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Abstract
In this work, we propose two different graphene-covered nanostructured metamaterial absorbers inspired by Penrose tiling. These absorbers allow spectrally tunable absorption within the terahertz spectrum corresponding to 0.2-20 THz. We have conducted finite-difference time-domain analyses to determine the tunability of these metamaterial absorbers. The proposed structures, Penrose models 1 and 2, perform differently from each other due to their design characteristics. Penrose model 2 reaches a perfect absorption at 8.58 THz. In addition, the relative absorption bandwidth calculated at full-wave at half-maximum in Penrose model 2 varies between 5.2% and 9.4%, which characterizes the metamaterial absorber as a wideband absorber. Also, we can observe that as we increase the Fermi level of graphene from 0.1 to 1 eV, the absorption bandwidth and relative absorption bandwidth both increase. Our findings show the high tunability of both models through varying graphene’s Fermi level, the graphene’s thickness, the substrate’s refractive index, and the proposed structures’ polarization. We can further observe multiple tunable absorption profiles that may find applications in designer infrared absorbers, optoelectronic devices, and THz sensors.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials are an artificial class of periodic materials that could achieve unprecedented features like a negative refractive index [1–4]. These unique features are immensely sought after and find applications in energy harvesting [5], sensing [6], cloaking [7], and medical imaging [8], to name a few. In recent years, metamaterial-based absorbers with specific functionalities in various spectrum regions have gained much attention [9–15]. They could be tuned to realize designer optical, thermal, and electronic solutions [16]. Their unique features can increase light-matter interactions, enhancing absorption via additional spectral resonances within the matter of interest [17–21].
1.1 Tunable metamaterial absorbers
Tunable metamaterial absorbers could be realized by carefully selecting design parameters and materials. Linear or nonlinear behavior, polarization insensitivity, quality factor, relative absorption bandwidth, broadband, narrowband, or multiband absorption profiles are all features that could be engineered in metamaterial absorbers [22–24]. These artificially made absorbers could be tailored for the intended application in various ranges of the spectrum from terahertz to infrared to be used in applications such as sensing [25], energy harvesting [26–28], and radiative cooling [29]. For this purpose, extensive research has been done on various design features and their impact on the absorption rate of these structures. Yang et al. [30] studied the impact of periodicity in metamaterial absorbers on the absorption profile. Their study showed that aperiodic metamaterial absorbers might behave similarly to periodic structures in some respects and vary in others. The effect of temperature was studied by Zhang et al. [31], who proposed flexibly tunable metamaterial absorbers that could achieve broadband or multiband absorption using vanadium oxide, a phase-changing material. Also, Li et al. [32] proposed a dynamically tunable broadband metamaterial absorber based on vanadium oxide. Luo et al. [33] proposed metamaterial absorbers that could simultaneously achieve absorption in GHz and THz frequencies. Duan et al. [34] investigated the impact of the dielectric spacer thickness on the intensity of the absorption of metamaterial absorbers and discussed applications in sensing by tuning the absorption peak in these structures.
1.2 Graphene-based metamaterial absorbers
One approach to realize increased absorption within metamaterial absorbers is to combine them with graphene-based structures [35–39]. Graphene, which is a 2D nano-material with one-atom-thickness, supports localized surface plasmon resonance and increases the absorption efficiency of the metamaterial absorbers [40]. Various designs for metamaterial absorbers have been proposed based on this mechanism in [41–43]. These absorbers are either broadband, narrowband, or multiband. Their spectral behavior could be tailored by varying the graphene’s chemical potential, the metamaterial absorber’s refractive index, and the graphene’s thickness, polarization, angle of incidence, and temperature. Despite an extensive amount of research that has been done on graphene-based metamaterial absorbers, metamaterial absorbers still encounter some shortcomings, such as low absorption [44] and fixed absorption bandwidths which need to be addressed through novel design and material selections. Zhu et al. [6] studied a graphene-based metamaterial absorber consisting of a cross-embedded ring with double outer rectangles. The proposed perfect absorber composed of SiO2 and graphene has applications in sensing within the terahertz band (0.5-2.5 THz).
