Open Access
Add to BibSonomy
Abstract
Due to the negative coefficient of thermal expansion of graphene, temperature changes of graphene-coated photonic surfaces could induce resonant mode shifts in diffractive optical absorptance and emission. This study focuses on the modification of optical properties through folding, or “origami,” of graphene covering a plasmonic metal channel grating. This work is especially critical to understanding tailored deep plasmon emission from geometrically-modulated conducting sheets such as graphene. Conformational changes in graphene on gratings are found to tailor cavity resonance emission and plasmonic oscillations such as magnetic polaritons (MPs) and surface plasmon polaritons (SPPs), respectively. Up to 46% reduction in radiative absorptance was observed through retarded MP. Excited SPP modes can increase narrowband absorptance of 0.5 through folding of graphene. Tailoring of optical absorptance can be used for applications such as photodetectors and thermal emitters.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Graphene has been shown to demonstrate negative thermal coefficient of expansion [1,2]. Therefore, its presence as a coating on metal plasmonic gratings for photonic emission could be affected by temperature changes when moving between different environments. While graphene’s ultrathin nature allows optical transparency, its bandgap-less and tunable electronic superconductivity in the infrared wavelengths has been shown to tailor radiative properties of narrowband emitters [3–7]. Because of these unique properties of graphene, its use is proposed in various optical science and engineering applications: photonic metamaterials, nanoantennas, photodetectors, and photovoltaics [8–10]. Applications such as photodetectors and thermal emitters require controlled absorptance of light, and researchers have harnessed the phenomena of cavity plasmonic resonances to induce narrowband spectrum and high contrast absorptance.
Plasmonic oscillations, specifically magnetic polariton (MP) and surface plasmon polariton (SPP) are utilized to enhance the optical absorptance by covering the grating by graphene [3–6]. An MP confines the electromagnetic field inside a resonant cavity, such as a 1D or 2D nano- or micro-patterned deep channel, and induces current when the substrate is made of a free-electron-rich metal [11–15]. On the other hand, SPP is the electromagnetic wave that is coupled with plasma oscillations on the surface of the metal, which strongly absorb or emit the photons [16–18]. Examples of nano- or micro-patterned gratings include 1D gratings covered by 2D nanosheets as well as using the dielectric spacer. For instance, graphene covering the metal gratings resulted in enhancing the absorptance to 70% to 80% when MP and SPP are excited [3,4]. By tuning the chemical potential of graphene, the grating becomes a wavelength-selective thermal emitter, due to the MP coupling with the graphene plasmons [5,6]. Other 2D materials such as black phosphorus, hexagonal boron nitride, and molybdenum disulfide on metallic gratings have shown lattice or strain-dependent plasmonic shifts [7,19,20]. These wavelength-selective thermal emitters were designed for wide range of incidence angles [17]. 2D grating structures with mesh-like, rotating, and complex geometric patterns have displayed absorptance augmentation through the utilization of MPs and SPPs [18,21,22]. Others utilized lattice phase-transformation materials such as vanadium dioxide to thermally switch absorptance peaks [23,24]. Therefore, the utilization of plasmonic responses is critical to enhancing light absorptance.
Realistically, with a negative coefficient of thermal expansion of graphene, the “accordion”-like corrugation of graphene has been observed experimentally [25–27]. This change in graphene formation could affect the optical properties, either through flaw or design. Folding of graphene for optical tuning, as well as for other 2D materials such as carbon nanotubes (CNTs), hexagonal boron nitride, tungsten disulfide, and molybdenum disulfide, has been suggested [28]. The optical properties of graphene-covered nanoparticles, graphene microflowers, and other carbon-based materials such as CNT and spherical fullerenes (C60, C70) have been studied [10,29–32]. Due to the combined effects of unique graphene deformation and electronic transport properties with photons, the radiative absorptance and reflection of the graphene-covered plasmonic grating is most interesting to us.
This study focuses in understanding plasmonic-mode disruptions and excitations that lead to optical properties tailoring from stress-free graphene folding on a plasmonic grating. The work shows graphene-covered grating absorptance spectra highlighting MP and SPP resonance peaks. Our model compares low-order (lifted single sheet) graphene to finely-discretized folded graphene with various types of folding configurations. It has been found that graphene plays an important role in confining the electromagnetic field, which enhances the absorptance in MP modes for flat graphene on the grating, while reduces narrowband absorptance when a gap is raised between graphene and the grating. SPP resonances not only appear along the metal grating surface, but also along the wrinkled graphene sheet above the grating groove. The effects of the shape characteristics of folding graphene is discussed with a comparison to a circuit model for MP resonance.
