer. Moreover, the high-quality factor of the absorption band (Q ∼ 128.86) is due to its Fano line shape, leading to a narrow bandwidth. Thus, the absorbing mode can be possibly used for refractive index sensing with the sensitivity of S ∼ 9000 nm/RIU (refractive index unit) and figure of merit of FOM ∼ 104 RIU−1. In the proposed structure, different optical, material, and geometrical parameters affect the optical response of the operating bands, offering a flexible design.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Graphene-coated infinite length cylindrical structures have been the focus of extensive research due to supporting tunable localized surface plasmon resonances [1]. For instance, the optical absorption enhancement in a cylindrical graphene shell can be achieved by coupling the plasmonic and whispering gallery modes [2]. Moreover, the refractive index sensing capability of graphene-based wires has been demonstrated using analytical formulation [3]. As another application, graphene-coated wires are proposed for guiding the electromagnetic waves with low loss and high confinement [4,5]. To provide more flexibility for manipulating the plasmonic response, multiple graphene shells are wrapped around the wires. For instance, by coupling the plasmonic resonances of three concentric graphene shells, a dual-band super-scatterer is proposed [6]. In the same device, Foster’s resonance theorem has been used to achieve a novel structure for simultaneous super- scattering and super-cloaking [7].
Plasmonic hybridization can be attained in another way by putting multiple graphene-coated particles in the proximity of each other. For this purpose, the plasmonic dimer design with infinite and finite-length graphene-based wires has been proposed, respectively, for multi-window cloaking and giant near field enhancement [8,9]. Interestingly, single-biomolecule manipulation or detection is feasible by exploiting the field enhancement or gradient force in the graphene-coated nanowire pairs [10]. Moreover, benefiting from the third-order nonlinearity of graphene material, an optical coupler is designed using a pair of single-mode graphene-coated nanowires [11]. The optical design has been extended to the trimer structure constructed by graphene-coated wires, where different point symmetry groups are considered to excite the dark modes [12]. By further increasing the number of particles, a graphene-coated oligomer, designed by cylindrical wires, is proposed for broadband discrete/continuous spectrum absorption enhancement [13]. In this paper, the limiting case of putting an infinite number of graphene-coated cylinders in the proximity of each other will be considered to design a novel optoelectronic device based on plasmonic hybridization. In this structure, plasmonic coupling results in the excitation of second and third-order localized surface plasmon resonances under some specific parameter combination, each with a distinct operation. The dual tunable operating modes of the structure including optical reflection and absorption are discussed in detail. Moreover, multi-controllable devices can be attained under either the temperature or a static magnetic field or a static electric field control of the constitutive parameters of the tunable materials [14]. To switch between the reflection/absorption modes, a thermally controlled phase change material is utilized. This material combination (graphene-VO2) has been previously used in a bi-functional metamaterial for mid-infrared bi-tunable asymmetric transmission and nearly perfect resonant absorption [15].
A periodic assembly of infinite length cylindrical wires made of plasmonic or dielectric materials had been considered for different applications, previously. For instance, the sharp spectral opacity window in a free-standing dielectric nano-rod array is the result of Fano resonance, originating from coherent multiple scattering in the array [16]. Moreover, a fiber array-based anti-reflection front electrode has been proposed to enhance the light-trapping capability of a perovskite solar cell [17]. It is also demonstrated that an array of core-shell silicon-gold nanowire resonators provides multiple high-quality factor absorption bands as a result of photonic and plasmonic mode interaction [18]. The purpose of the present paper is to use the same geometries for the optical design, benefiting from the plasmonic resonances of the graphene shells with circular cross-sections, so-called as wire grating. Interestingly, many pieces of research prove that magnetic/electric resonances of dielectric/metallic square gratings enhance the plasmonic resonance of the graphene sheet [19–21]. In these designs, by using un-patterned graphene in the optical design, the edge effects are avoided [22]. In this research, an edge-less graphene-coated wire grating (due to its circular cross-section [11]) is considered for optoelectronic applications. Note that one-dimensional (1D) periodic arrays are inherently polarization-sensitive, thus, two-dimensional (2D) arrays are preferred [23]. There are some techniques to eliminate the polarization sensitivity in 1D arrays, by crossly stacking double arrays [24] or using different types of resonances in the optical design of each polarization [25].