1.2.1 Broadband and multiband graphene-based metamaterial absorbers
In an earlier work represented in [45], the authors proposed another perfect metamaterial absorber based on graphene, made of the rectangular ring and strip cross graphene structures that achieved perfect broadband absorption in the terahertz regime (1.259–1.504 THz). Bao et al. [46] suggested a multi-layer tunable metamaterial made of SiO2, graphene, and SiC, including a reflective Ag layer at the bottom of the structure within the 2.5-7 THz range with applications in THz imaging and sensing. Lin et al. [47] proposed a metamaterial absorber made of SiO2, gold, and a double-layer graphene structure consisting of layered hexagonal rings, which achieved broadband absorption within the 0.5-2.5 THz region. Chen et al. [37] suggested a tunable graphene-based metamaterial absorber based on Topas and a reflective gold bottom layer that achieved dual-band terahertz perfect absorption within the 1-10 THz. Mostaan et al. [35] designed a broadband metamaterial absorber consisting of arrays of graphene rectangular splits placed upon dielectric material and a bottom gold layer that achieved very high relative bandwidth within the far-infrared region in the 4-22 THz range. Dave et al. [48] proposed a tunable hexagonal circular absorber in the far-infrared region (1-7 THz) that can achieve broadband absorption and find potential for applications in sensing and modulation. Feng et al. [49] designed a broadband THz graphene metamaterial absorber in the 0.1-3 THz range that reached very high absorption when periodic arrays of cross-shaped graphene structures embedded in a ring were placed on top of a dielectric substrate with a gold bottom layer. Huang et al. [36] proposed a mid-infrared metamaterial absorber in the spectral range of 70-130 THz, based on graphene, which achieved broadband absorption in a Jerusalem cross placed upon a dielectric substrate with a gold bottom layer. Parvaz et al. [50] designed a metamaterial absorber consisting of a ring-shaped structure placed upon a monolayer of graphene in a metamaterial absorber that achieved multiband absorption within 3-10 THz. Mishra et al. [51] proposed a squared-patterned graphene-based absorber that achieved broadband absorption within 0.1-4 THz region. Suo et al. [52] proposed a transparent absorber comprising five layers that can achieve broadband absorption. The absorber achieved more than 90% absorption with a relative absorption bandwidth of about 65.72% and showed good agreement between the experimental and theoretical match of results. Shen et al. [53] proposed a perfect THz metamaterial absorber of BDS and STO, which was tunable based on Fermi energy and can achieve absorption rates of between 89% to 100%. In addition, the central frequency of the absorber could be tuned based on the STO temperature. One of the strengths of the absorber was its insensitivity to the angle of incidence. Xiong et al. [54] proposed a tunable terahertz absorber based on graphene and Dirac semimetal. The absorber can achieve over 90% absorption in the 4.79-8.99 THz range for both TE and TM polarizations and is polarization insensitive.
1.2.2 Dual-band and narrowband graphene-based metamaterial absorbers
Ye et al. [55] proposed a graphene-based absorber based on single- and double-layer graphene in the shape of decussate graphene ribbon arrays. They showed that these structures are tunable within the 2-14 THz range, showing a single narrowband absorption peak and angular stability. The same authors also studied a tunable patterned graphene THz absorber made of a monolayer of graphene and showed the stability of their proposed designs with respect to changes in polarization [56]. Qi et al. [57] proposed an hourglass-shaped patterned graphene structure as a THz absorber. They analyzed both single-layer and bilayer graphene structures and compared the absorption profile of these structures against each other. The bilayer structure showed enhanced absorption profiles and achieved a dual-band tunable absorption. In addition, with the current state-of-the-art fabrication techniques, it is possible to realize the fabrication of patterned dual-layer graphene structures similar to the Penrose tiling structures proposed in this work. Yi et al. [58] introduced a novel synthesis method for a selectively patterned grown graphene using single- and double-layer graphene produced by a sequential chemical vapor deposition (CVD) process. Realizing fabrication of ordered patterned single and multi-layer graphene with alternative patterns is possible through this method and is easy to implement as a scalable approach.