2. Methodology
2.1 Plasmonic grating modeling
In this work, Rigorous Coupled-Wave Analysis (RCWA) is used to calculate the optical properties and electromagnetic fields of the structure, which is often used for 1-dimensional or 2-dimensional grating structures [33,34]. The calculation focuses on transverse magnetic (TM) waves [11–19]. Considering that the grating supporting surface is opaque, the optical spectral directional absorptance of the whole structure is calculated by α = 1− R, where R is the spectral directional reflectivity obtained by RCWA [3]. At least 200 diffraction orders are executed to ensure sufficient reflected waves from small features.
The plasmonic grating substrate material is chosen as silver (Ag) and the dielectric function of Ag is obtained from Drude free electron model as expressed in Eq. (1),
It has been shown that the deep silver gratings excite strong MP resonances which can be described by the inductor-capacitor (LC) circuit [3,15]. The metal grating and the graphene acts as the inductor LAg, LG and the groove acts as capacitor C, creating an enclosed current loop around the trench. The capacitor is expressed as C = 0.27ɛ0h/b, where h and b are the groove geometrical parameters trench height and width, respectively. This single-mode LC circuit can only predict the first-order MP mode, where its frequency can be written as ${\omega _{\textrm{MP1}}} = {1 / {\sqrt {LC} }}$. L is the total inductance expressed as $L = {{{L_{\textrm{Ag}}}{L_\textrm{G}}} / {({{L_{\textrm{Ag}}} + {L_\textrm{G}}} )}}$, where the inductor scales with groove geometrical parameters and proportional to the dielectric function, ɛ′/ω2(ɛ′2 + ɛ″2) [6,35,36].
The predictions for higher MP modes are available by including the SPP interactions seen near MP resonance frequencies, where mutual inductance (M) between SPP and MP resonances is considered [35,36]. Mutual LC (MLC) circuit can be used to predict higher-order MP resonance frequencies. The inductance of the trench wall, LAg,w and the inductance on the surface, LAg,s of the grating interacts each other by creating a mutual inductance, $M = \kappa \sqrt {{L_{\textrm{Ag,w}}} \cdot {L_{\textrm{Ag,s}}}} $ (κ is the coupling coefficient). Table 1 shows the coupling and inductor coefficients used to predict MP modes N from 1 through 4 (the coefficients of mode 5 is yet to be determined) [36]. LAg,s is a function of frequency ω and SPP resonant frequency ωSPP, which is obtained from the SPP dispersion intersection with the light line of the grating, expressed by,
Table 1. MLC coupling and inductor coefficients of MP modes for Ag deep grating with b = 0.1 µm width and h = 0.5 µm depth.
2.2 Properties of graphene
The 2D conductor, graphene (G), has Dirac cone bandgap-less conduction. For µ >> kBT, the sheet conduction of electrons occupying π-π out-of-lattice plane orbitals is calculated using,
2.3 Graphene folding model
We approach wrinkles as periodic tent-like foldings, for simplicity. In this paper, we consider two periodic bonding situations: One is attached at a point on the grating surface (weak bond), and another is which graphene is stuck onto the silver grating, due to either annealing or van der Waals force (strong bond). Figure 1(a) illustrates the silver grating covered with “origami” folded graphene assuming weak bonding. With strong bonding, graphene adheres to the top surface of the silver substrate (pink). In order to calculate the angled graphene, the graphene sheet must be divided into segmented horizontal layers so that it forms a set of discretized “stairs” of graphene going up and down per period. In Fig. 1(c), we make simplifying approximations starting from 0th order approximation, where a graphene sheet is floating over the grating at the height of Hw/2. These approximations serve to extrapolate the converging plasmonic characteristics of a thin Fermi film above gratings [6]. Then, 1st order approximation and higher-order “stair type” approximations are made by increasing the number of disjointed graphene layers. The 0th and 1st order graphene sheet dimensions are dictated by the equivalent area of Hw/2 multiplied by the grating period. The number of equal width graphene monolayers of “stair type” discretizations is 91 and 68 for weak and strong bond, respectively, plus the one graphene sheet attached to the substrate. The air gap vertical separation between “steps” is exactly Δg.