The paper is organized as follows. Initially, using a thermally controlled phase change material, a bi-functional device for optical reflection/absorption is proposed. Later, the two operating modes are investigated separately to give some insight into the underlying operating mechanism. To this end, a free-standing graphene-coated wire grating is considered first and its performance is investigated regarding different design parameters. The design parameters are used to manipulate the Lorentzian and Fano resonances of the structure for the potential use respectively in the optical reflectors and absorbers. The former performs based on the hybridized second-order plasmonic resonances while the latter benefits from the third-order plasmonic Fano resonance. Finally, detailed information about the refractive index sensing capability of the Fano-resonance-based absorber is provided.
Note that a prototype of a grating coupled graphene-based absorber has been realized using a combination of nanofabrication techniques such as sputtering, chemical vapor deposition (CVD), and electron beam lithography, achieving excellent agreement between experimental results and numerical simulations [26]. Using the tape-assist transfer or spin-coating methods, graphene-coated wires can be realized as well [27]. Considering all these techniques, we believe that our proposed device can be fabricated using the current technologies.
2. Bi-functional tunable optical device using VO2 assisted graphene-coated cylindrical wire grating
In the following paragraphs, a tunable bi-functional optical device using VO2 assisted graphene-coated cylindrical wire grating is presented. The tunability arises from the 2D nature of graphene material while the bi-functionality is the result of using a phase change material. Note that a switchable absorber/reflector enables a wide range of applications including active camouflage, imaging, modulating, and electro-optic switching [28]. A comprehensive review of the metasurface-based absorption and reflection control can be found in [29].
2.1 Bi-functional tunable optical reflector/absorber
Let us consider a periodic arrangement of graphene-coated cylindrical wires on top of the substrate, as shown in Fig. 1(a). The core permittivity of each infinite length dielectric cylinder is ε1 and an atomically thin graphene shell covers its surface. In all simulations, the cylinders are considered hollow, unless otherwise stated (section 2.2). The radii of the cylinders are considered R and associated graphene shells are characterized by their surface conductivity σ [30]. Graphene surface conductivity can be used to control the optical response through relaxation time τ, chemical potential μc, and temperature T. Moreover, the inter-element spacing is p in the y-direction. The design parameters are R=0.5 µm, τ=1.5 ps, p=1.5 µm. The particles have resided on top of a dielectric substrate backed by VO2 phase change material with the thickness of h2=100 nm under thermal control of the metal-insulator transition. In the transition temperature, VO2 behaves as an inherent metamaterial with mixed metallic-insulator features [31]. For T=350 K (hot phase), the surface conductivity of the VO2 is 2.0×105 S/m while at T=300 K (cold phase) it equals 200 S/m [32]. Note that, recently, the hysteresis phenomenon during cold-to-hot versus hot-to-cold transitions of VO2 has been explored, where the stability of VO2, as measured by optical hysteresis contrast, is a function of the deposition process and the substrate [33]. This material is modeled by assigning the surface conductivity of 200 S/m to a dielectric material with the permittivity 9 during the simulations of the insulator phase [34], while it is modeled as lossy metal in the metallic phase. Graphene’s temperature-dependent surface conductivity is taken into account when switching between these two cases. Moreover, the dielectric constant of the substrate is considered ε2=2 [35], and its height is h1=1.2 µm. The substrate height is the optimized value to reach perfect absorption when replacing the metallic VO2 layer with PEC (ideal condition) for the chemical potential of μc=1.3 eV (section 2.3).
Fig. 1. (a) An array of graphene-coated infinite length dielectric cylinders on top of the VO2 backed dielectric substrate. The dielectric constant of the substrate is considered ε2=2 and its optimized height is h1=1.2 µm. The thickness of the VO2 layer is h2=100 nm. (b)-(c) 2D and (b) 3D views of the free-standing particles. The parameters are as follows: R is the cylinder radius and ε1 is its core permittivity. In each particle, the atomically thin graphene shell is characterized by the relaxation time τ, chemical potential μc, and temperature T. The periodicity is p in the y-direction. (d) Replacing VO2 with a PEC plane. A medium with an unknown refractive index (RI) is positioned on top of the substrate to evaluate the sensing performance of the device in the last section.
To investigate the performance, a unit cell of the structure is simulated in the CST software using Floquet ports with the zero-order TE and TM propagating modes as the excitation source. The scattering parameters of the simulated structure, S11, and S12 respectively manifest the reflection and transmission coefficients. The absorption A can be calculated via $A = 1 - {|{{S_{12}}} |^2} - {|{{S_{11}}} |^2}$. Note that to prevent undesired plasmonic resonances, graphene shells should be carefully drawn such that no disks be present at the ends of the wires. The resonances of these disks in the finite length graphene-coated wires have been used elsewhere [9,13], but here is not of interest.