This work presents two Penrose tiling-inspired graphene-based metamaterial absorbers highly tunable within the terahertz spectrum, covering a large spectral region from 0.2 to 20 THz. These structures, Penrose model 1 and Penrose model 2, can be tuned to achieve multiband absorption (8 bands) with near-perfect absorption in some parts of the spectrum and very high absorption elsewhere. The number of absorption bands (8 bands) observed through the proposed structures surpasses the reported results in the earlier works. We here provide our numerical findings based on the finite-difference time-domain (FDTD) method [59] and show the impact of the Fermi level of graphene, graphene’s thickness, and the refractive index of the dielectric material, relative bandwidth of absorption and polarization on the tunability of the proposed structures. As the Fermi level of graphene gradually increases from 0.1 to 1 eV, the absorption bandwidth increases from 0.45 to 0.82 THz, and the relative absorption bandwidth also increases from 5.2% to 9.4%. In addition, it can be seen that the quality factor decreases from 19 to 10.4 as the Fermi level increases. These graphene-based metamaterial absorbers could be tuned based on their geometrical and optical parameters and may find applications in infrared absorbers [60], THz sensors [61], and modulators [62].
2. Physical structure
The schematics of the proposed structure are depicted in Fig. 1. The dielectric layer has a refractive index of 3.4. It is 19 µm long (h2) and bottomed by a thin gold layer as demonstrated in the figure which has a thickness h1 of 100 nm. The graphene-based Penrose tiling structures consist of polygons and triangles and are placed upon the dielectric layer [63]. The schematics of the design of the two suggested Penrose tiling structures are also provided in Fig. 1(a)–(b). The surrounding environment is assumed to be a vacuum. In Fig. 1(c)–(d), the schematics of the 2D cross-section are illustrated. Figure 1(e) demonstrates the side view of the proposed model with the bias voltage Vg applied across patterned graphene and a bottomed gold layer. The Penrose tiling is 2.4 µm long in the x-direction (L) and 2.3 µm along the y-direction (w) and is assumed to be repeated from both directions. In the proposed metamaterial absorber, the substrate is silicon (Si), an abundant and cheap material for optoelectronic applications. The gold bottom layer acts as a reflector metal, increasing the absorption efficiency within the dielectric layer. Graphene, an abundant material, is composed of a single atom layer of carbon and is used as the 2D material of the Penrose tiling. In addition, graphene has a wide absorption band and, within the frequency range of interest in this work (0.2-20 THz), shows highly tunable absorption profiles. The complex frequency-dependent conductivity of graphene can be obtained based on the Kubo formula, which illustrates the dependency of the absorption and conduction profiles of graphene on its chemical potential [64]. The permittivity of graphene is given in [36].
Fig. 1. (a-b) Perspective views of proposed Penrose absorbers model 1 and 2. h1 and h2 are 100 nm and 19 µm, respectively, (c-d) top views of Penrose models 1 and 2 for a unit cell. L and w are 2.4 µm and 2.3 µm, respectively, and (e) side view of the proposed model with the bias voltage Vg applied across patterned graphene and a bottomed gold layer.
3. Simulation setup
We performed 3D simulations using the well-known FDTD method with commercially available software (FDTD solution, Lumerical, Inc.). Throughout our analysis, light (i.e., excitation source) is illuminated perpendicularly from the top of the structure, along the z-axis, in a backward direction. It is considered to be a plane wave source. We have adopted periodic boundary conditions in the x and y directions and a perfectly matched layer (PML) along the z-axis. We placed two z-normal monitors to record the reflection and transmission of electric and magnetic fields, as depicted in Fig. 2. Another monitor (shown as a graphene monitor in Fig. 2) is located right underneath the Penrose tiling to record the fields across the graphene-based structure. We applied an extra mesh layer over the Penrose tiling based on the principles of advanced mesh refinement technique to increase the accuracy of the calculated fields across graphene-based structures. This technique creates a "very fine" mesh where the graphene layer exists and a coarser mesh everywhere else. This mesh size is 0.1 nm, allowing at least 6 grid points for our two-layer thick graphene surface (which is 0.68 nm thick). The mesh size everywhere else is 100 nm in the z-direction and 25 nm in the x- and y-directions, which is enough to construct the smallest wavelength considered in our simulations. This way, we ensure that the proper resolution is achieved, numerical errors are avoided in our calculations, and the simulations can be run in a reasonable time. In Lumerical FDTD software, the user can define the graphene material properties by setting up the scattering rate, chemical potential, temperature, and conductivity scaling. The graphene formulation is based on the Falkovsky (mid-IR) material model in which conductivity scaling accounts for the number of graphene layers [65].