Fig. 1. a) Schematic of reflected incident light beam by the origami graphene on the Ag grating, b) geometry nomenclature of the folded graphene above the grating (weak bond), and c) diagrams of 0th order, 1st order, weak bond stair type, and strong bond stair type.
The grating parameters are period Λ0 = 0.4 µm, height h0 = 0.5 µm, and trench width b0 = 0.1 µm, whose metal substrate filling ratio is f = 0.75. This high filling ratio dispersion results in multiple MPs in visible (VIS) to mid-infrared (MIR) regions. These default parameters represent the grating at the warm state, when graphene is initially placed onto the substrate. These parameters change after the structure is cooled to nominal temperature, for this case is 300 K. The peak folded graphene height is from displacement geometry derivations of an unconstrained graphene sheet at the out-of-plane boundaries, and is expressed as,
On the other hand, graphene could be attached to the silver substrate via van der Waals attraction between electron-rich elements. The graphene tent will now only appear above the vacuum groove. The graphene height in strong bond is calculated using Eq. (5) but with the supposition that an annealing process at 900 K is done during blanketing of flat graphene [1]. This leads to expanding the period of the grating and further shrinking the length of graphene when strongly attached to the substrate. When both materials are cooled to 300 K, the graphene height above the substrate surface is now Hs = 20.1 nm, shown in Fig. 1(c). Considering the graphene attached to the substrate surface, it has been observed that the transparency of graphene can be affected by strain-stretching the substrate [41]. These slight changes in optical properties are due to rotation of incident polarization which is induced by Dirac point placement [42]. In this case, graphene sitting on the metal strip have little contribution to optical properties due to dominance of Ag surface plasma effects.
3. Results and discussion
3.1 Spectral radiative properties
The absorptance spectrum is calculated in RCWA with the incidence angle of θi = 10°. We have conducted calculations on 0th order, 1st order, and stair type, in order to catch the physical phenomena when graphene is lifted above the grating, and observe the convergence toward folding graphene. Figure 2(a) shows the absorptance in visible to infrared spectra comparison of 0th order, and 1st order, and stair type approximation. Eight peaks represent the MPs, SPPs along the silver grating in visible wavelength range and narrowband SPP along the graphene in mid-infrared region, which is excited only in “stair type” approximation and its absorptance of 0.5 is induced compared to no absorptance peak at around the same wavenumber for flat graphene on the grating. The result shows the reduction in absorptance up to 46% in stair type weak bond at MP2 mode due to the less contact between graphene and the silver grating, indicating that MP2 mode is strongly dependent on graphene contact on the grating groove [3,4]. Absorptance is gradually reduced as the order increases from 0th to 1st order to stair type, showing the significance of graphene shape attached to the grating. The outcome also shows the MPs and SPPs resonance frequencies shift due to the groove shrinking effect. This causes red shifts up to 173 cm-1 in MPs and blue shifts up to 145 cm-1 in SPPs, when temperature cools down to 300 K. This resonance shift is also significant when changing the size of the trench in width (Fig. 2(b)), indicating that groove expansion or shrinking in the x-direction shifts the absorptance peaks. Furthermore, several resonance interactions including MP1/SPPG, MP3/SPP1, and MP5/SPP2 interactions are observed. Since MP resonance frequencies is inversely propotional to inductance and capacitance, the MP resonances red-shift as trench width decreases as described in Eq. (3). Trench width reduces inductance in this LC circuit model that describes red shiting in MP resonant frequencies (ωMP), and the increased ratio of substrate surface-to-groove bottom blue shifts the SPPs. On the other hand, SPPG is independent of trench width, but the shifting MP1 may overlap its presence. SPPG is mostly dependent on incidence angle and geometry of graphene above the trench, and will be illustrated in field density calculations in the following sections. Figure 2(c) demonstrates the shift in this newly-found SPPG narrowband mode, where tuning the folding angle θe between the raised graphene and substrate reveals frequency shifts of the emission peak. Meanwhile, the MP1 resonance remains unchanged. Through the varying folding angles, there are at least 46 equally-spaced graphene monolayer discretizations captured. These results spark the need to not only develop an understanding of angled conducting monolayer on plasmonic surface, but also to emphasize the interest in displacement-based optical sensing and emission.