Figures 2(a)-2(b) respectively show the reflection coefficient and absorption rate of the bi-functional device at the insulator phase of the VO2 material, applying different chemical potentials to the graphene shells. As Fig. 2(a) shows, a high reflection rate of above 90% is achieved for any considered chemical potential, gradually turning to the near-perfect reflection for higher chemical potentials. Figure 2(b) confirms that the absorption rate of this phase is far less than the complete absorption rate due to the transmitted wave, as will be further clarified later. Moreover, Figs. 2(c)-2(d) respectively show the same information as Figs. 2(a)-2(b) at the metallic phase of the VO2 material. Figure 2(c) indicates that in this case, there is not any narrow reflection peak, instead, there are two pronounced reflection dips, resulting in a high absorption rate in Fig. 2(d). There are some regions between these two peaks, partially having a reflection coefficient above 90%. Since the reflector attained in the dielectric mode has sharper behavior at cut-off-frequency, it is of interest. Figure 2(d) illustrates that a high absorption rate of above 90% can be attained in this phase for frequencies above 16 THz. Similarly, near-perfect absorption is feasible for higher chemical potentials. Thus, a bi-functional tunable optical reflector/absorber is realized.
Fig. 2. The reflection coefficient and absorption rate of the bi-functional device by varying the chemical potential
µc (eV) of graphene shells respectively at the (a)-(b) insulator phase and (b)-(c) metallic phase of the VO2 material.
The spatial distribution of the electric field at the reflection/absorption peak is illustrated in Fig. 3 for μc=1.3 eV. Based on the results, the second and third-order plasmonic resonances are attained respectively in these two operating modes. Note that the order of the excited surface plasmon resonances can be distinguished by the number of electric field oscillations and they are illustrated for a single-cylinder in [36]. Moreover, the excitation of higher-order resonances is the result of hybridization due to the proximity of plasmonic wires, where they are not excitable in isolated cylinders [37]. Interestingly, it is not necessary to excite the fundamental mode for the enhanced light-matter interaction [13,24,38]. Note that since the cylinders are hollow, no other Mie cavity resonance occurs [39], confirming the necessity of the plasmonic resonances of graphene shells in the design. Moreover, although graphene-based planar structures, compatible with a layer-by-layer fabrication technology, have been proposed for optical applications [40], the combined use of localized surface plasmons and a method for reducing the associated radiative damping (Fano resonances in this paper) results in superior features [41].
Fig. 3. Spatial distribution of the electric field at the reflection/absorption peak considering μc=1.3 eV
To understand the underlying physics of the performance, in the following two sections, the reflection and absorption bands are considered, separately. For simplicity, in the insulator phase, the substrate and VO2 layers are neglected while in the metallic phase, the VO2 layer is replaced by a perfect electric conductor (PEC). The trivial influence of these modifications in the desired response is illustrated in Fig. 4. Specifically, as Fig. 4(a) shows, by removing the substrate and VO2 in the insulator phase, a blue shift of the operating spectrum happens, which can be later tuned via design parameters. The second resonance in this figure does not have any functionality in the insulator phase and its modulation is not discussed. Moreover, as Fig. 4(b) indicates, the absorption peak (second resonance) is maintained under PEC or metallic VO2 back layer. The full width at half maximum (FWHM) is 86.08 nm for this resonance (considering the PEC plane). The Q-factor of the resonance, defined as λres/FWHM [42], is 128.86 which is higher than that of the recently proposed graphene ultraviolet ultra-high-Q perfect absorber (Q=70) [43]. Note that under some specific design methods such as using nanoslit array (Q ∼700), strong coupling between plasmonic and photonic modes (Q ∼ 1375), and incorporating gain-assisted spoof plasmonic resonances (Q ∼ 21000), ultra-high Q factors can be achieved [44–46]. The ultra-high-Q factor is reported for simple structures like nano-grating and a metamaterial formed by Aluminum disks, respectively as Q ∼ 40 and beyond Q ∼ 80 [47,48]. Interestingly, the above discussion proposes the idea of a single functional device by removing the VO2 layer.
Fig. 4. The optical performance of the bi-functional device with the specified parameters in section 2.1, (a) removing the substrate and VO2 in the insulator phase and (b) replacing VO2 with PEC in the metallic phase (µc=1.3 eV).