4. Results and discussions
We here analyzed the tunability of the proposed metamaterial absorber under a varying Fermi level. Graphene-based metamaterial absorbers are highly tunable within specific frequency ranges. The relationship between the Fermi level and the bias voltage in graphene-based metamaterial absorbers is described as follows:
where $q_{e}$, $V_g$, and $V_f$ are the electric charge, the bias voltage, and the Fermi velocity, respectively. $\varepsilon _{0}$ and $\varepsilon _{r}$ are the permittivity of the free space, and the relative permittivity, respectively. $h$, $\hbar$, and $\mu _{c}$ are the thickness of the substrate, the reduced Planck’s constant, and the chemical potential, respectively [66,67]. The absorption in the graphene-based metamaterial absorbers can be expressed as $A=1-R-T$ where $A$, $R$, and $T$ are the absorption, reflection, and transmission respectively [13,68]. In addition, the reflection and transmission coefficients can be defined as $R=|S_{11}|^2$ and $T=|S_{21}|^2$, respectively. Since the bottom layer of the metamaterial structure is gold, and therefore the electromagnetic waves are totally reflected, the transmission $T$ is $0$, and the absorption could be written as $A=1-R$ which yields $A=1-|S_{11}|^2$.The electric field $|E|$ and magnetic field $|H|$ distributions for both Penrose models 1 and 2 at the highest absorption peak frequencies, recorded via graphene monitor, are depicted in Fig. 3 and Fig. 4, respectively. The electric field distributions of the proposed absorbers as depicted in Fig. 3, reveal that the main multiband absorption is due to the trapped electric field within the gaps of patterned Penrose graphene patches. At low frequencies ($f_1=3.65$ THz and $f_2=6.11$ THz) in both Penrose models 1 and 2, the strong coupling effect happens between the edges of the periodic patterned Penrose graphene patches which can depict the excitation of dipolar Plasmonic resonance by the chosen unit cell. However, at higher frequencies ($f_3=8.57$ THz and $f_4=11.07$ THz) the strong coupling is due to the confinement of the electric field in the middle of the Penrose structure. We can observe that the confinement of the fields in Penrose model 2, at higher frequencies, is higher than in Penrose model 1. This happens because, in model 2, the middle hexagon is made of graphene, whereas in model 1, the middle of the structure is empty. These characteristics of the proposed absorber show that the main contributions to multiband resonance achieved for the structure under study come from the coupling effect and confinement of the electric field at the edges of the periodic structure and also within the middle of the structure. Further discussions on the absorption mechanism in graphene-based metamaterial absorbers can be found in [13,15,68–70].
Fig. 3. Electric field $|E|$ distribution for Penrose model 1 (top row) and Penrose model 2 (bottom row) at the highest absorption peak frequencies.
Fig. 4. Magnetic field $|H|$ distribution for Penrose model 1 (top row) and Penrose model 2 (bottom row) at the highest absorption peak frequencies.
In order to measure the tunability of the proposed structure, we first conducted a sweeping analysis to observe the effect of varying the chemical potential (indicated as $\xi$) of graphene. For this purpose, we considered a two-layer thick graphene for the Penrose models 1 and 2 (denoted in Figures by N=2). The substrate refractive index was kept fixed at 3.4, and chemical potential varied from 0.1 to 1 eV. In Figs. 5(a) and 5(b), we illustrate the absorption intensity profiles for Penrose models 1 and 2 under the aforementioned settings within the frequency range of 0.2-20 THz. Our analysis suggests that the change in the chemical potential of graphene results in a higher enhancement in the absorption intensity of the proposed metamaterial absorber with Penrose model 2. In order to depict this observation clearly, in Figs. 5(c) and 5(d), for both Models, we have plotted the results for chemical potentials of 0.1 eV, 0.6 eV, and 1 eV, respectively.