Fig. 2. a) The absorptance spectra of 0th, 1st, and weak bond configuration graphene on silver deep grating, with b0 = 0.1 µm, Λ0 = 0.4 µm, and h0 = 0.5 µm. b) Absorptance contour of folded graphene, showing surface plasmon polariton (SPP) dispersions for graphene (G) and grating (1&2 – green dots), and magnetic polariton (MP – white lines) for Nth modes from Table 1. c) Spectrum showing constant MP1 and shifting SPPG relative to the graphene folding angle θe.
Figure 3(a) shows the comparison of absorptance spectra of weak and strong bond, which shows that the difference in graphene-silver substrate bonding plays an important role in peak shifts and controlling absorptance. The absorptance in the MP modes (except in MP2) are larger in strong bond. Note that from Fig. 2(a), the absorptance reduction observed in strong bond at MP2 is 50% which is slightly larger than reduction in weak bond (46%). This means that MP2 mode is sensitive to graphene and the possible reason of decrease in absorptance is due to sharper top angle of stair type graphene in strong bond. In addition, peak shifts is significant in VIS region, where the SPP2 and MP5 peaks of weak bond is close to that with no graphene covering the grating and its peaks for strong bond is similar to the flat graphene sitting on the grating (Fig. 3(b)). This signifies that for shorter wavelength, the absorptance spectrum is highly dependent on the graphene position above the groove. The effect of graphene on the grating is also critical in MIR region. SPP along the graphene (SPPG) is smaller in strong bond due to shorter distance separated from gratings, whereas in weak bond, SPPG is stronger. It is considered that the absorptance in SPPG is enhanced because magnetic field inside the trench converts to SPP excitation along the graphene. While, the absorptance in MP1 is reduced in weak bond and is enhanced in strong bond as shown in Fig. 3(c), indicating that high angle between graphene and the grating in strong bond is important. More will be discussed in the following section in explanation of this phenomena.
Fig. 3. a) Comparison of weak and strong bond with Λ0 = 0.4 µm, b0 = 0.1 µm, and h0 = 0.5 µm b) in MIR region, c) in VIS region, and d) the effect of chemical potential to absorptance spectra.
Figure 3(d) represents the effect of chemical potential of graphene, where the chemical potential can be adjusted by DC voltage bias, site doping, and strain-induced band structure changes [9,43]. As chemical potential gets larger, the absorptance of the structure at SPPG gets higher and it reaches to 0.96 at µ = 0.4 eV in weak bond. Additionally, these SPPG peaks blue shift due to the interband transition in graphene. Absorptance in SPPG is produced by converting the magnetic field within the groove to the electric field along the graphene, while absorptance in MP1 is reduced and eventually disappears. Whereas, in strong bond, absorptance peak at MP increases. By observation, as its chemical potential increases, the MP contribution to the radiative absorptance grows, and its frequency shift can be explained by LC model to be developed for “origami” graphene. The reduction of inductance L cause blue shifting MP as chemical potential increases due to the interband transition that makes imaginary part of conductivity negative in graphene. The capacitance C does not affect the shifting because it is independent of chemical potential. Therefore, only small frequency variation is observed in MP as shown in Fig. 3(d).
With high chemical potential, the augmentation of either SPPG or MP resonances can be seen in weak and strong bond; however, its effect is relatively small if the chemical potential is low as shown in Fig. 3(d). Also notice that in the case of same chemical potential, absorptance at SPPG in weak bond is higher than strong bond, while absorptance from MP in weak bond is stronger. Nevertheless, its absorptance of both SPPG and MP is larger in weak bond for graphene at 0.2 eV which does not follow the former pattern. This means that the effect of geometry or the bond strength is much more significant in small chemical potential. The presence of a strong bond graphene at 0.2 eV does not significantly interfere with the MP nor induce a strong SPP resonance. A large chemical potential graphene (0.4 eV) will induce both MP1 augmentation and SPPG at 4729 cm-1, while making a large 1623 cm-1 blue shit of SPPG from 0.3 eV. Since the geometric parameters of folding graphene is different in weak and strong bond, such resonance differences are likely to be dependent on both the height and the edge angle of the triangle-shaped cavity formed between the lifted graphene and the silver grating substrate.