2.2 Free-standing graphene-coated wire grating as a tunable optical reflector
In this section, the optical performance of the free-standing graphene-coated wire grating (Figs. 1(b)-1(c)) is considered, to understand how the optical performance of the reflecting band can be manipulated regarding the design parameters. The parameters are mentioned in the caption of Fig. 4, and in each sub-figure, only one of the parameters is manipulated. Figure 5(a) shows the bandpass filtering characteristic of the proposed electric mirror with a nearly perfect reflection spectrum. Interestingly, a magnetic mirror has been previously designed using a lithium tantalate micro cylindrical rod array on a Teflon substrate [49]. In Fig. 5(b), the relative permittivity of the wire core is varied from 1 − 1.6. A redshift of the reflectance spectrum is observed by this modification. Notably, higher-order resonances gradually disappear with the increase of the core permittivity. Since these resonances are of interest in the next section, we have considered hollow cylinders in the following simulations. Note that graphene-coated hollow particles are realizable with current fabrication technologies [50].
Fig. 5. (a) The scattering parameters of structure in Fig. 1 for the initial parameters of R=0.5 µm, μc=0.8 eV, τ=1.5 ps, p=1.5 µm. (b) The reflection coefficient for various core materials with the relative permittivity of 1 − 1.6.
For further examination, the modulation of the reflection coefficient with geometrical parameters is shown in Fig. 6. Based on Fig. 6(a), as the radii of the shells are increased, maintaining the same distance among the wires, the reflection is increased as well. Moreover, another higher-order sharp resonance appears. This is expected since more multi-poles contribute to the optical response of the electrically large structures. Furthermore, as Fig. 6(b) illustrates, the periodicity of the wires in the lattice impacts the reflectance spectrum, the smaller ones having near-perfect reflection coefficients at lower frequencies and with more higher-order resonances, originating from the stronger coupling.
Fig. 6. The reflectance of the structure in Fig. 1 for the initial design parameters of R=0.5 µm, μc=0.8 eV, τ=1.5 ps, p=1.5 µm. In (a) the core radius R (µm) and in (b) the periodicity p (µm) of the elements is varied.
Next, the influence of the optical parameters of graphene on the reflection coefficient is investigated. Based on Fig. 7(a), the amount of reflection can be increased by using larger relaxation times. Moreover, the third-order plasmonic resonance can be made deeper by high-quality graphene materials, which is of interest in absorber design. Finally, Fig. 7(b) shows that the prefect reflection frequency can be modulated by changing the gate voltage. Also, higher chemical potentials result in the deeper third-order resonance, suitable for the optical absorber design.
Fig. 7. The reflectance of the structure in Fig. 1 for the initial design parameters of R=0.5 µm, μc=0.8 eV, τ=1.5 ps, p=1.5 µm. In (a)-(b) respectively the graphene relaxation time (ps) and chemical potential (eV) are varied.
2.3 Reflector backed wire grating as a high-Q tunable absorber
Further examination of the reflectance curve in Figs. 4–7 reveals that apart from the perfect reflection resonance, there are one or two Fano resonances in the spectrum, depending on the parameters of the structure. Fano resonances in isolated graphene-coated wires with single and double shells have been reported previously [8,51] and they are known for their sharp resonance line shape and can be potentially used in the design of absorbers with high-quality factors [43]. To investigate the possibility of optical absorber design using the proposed graphene-coated wire grating, the VO2 layer is replaced by a PEC plane. The ground plane can be replaced by any other metallic substrate considering dispersive permittivity when the bi-functional device is not of interest [52]. To understand the necessity of using a reflector to achieve a high absorption rate, let us reconsider the free-standing graphene-coated wires and assign a multipolar polarizability to each particle. By proper selection of the design parameters, an assembly of symmetric polarizable elements can absorb at most half of the incoming electromagnetic wave [8,53]. To reach a perfect absorption, the transmitted wave must be blocked, commonly using a metallic mirror [54]. This fact can be further confirmed by considering the S12 parameter in Fig. 5(a). As the figure illustrates, although a nearly perfect impedance matching to the free space intrinsic impedance occurs in the second resonance, the perfect absorption is not feasible due to the transmitted wave.
The sensitivity of the optical absorption for the illumination angle is shown in Figs. 8(a)-8(b) respectively for the transverse electric (TE) and transverse magnetic (TM) waves. Under the TE illumination, the absorber tolerates the oblique incidence with absorption above 90% for the angles up to around 60 degrees. Moreover, it is observed that under certain angles, the perfect absorption is achieved for TM waves. The angular selectivity is due to the different scenarios of the coupling of TE and TM waves for the oblique incidence. On the other hand, under normal illumination, TE and TM modes of the cylindrical structures are decoupled and for oblique incidence, these modes become coupled [55]. Noticeably, change of polarization is expected to lead to the switching between reflection and absorption, according to the results in Fig. 8. The transmission is completely blocked by the PEC plane and the spectrum in which the absorption is negligible leads to a high rate of reflection.