3.2 Grating MP modes
Here, we explain the characteristic absorptance differences due to shape changes in graphene on gratings. Figure 4(a) shows the absorptance contour of folding graphene covering the silver grating in respect to wavevector kx = 2πνsin(θi). The blank area at lower-right corner of the figure is due to no existence of propagation wave in vacuum [4]. In this analysis, incidence angle is chosen as 10 degrees so that the multiple MPs and SPPs appear in absorptance spectrum to understand the contrast of MP/SPP interactions. Note that two SPPs are present in Fig. 4(a) because of the symmetry of the grating in Bloch-Floquet condition [16,33]. SPP along the graphene have a strong narrowband absorptance, while MP1 have very weak absorptance due to small difference between both resonant frequencies. Resonance peak shifting in MP3, MP4, and MP5 is seen due to MP/SPP interactions compared to steady MP2. Figures 4(b), (c), (d), and (e) show the electromagnetic field at MP1 (3787 cm-1), MP2 (11166 cm-1), MP3 (17836 cm-1), MP4 (24273 cm-1), and MP5 (29221 cm-1) for weak bond respectively. MP2 and MP3 present strong coupling between the resonances inside and outside the grating trench compared to that of the silver grating without graphene on top of the groove, whereas coupling in MP1 is weaker. This indicates that the graphene sheet confines the electromagnetic field inside the trench, which ultimately enhances the absorptance. Electric current loops are produced around the trench and the number of loops match the order of MP resonance [14]. The electromagnetic field within the trench is weaker in MP4 and MP5 due to smaller current loops in spite of their light absorptance. In addition, MP/SPP interactions are seen in MP3, MP4, and MP5 along the surface of silver grating. The electric field is induced along the surface of the Ag grating because their resonance frequencies are close to SPP resonances (21351 cm-1 at SPP1 and 27695 cm-1 at SPP2). Furthermore, surface effects on MP3 and MP5 are symmetric, where a similar electromagnetic field is induced in left and right end of the grating. However, it is asymmetric in MP4, and possible reason is that the pattern of the field is disturbed by the two SPP resonances sandwiching the MP4 near its resonant frequency. As a consequence, absorptance at MP4 is greatly reduced.
Fig. 4. a) Absorptance contour of stair type (weak bond). The white lines shows the light line at incidence angle θi = 10°. b) Electromagnetic field at MP1, c) MP2, d) MP3, e) MP4, and f) MP5. The contour shows the magnitude of the magnetic field, and the arrows show the local electric field magnitude.
The prediction of MP1 mode peak could be simply described by applying the LC circuit. MP1 is most profound as its frequency is close to the SPPG mode. The resonant wavenumber of 1st order MP can be predicted as 3760 cm-1 which is close to 3755 cm-1 calculated in RCWA for flat graphene on silver grating. However, this prediction may not be applicable for weak and strong bond because MP1 is dependent on bond strength or geometric parameters of folding graphene. In other words, MP1/SPPG interaction should be included in LC circuit model for origami graphene covering the grating. In fact, this is somewhat similar to the discussion made on recent study on LC circuit which consists of MP/SPP interaction, namely mutual LC (MLC) circuit [35,36]. For instance, MP3 is predicted 18315 cm-1, which is close to 17836 cm-1 calculated in RCWA. Other MP modes demonstrate electric field excitation in graphene, however at smaller magnitudes. This is potentially due to the small height change in folded graphene. Although its effect is not small for MP1; therefore, a modified graphene covered MLC circuit is being developed for folding graphene topping the grating so that additional resonance in graphene is considered to predict the MP resonance frequency more accurately.
3.3 Graphene SPP modes
In this section, absorptance phenomena under MP and SPP coupling is discussed by comparing electromagnetic field in weak-versus strong-bond “origami” graphene. Strong coupling between SPP mode in graphene and MP was seen for flat graphene on a plasmonic grating [6]. Here, the coupling mechanism between SPP of the folded graphene (SPPG) and magnetic polariton (MP1) is observed. Figure 5(a) illustrates the electric field vectors (black arrows) and magnetic field density (contour) along the folded graphene sheet at the SPP mode frequency for weak bond. The electric field is strong along the graphene fold point just above the trench, and it can be seen that magnetic field from the trench affects the electric field, where the field is reduced and shifted above the graphene sheet. For this reason, SPPG has a strong absorptance peak due to the distance extended by the larger folding angle of graphene above the trench. Although the magnetic field around the trench is not strong as shown at MP1 in Fig. 4(b), the SPPG strengthens the electric field loops above the trench.
Fig. 5. Electric field vectors (arrows) and magnetic field density (|Hy|) contours for SPPG along the folded graphene sheet for a) weak and c) strong bond. Magnetic field density inside the grating trench for b) weak and d) strong bond; the electric field vectors shown across the broader groove are not in the plane of the graphene sheet.
On the other hand, SPPG in the strong bond configuration is relatively small due to small electric field shifts compared to that in weak bond one as shown in Fig. 5(b). The magnetic field inside the trench is stronger, with deeper penetration depth and stronger absorptance of light, due to the proximity to the 1st order MP mode Fig. 5(d). In Fig. 5(c), the magnitude of magnetic field shadowed by the trench resonance is weaker, and the electric field along the graphene is also weak (negligible black lines). In this case, the magnetic field is much more confined inside the trench, therefore the SPPG mode is effectively canceled. By observation of exchanging contribution of magnetic field confinement in trench versus the effect of folding graphene in either strong and weak bond, is significant in enhancing narrowband absorptance of either SPPG or MP1 mode. Additionally, it can be seen that graphene is effective for field confinement only above the trench as shown in Fig. 5(a) and (c), where inductance of graphene may be critical compared to graphene on edges. This indicates that the geometry of graphene may play a significant role in controlling optical properties of the structure. On the other hand, graphene above the metal strips have little influence on optical properties, but rather due to the surface effects of silver. These results further inspire the development of an angle-dependent LC circuit model which captures the tenting effect of 2D conducting sheet above the plasmonic grating.
4. Conclusions
The effects of changes in graphene conformation, due to negative thermal expansion of graphene, on plasmonic grating’s optical properties have shown to disrupt MP resonances in the visible to near-IR, while induce a SPP resonance peak in the far-IR. The comparison of weak versus strong bond of periodic stair-type graphene on the silver grating demonstrates: The absorptance is reduced up to 46% and 50% in weak and strong bond, respectively because of detachment of graphene and the grating. While most of the MPs blue shifts, SPPs red shifts, and these shifts could be predicted by validated MLC circuit models. These shifts correspond intuitively with the relative mechanical deformations of the two materials. The distinctive SPPG mode shifts with the raised graphene angle, which motivates the study of a geometry-dependent multi-loop LC circuit dispersion. SPP and MP interact each other if both frequencies are close to each other which is seen at MP1, MP3, MP4, and MP5. The effect of bonding strength or geometry is seen in both VIS and MIR regions. SPPG is induced and its absorptance can be enhanced by MP or by increasing the chemical potential of the graphene, and its change in geometry could be used for optical manipulation. Hence, this study provides the idea of tuning the absorptance of the optical applications with corrugated graphene, carbon-based materials, and other 2D materials including boron nitride, tungsten disulfide, and molybdenum disulfide.
Disclosures
The authors declare no conflicts of interest.
References
1. H. Zhang, F. Miao, C. Dames, W. Bao, C. N. Lau, Z. Chen, and W. Jang, “Controlled ripple texturing of suspended graphene and ultrathin graphite membranes,” Nat. Nanotechnol. 4(8), 523–527 (2009). [CrossRef]
2. D. Yoon, Y. Son, and H. Cheong, “Negative Thermal Expansion Coefficient of Graphene Measured by Raman Spectroscopy,” Nano Lett. 11(8), 3227–3231 (2011). [CrossRef]