Fig. 8. The incident angle sensitivity of the optical absorption under (a) TE and (b) TM illumination for the structure in Fig. 1(d).
To investigate the potential of our proposed absorber in refractive index sensing, an ambient medium with a thickness of h3=1 µm and a refractive index ranging from n=1.333-1.363 is simulated and the results are illustrated in Fig. 9. The performance of the sensor is evaluated using the sensitivity S=Δλ/Δn and figure of merit FOM = S/FWHM, the former being the shift of the resonant wavelength (λ) due to change of refractive index (n) in the surrounding medium [56]. For our proposed sensor, it can be shown that S ∼ 9000 nm/RIU (refractive index unit) and FOM∼104 RIU−1. The sensitivity is considerably enhanced concerning the metallic structure with S=1518 nm/RIU [57]. In comparison to graphene concentric ring arrays, the sensitivity is in the same range and the FOM has been improved considerably [58]. Note that in actual bio-sensing or refractive-index sensing applications, the target analytes will probably be confined to a much thinner region than h3=1µm, so the optical field decaying away from the resonance would interact with this thin layer [59,60] and shift the resonance less. The reason for choosing the medium thickness equal to the diameter of the particles is to provide a homogenous medium inside and around the graphene cover. The impact of the inhomogeneity caused by thinner ambient media will be clarified in the next paragraphs. For the sake of comparison, the sensing features for h3=100 nm in which the resulted inhomogeneity does not considerably influence the absorption rate is calculated and the results are S=1575 nm/RIU and FOM=11 RIU−1.
Fig. 9. Absorption spectrum considering a h3=1 µm thick ambient medium on top of the absorber, varying the surrounding medium refractive index in the range of n3=1.333-1.363.
Finally, in Fig. 10 the refractive index of the ambient medium is fixed to n3=1.333 and thickness-dependent absorption spectra are provided. Due to the assumption of hollow cylinders in the simulations, the ambient medium penetrates the cylinders, and a partially filled graphene-coated cylinder in an inhomogeneous medium is attained. This influences the absorption rate in the second and third resonances, and under some specific thicknesses, the absorption of the third resonances becomes dominant.
Fig. 10. Thickness-dependent absorption spectra for the refractive index of the ambient medium fixed to n3=1.333
For further visualization of the excited surface plasmons, the spatial electric field distribution at the second and third peaks are illustrated in Fig. 11 for h3=500 nm.
3. Conclusions
Using a phase change material, a bi-functional device showing optical reflection or absorption can be designed. These functionalities are respectively attained at the insulator and metallic states of the phase change material, supporting an array of graphene-coated hollow cylindrical wires. The analysis of a free-standing array of graphene-coated hollow cylindrical wires shows a Lorentzian resonance with near perfect reflection, where the operating spectrum of the device can be manipulated through various available parameters. For some specific parameter combinations, there is a higher-order resonance with Fano line shape that can be potentially used for refractive index sensing with high sensitivity and figure of merit.
Funding
Iran National Science Foundation (98012903).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
References
1. S. H. Raad, Z. Atlasbaf, and M. Cuevas, “Scattering from multilayered graphene-based cylindrical and spherical particles,” in Nanoplasmonics. 2020, IntechOpen.
2. T.-H. Xiao, L. Gan, and Z.-Y. Li, “Efficient manipulation of graphene absorption by a simple dielectric cylinder,” Opt. Express 23(15), 18975–18987 (2015). [CrossRef]
3. E. A. Velichko, “Evaluation of a graphene-covered dielectric microtube as a refractive-index sensor in the terahertz range,” J. Opt. 18(3), 035008 (2016). [CrossRef]
4. D. Correas-Serrano, J. S. Gomez-Diaz, A. Alu, and AÁ Melcón, “Electrically and magnetically biased graphene-based cylindrical waveguides: analysis and applications as reconfigurable antennas,” IEEE Trans. Terahertz Sci. Technol. 5(6), 951–960 (2015). [CrossRef]
5. Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014). [CrossRef]
6. S. H. Raad, C. J. Zapata-Rodríguez, and Z. Atlasbaf, “Multi-frequency super-scattering from sub-wavelength graphene-coated nanotubes,” J. Opt. Soc. Am. B 36(8), 2292–2298 (2019). [CrossRef]
7. S. H. Raad, C. J. Zapata-Rodríguez, and Z. Atlasbaf, “Graphene-coated resonators with frequency-selective super-scattering and super-cloaking,” J. Phys. D: Appl. Phys. 52(49), 495101 (2019). [CrossRef]
8. M. Naserpour, C. J. Zapata-Rodríguez, S. M. Vuković, H. Pashaeiadl, and M. R. Belić, “Tunable invisibility cloaking by using isolated graphene-coated nanowires and dimers,” Sci. Rep. 7(1), 12186 (2017). [CrossRef]
9. S. H. Raad, Z. Atlasbaf, and C. J. Zapata-Rodríguez, “Multi-frequency near-field enhancement with graphene-coated nano-disk homo-dimers,” Opt. Express 27(25), 37012–37024 (2019). [CrossRef]
10. B. Zhu, G. Ren, Y. Yang, Y. Gao, B. Wu, Y. Lian, J. Wang, and S. Jian, “Field enhancement and gradient force in the graphene-coated nanowire pairs,” Plasmonics 10(4), 839–845 (2015). [CrossRef]
11. Y. Gao and I. V. Shadrivov, “Nonlinear coupling in graphene-coated nanowires,” Sci. Rep. 6(1), 1–6 (2016). [CrossRef]
12. V. I. Fesenko, V. I. Shcherbinin, and V. R. Tuz, “Multiple invisibility regions induced by symmetry breaking in a trimer of subwavelength graphene-coated nanowires,” J. Opt. Soc. Am. A 35(10), 1760–1768 (2018). [CrossRef]
13. S. H. Raad and Z. Atlasbaf, “Broadband continuous/discrete spectrum optical absorber using graphene-wrapped fractal oligomers,” Opt. Express 28(12), 18049–18058 (2020). [CrossRef]
14. P. Kumar, A. Lakhtakia, and P. Kumar Jain, “Tricontrollable pixelated metasurface for stopband for terahertz radiation,” J. Electromagn. Waves Appl. 34(15), 2065–2078 (2020). [CrossRef]
15. H. Hajian, A. Ghobadi, A. E. Serebryannikov, B. Butun, G. A. Vandenbosch, and E. Ozbay, “VO 2-hBN-graphene-based bi-functional metamaterial for mid-infrared bi-tunable asymmetric transmission and nearly perfect resonant absorption,” J. Opt. Soc. Am. B 36(6), 1607–1615 (2019). [CrossRef]
16. P. Ghenuche, G. Vincent, M. Laroche, N. Bardou, R. Haïdar, J.-L. Pelouard, and S. Collin, “Optical extinction in a single layer of nanorods,” Phys. Rev. Lett. 109(14), 143903 (2012). [CrossRef]
17. T. K. Nguyen, P. T. Dang, and K. Q. Le, “Numerical design of thin perovskite solar cell with fiber array-based anti-reflection front electrode for light-trapping enhancement,” J. Opt. 18(12), 125901 (2016). [CrossRef]
18. J. Zhou, Z. Liu, X. Liu, P. Pan, X. Zhan, and Z. Liu, “Silicon-Au nanowire resonators for high-Q multiband near-infrared wave absorption,” Nanotechnology 31(37), 375201 (2020). [CrossRef]
19. J. Zhou, S. Yan, C. Li, J. Zhu, and Q. H. Liu, “Perfect ultraviolet absorption in graphene using the magnetic resonance of an all-dielectric nanostructure,” Opt. Express 26(14), 18155–18163 (2018). [CrossRef]
20. Y. Fan, C. Guo, Z. Zhu, W. Xu, F. Wu, X. Yuan, and S. Qin, “Monolayer-graphene-based broadband and wide-angle perfect absorption structures in the near infrared,” Sci. Rep. 8(1), 13709 (2018). [CrossRef]