3. B. Zhao, J. M. Zhao, and Z. M. Zhang, “Enhancement of near-infrared absorption in graphene with metal gratings,” Appl. Phys. Lett. 105(3), 031905 (2014). [CrossRef]
4. B. Zhao, J. M. Zhao, and Z. M. Zhang, “Resonance enhanced absorption in a graphene monolayer using deep metal gratings,” J. Opt. Soc. Am. B 32(6), 1176 (2015). [CrossRef]
5. H. Wang, Y. Yang, and L. Wang, “Infrared frequency-tunable coherent thermal sources,” J. Opt. 17(4), 045104 (2015). [CrossRef]
6. B. Zhao and Z. M. Zhang, “Strong Plasmonic Coupling between Graphene Ribbon Array and Metal Gratings,” ACS Photonics 2(11), 1611–1618 (2015). [CrossRef]
7. Y. M. Qing, H. F. Ma, and T. J. Cui, “Strong coupling between magnetic plasmons and surface plasmons in a black phosphorus-spacer-metallic grating hybrid system,” Opt. Lett. 43(20), 4985–4988 (2018). [CrossRef]
8. P. Chen, C. Argyropoulos, M. Farhat, and J. S. Gomez-Diaz, “Flatland plasmonics and nanophotonics based on graphene and beyond,” Nanophotonics 6(6), 1239–1262 (2017). [CrossRef]
9. R. Wong, X.-G. Ren, Z. Yan, L.-J. Jiang, W. E. I. Sha, and G.-C. Shan, “Graphene based functional devices: A short review,” Front. Phys. 14(1), 13603 (2019). [CrossRef]
10. Z. Wang and P. Cheng, “Enhancements of absorption and photothermal conversion of solar energy enabled by surface plasmon resonances in nanoparticles and metamaterials,” Int. J. Heat Mass Transfer 140, 453–482 (2019). [CrossRef]
11. B. J. Lee, L. P. Wang, and Z. M. Zhang, “Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film,” Opt. Express 16(15), 11328 (2008). [CrossRef]
12. L. P. Wang and Z. M. Zhang, “Resonance transmission or absorption in deep gratings explained by magnetic polaritons,” Appl. Phys. Lett. 95(11), 111904 (2009). [CrossRef]
13. L. P. Wang and Z. M. Zhang, “Phonon-mediated magnetic polaritons in the infrared region,” Opt. Express 19(S2), A126–A135 (2011). [CrossRef]
14. L. Wang and Z. Zhang, “Wavelength-selective and diffuse emitter enhanced by magnetic polaritons for thermophotovoltaics,” Appl. Phys. Lett. 100(6), 063902 (2012). [CrossRef]
15. B. Zhao and Z. M. Zhang, “Study of magnetic polaritons in deep gratings for thermal emission control,” J. Quant. Spectrosc. Radiat. Transfer 135, 81–89 (2014). [CrossRef]
16. Y.-B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiators,” Opt. Commun. 269(2), 411–417 (2007). [CrossRef]
17. B. Zhao, L. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637–645 (2013). [CrossRef]
18. H. Wang and L. Wang, “Tailoring thermal radiative properties with film-coupled concave grating metamaterials,” J. Quant. Spectrosc. Radiat. Transfer 158, 127–135 (2015). [CrossRef]
19. B. Zhao and Z. M. Zhang, “Perfect mid-infrared absorption by hybrid phonon-plasmon polaritons in hBN/metal-grating anisotropic structures,” Int. J. Heat Mass Transfer 106, 1025–1034 (2017). [CrossRef]
20. L. Long, Y. Yang, H. Ye, and L. Wang, “Optical absorption enhancement in monolayer MoS2 using multi-order magnetic polaritons,” J. Quant. Spectrosc. Radiat. Transfer 200, 198–205 (2017). [CrossRef]
21. A. Sakurai, B. Zhao, and Z. M. Zhang, “Resonant frequency and bandwidth of metamaterial emitters and absorbers predicted by an RLC circuit model,” J. Quant. Spectrosc. Radiat. Transfer 149, 33–40 (2014). [CrossRef]
22. L. Zhao, Z. He, Q. Niu, X. Yang, and S. Dong, “Near-field-coupled lighting-rod effect for emissivity or absorptivity enhancement of 2-D (1, 2) magnetic plasmon mode by rotating the square resonators array,” J. Quant. Spectrosc. Radiat. Transfer 240, 106631 (2020). [CrossRef]
23. H. Wang, Y. Yang, and L. Wang, “Wavelength-tunable infrared metamaterial by tailoring magnetic resonance condition with VO2phase transition,” J. Appl. Phys. 116(12), 123503 (2014). [CrossRef]