21. J. Yang, Z. Zhu, J. Zhang, W. Xu, C. Guo, K. Liu, M. Zhu, H. Chen, R. Zhang, and X. Yuan, “Mie resonance induced broadband near-perfect absorption in nonstructured graphene loaded with periodical dielectric wires,” Opt. Express 26(16), 20174–20182 (2018). [CrossRef]
22. C. Guo, J. Zhang, W. Xu, K. Liu, X. Yuan, S. Qin, and Z. Zhu, “Graphene-based perfect absorption structures in the visible to terahertz band and their optoelectronics applications,” Nanomaterials 8(12), 1033 (2018). [CrossRef]
23. D. U. Yildirim, A. Ghobadi, M. C. Soydan, A. E. Serebryannikov, and E. Ozbay, “One-way and near-absolute polarization insensitive near-perfect absorption by using an all-dielectric metasurface,” Opt. Lett. 45(7), 2010–2013 (2020). [CrossRef]
24. S. H. Raad, Z. Atlasbaf, and C. J. Zapata-Rodríguez, “Broadband absorption using all-graphene grating-coupled nanoparticles on a reflector,” Sci. Rep. 10(1), 1–15 (2020). [CrossRef]
25. J. Wu, C. Zhou, H. Cao, and A. Hu, “Polarization-dependent and-independent spectrum selective absorption based on a metallic grating structure,” Opt. Commun. 309, 57–63 (2013). [CrossRef]
26. M. Grande, M. Vincenti, T. Stomeo, G. Bianco, D. De Ceglia, N. Aközbek, V. Petruzzelli, G. Bruno, M. De Vittorio, and M. Scalora, “Graphene-based perfect optical absorbers harnessing guided mode resonances,” Opt. Express 23(16), 21032–21042 (2015). [CrossRef]
27. M. Hajati and Y. Hajati, “Plasmonic characteristics of two vertically coupled graphene-coated nanowires integrated with substrate,” Appl. Opt. 56(4), 870–875 (2017). [CrossRef]
28. Y. T. Zhao, B. Wu, B. J. Huang, and Q. Cheng, “Switchable broadband terahertz absorber/reflector enabled by hybrid graphene-gold metasurface,” Opt. Express 25(7), 7161–7169 (2017). [CrossRef]
29. T. Badloe, J. Mun, and J. Rho, “Metasurfaces-based absorption and reflection control: perfect absorbers and reflectors,” J. Nanomater. 2017, 1–18 (2017). [CrossRef]
30. L. A. Falkovsky, “Optical properties of graphene and IV–VI semiconductors,” Phys.-Usp. 51(9), 887–897 (2008). [CrossRef]
31. M. C. Cakir, H. Kocer, Y. Durna, D. U. Yildirim, A. Ghobadi, H. Hajian, K. Aydin, H. Kurt, N. Saglam, and E. Ozbay, “Unveiling the optical parameters of vanadium dioxide in the phase transition region: a hybrid modeling approach,” RSC Adv. 10(50), 29945–29955 (2020). [CrossRef]
32. X.-R. Kong, H.-F. Zhang, and R.-N. Dao, “A switchable polarization-independent THz absorber using a phase change material,” Opt. Quant. Electron. 51(9), 306 (2019). [CrossRef]
33. R. E. Marvel, R. R. Harl, V. Craciun, B. R. Rogers, and R. F. Haglund Jr, “Influence of deposition process and substrate on the phase transition of vanadium dioxide thin films,” Acta Mater. 91, 217–226 (2015). [CrossRef]
34. M. Liu, Q. Xu, X. Chen, E. Plum, H. Li, X. Zhang, C. Zhang, C. Zou, J. Han, and W. Zhang, “Temperature-controlled asymmetric transmission of electromagnetic waves,” Sci. Rep. 9(1), 4097 (2019). [CrossRef]
35. 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]
36. M. Riso, M. Cuevas, and R. A. Depine, “Tunable plasmonic enhancement of light scattering and absorption in graphene-coated subwavelength wires,” J. Opt. 17(7), 075001 (2015). [CrossRef]
37. G. Rosolen and B. Maes, “Asymmetric and connected graphene dimers for a tunable plasmonic response,” Phys. Rev. B 92(20), 205405 (2015). [CrossRef]
38. S. H. Raad and Z. Atlasbaf, “Broadband/multiband absorption through surface plasmon engineering in graphene-wrapped nanospheres,” Appl. Opt. 59(28), 8909–8917 (2020). [CrossRef]
39. S. H. Raad, Z. Atlasbaf, C. J. Zapata-Rodríguez, M. Shahabadi, and J. Rashed-Mohassel, “Dyadic Green's function for the electrically biased graphene-based multilayered spherical structures,” J. Quant. Spectrosc. Radiat. Transfer 256, 107251 (2020). [CrossRef]
40. R. P. Gollapalli, “Enhanced sensitivity in graphene-based SPR biosensors using electrical bias,” Opt. Lett. 45(10), 2862–2865 (2020). [CrossRef]
41. R. Alharbi, M. Irannejad, and M. J. P. Yavuz, “Gold-graphene core-shell nanostructure surface plasmon sensors,” Plasmonics 12(3), 783–794 (2017). [CrossRef]
42. Y.-F. Chou Chau, C.-T. Chou Chao, H. J. Huang, M. R. R. Kooh, N. Kumara, C. M. Lim, and H.-P. Chiang, “Perfect dual-band absorber based on plasmonic effect with the cross-hair/nanorod combination,” Nanomaterials 10(3), 493 (2020). [CrossRef]
43. Z. Yan, Q. Zhu, M. Wan, X. Lu, X. Pu, C. Tang, and L. Yu, “Graphene ultraviolet ultrahigh-Q perfect absorption for nanoscale optical sensing,” Opt. Express 28(5), 6095–6101 (2020). [CrossRef]
44. L. Guo, M. Guo, H. Yang, J. Ma, and S. Chen, “Ultra-Narrow-Band Filter Based on High Q Factor in Metallic Nanoslit Arrays,” Sensors 20(18), 5205 (2020). [CrossRef]
45. Z. Liu, G. Liu, X. Liu, and G. Fu, “Plasmonic sensors with an ultra-high figure of merit,” Nanotechnology 31(11), 115208 (2020). [CrossRef]
46. J. Cai, Y. J. Zhou, Y. Zhang, and Q. Y. Li, “Gain-assisted ultra-high-Q spoof plasmonic resonator for the sensing of polar liquids,” Opt. Express 26(19), 25460–25470 (2018). [CrossRef]
47. H. T. Chorsi, Y. Lee, A. Alu, and J. X. Zhang, “Tunable plasmonic substrates with ultrahigh Q-factor resonances,” Sci. Rep. 7(1), 15985 (2017). [CrossRef]
48. J. Wang, C. Hu, Q. Tian, W. Yu, H. Tian, L. Li, J. Liu, and Z. Zhou, “Ultrahigh-Q and Polarization-Independent Terahertz Metamaterial Perfect Absorber,” Plasmonics 15(6), 1943–1947 (2020). [CrossRef]
49. H. Song, L. Sun, and G. P. Wang, “Tunable perfect magnetic mirrors and retroreflectors in terahertz band,” Opt. Express 28(1), 753–759 (2020). [CrossRef]
50. D. Cai, L. Ding, S. Wang, Z. Li, M. Zhu, and H. Wang, “Facile synthesis of ultrathin-shell graphene hollow spheres for high-performance lithium-ion batteries,” Electrochim. Acta 139, 96–103 (2014). [CrossRef]
51. C. Wang, Y. Wang, H. Hu, D. Liu, D. Gao, and L. Gao, “Reconfigurable sensor and nanoantenna by graphene-tuned Fano resonance,” Opt. Express 27(24), 35925–35934 (2019). [CrossRef]
52. M. A. Ordal, L. Long, R. Bell, S. Bell, R. Bell, R. Alexander, and C. Ward, “Optical properties of the metals al, co, cu, au, fe, pb, ni, pd, pt, ag, ti, and w in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1119 (1983). [CrossRef]
53. S. Thongrattanasiri, F. H. Koppens, and F. J. G. De Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012). [CrossRef]
54. A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012). [CrossRef]
55. S. H. Raad and Z. Atlasbaf, “Dyadic analysis of a cylindrical wire consisting of a cover with fully-populated surface conductivity tensor,” Opt. Express 27(15), 21214–21225 (2019). [CrossRef]
56. G. Lan, Z. Jin, J. Nong, P. Luo, C. Guo, Z. Sang, L. Dong, and W. Wei, “Narrowband perfect absorber based on dielectric-metal metasurface for surface-enhanced infrared sensing,” Appl. Sci. 10(7), 2295 (2020). [CrossRef]
57. Y. Cheng, H. Zhang, X. S. Mao, and R. Gong, “Dual-band plasmonic perfect absorber based on all-metal nanostructure for refractive index sensing application,” Mater. Lett. 219, 123–126 (2018). [CrossRef]
58. K. Li, X. Ma, Z. Zhang, J. Song, Y. Xu, and G. Song, “Sensitive refractive index sensing with tunable sensing range and good operation angle-polarization-tolerance using graphene concentric ring arrays,” J. Phys. D: Appl. Phys. 47(40), 405101 (2014). [CrossRef]
59. D. U. Yildirim, A. Ghobadi, M. C. Soydan, M. Gokbayrak, A. Toprak, B. Butun, and E. Ozbay, “Colorimetric and near-absolute polarization-insensitive refractive-index sensing in all-dielectric guided-mode resonance based metasurface,” J. Phys. Chem. C 123(31), 19125–19134 (2019). [CrossRef]
60. A. J. Haes and R. P. Van Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124(35), 10596–10604 (2002). [CrossRef]