24. L. Long, S. Taylor, X. Ying, and L. Wang, “Thermally-switchable spectrally-selective infrared metamaterial absorber/emitter by tuning magnetic polariton with a phase-change VO2 layer,” Mater. Today Energy 13, 214–220 (2019). [CrossRef]
25. S. Deng and V. Berry, “Wrinkled, rippled and crumpled graphene: an overview of formation mechanism, electronic properties, and applications,” Mater. Today 19(4), 197–212 (2016). [CrossRef]
26. J. Zang, S. Ryu, N. Pugno, Q. Wang, Q. Tu, M. J. Buehler, and X. Zhao, “Multifunctionality and control of the crumpling and unfolding of large-area graphene,” Nat. Mater. 12(4), 321–325 (2013). [CrossRef]
27. B. Deng, Z. Pang, S. Chen, X. Li, C. Meng, J. Li, M. Liu, J. Wu, Y. Qi, W. Dang, H. Yang, Y. Zhang, J. Zhang, N. Kang, H. Xu, Q. Fu, X. Qiu, P. Gao, Y. Wei, Z. Liu, and H. Peng, “Wrinkle-Free Single-Crystal Graphene Wafer Grown on Strain-Engineered Substrates,” ACS Nano 11(12), 12337–12345 (2017). [CrossRef]
28. A. L. Ivanovskii, “Graphene-based and graphene-like materials,” Russ. Chem. Rev. 81(7), 571–605 (2012). [CrossRef]
29. B. Yang, T. Wu, Y. Yang, and X. Zhang, “Tunable subwavelength strong absorption by graphene wrapped dielectric particles,” J. Opt. 17(3), 035002 (2015). [CrossRef]
30. T. Naseri and F. P-Khavaari, “Bimetallic core-shell with graphene coating nanoparticles: enhanced optical properties and slow light propagation,” Plasmonics 15(4), 907–914 (2020). [CrossRef]
31. C. Chen, C. Chen, J. Xi, J. Xi, E. Zhou, E. Zhou, L. Peng, L. Peng, Z. Chen, Z. Chen, C. Gao, and C. Gao, “Porous Graphene Microflowers for High-Performance Microwave Absorption,” Nano-Micro Lett. 10(1), 1–11 (2018). [CrossRef]
32. O. Kozák, M. Sudolská, G. Pramanik, P. Cígler, M. Otyepka, and R. Zbořil, “Photoluminescent Carbon Nanostructures,” Chem. Mater. 28(12), 4085–4128 (2016). [CrossRef]
33. Z. M. Zhang, Nano/Microscale Heat Transfer (McGraw-Hill, 2007).
34. M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068 (1995). [CrossRef]
35. Y. Guo, Y. Shuai, and H. Tan, “Mechanism of polaritons coupling from perspective of equivalent MLC circuits model in slit arrays,” Opt. Express 27(15), 21173–21184 (2019). [CrossRef]
36. Y. Guo, Y. Shuai, and J. Zhao, “Tailoring radiative properties with magnetic polaritons in deep gratings and slit arrays based on structural transformation,” J. Quant. Spectrosc. Radiat. Transfer 242, 106788 (2020). [CrossRef]
37. G. Hanson, “Dyadic Green's functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]
38. R. Z. Zhang and Z. M. Zhang, “Tunable positive and negative refraction of infrared radiation in graphene-dielectric multilayers,” Appl. Phys. Lett. 107(19), 191112 (2015). [CrossRef]
39. R. Z. Zhang, X. L. Liu, and Z. M. Zhang, “Near-field radiation between graphene-covered carbon nanotube arrays,” AIP Adv. 5(5), 053501 (2015). [CrossRef]
40. X. L. Liu, R. Z. Zhang, and Z. M. Zhang, “Near-perfect photon tunneling by hybridizing graphene plasmons and hyperbolic modes,” ACS Photonics 1(9), 785–789 (2014). [CrossRef]
41. J. Zang, S. Ryu, N. Pugno, Q. Wang, Q. Tu, M. J. Buehler, and X. Zhao, “Multifunctionality and control of the crumpling and unfolding of large-area graphene,” Nat. Mater. 12(4), 321–325 (2013). [CrossRef]
42. V. M. Pereira, R. M. Ribeiro, N. M. R. Peres, and A. H. Castro Neto, “Optical properties of strained graphene,” Europhys. Lett. 92(6), 67001 (2010). [CrossRef]
43. Y. Fu, J. Hansson, Y. Liu, S. Chen, A. Zehri, M. K. Samani, N. Wang, Y. Ni, Y. Zhang, Z. Zhang, Q. Wang, M. Li, H. Lu, M. Sledzinska, C. M. S. Torres, S. Volz, A. A. Balandin, X. Xu, and J. Liu, “Graphene related materials for thermal management,” 2D Mater. 7(1), 012001 (2019). [CrossRef]