Fig. 5. Absorption intensity as a function of frequency and varying graphene’s chemical potential $\xi$ for (a) Penrose model 1 and (b) Penrose model 2. Absorption versus frequency for chemical potentials of 1 eV, 0.6 eV, and 0.1 eV for (c) Penrose model 1 and (d) Penrose model 2.
The absorption intensity in Penrose model 2 reaches 0.9 at 6.11 THz and 0.99 at 8.58 THz (Fig. 5(d)), whereas model 1 shows an absorption intensity of 0.62 at 6.11 THz and 0.71 at 8.57 THz (Fig. 5(c)), which are its two highest absorption peaks. The figures show that as we increase the chemical potential, the absorption intensity increases in both models. We further observe that Penrose model 2 achieves a higher absorption intensity in comparison to Penrose model 1, which may be associated with the geometric specifications of Penrose model 2. Compared with Penrose model 1, the additional graphene-made central polygon could contribute to the increased graphene-based absorption enhancement in model 2. Furthermore, we here present the analyses results for the relative absorption bandwidth ($\beta _{w}$), which is used to estimate the modulation degree of the metamaterial absorber and is defined as the ratio of the bandwidth to the central frequency and is given in Eq. (1):
if the relative absorption bandwidth, $\beta _{w}<1\%$, it is assumed that the absorption bandwidth is narrowband, and for $1\%<\beta _{w}<25\%$, the absorption bandwidth is wideband, and if $\beta _{w}>25\%$, the absorption bandwidth is said to be ultra-wideband [6,71]. In Table 1, we illustrate the change in the relative absorption bandwidth based on the change in the Fermi level of graphene in Penrose model 2. As the Fermi level is changed from 0.1 to 1 eV, both the bandwidth $A_B$ and relative absorption bandwidth $\beta _{w}$ increase gradually from 0.48 to 0.82 and 5.2% to 9.4%, respectively. Based on the above definition, Penrose model 2 has wideband absorption bandwidth. In addition, the quality factor, which is defined as the ratio of the central frequency $f_c$ to bandwidth $A_B$, which is inversely proportional to $\beta _{w}$, decreases as the Fermi level increases from 0.1 to 1 eV. In Fig. 6, the absorption profile under a varying Fermi level between 0.1 and 1 eV for the frequency range of 0.2-20 THz for the Penrose model 2 is depicted. Next, we analyzed the impact of the thickness of graphene layers (denoted by conductivity scaling, N) on the absorption profile of the suggested structures. We analyzed the absorption intensity while the conductivity scaling varied between 1 and 10. The results are illustrated in Figs. 7(a) and 7(b). In addition, in order to further elucidate the results, we plotted the conductivity scaling of 1, 2, and 5 for both models in Figs. 7(c) and 7(d). In this case, Penrose model 2 shows more sensitivity to the change of thickness of graphene layers. As the graphene layer thickness increases, the absorption intensity also increases. In model 2, for the case of conductivity scaling of 5 (N=5), three peaks out of the eight reach above 90% absorption with 95% at 6.11 THz, 92% at 8.53 THz, and 99% at 11.07 THz. However, in Penrose model 1, only at 6.11 THz, the absorption peak is 93%, and the rest of the peaks reach absorption intensities under 90%. In both models, we observe that the enhancement of the absorption profiles due to an increase in the thickness of graphene affects the absorption profile for frequencies above 5 THz. For those below 5 THz (i.e., 0.2-5 THz), for instance, at 1.19 THz and 3.65 THz, the conductivity scaling of 2 (N=2) shows a higher absorption intensity than N=5.Fig. 7. Absorption intensity as a function of frequency and varying graphene’s conductivity scaling N for (a) Penrose model 1 and (b) Penrose model 2. Absorption versus frequency for conductivity scaling of 1, 2, and 5 for (c) Penrose model 1 and (d) Penrose model 2.
Table 1. Absorption range, central frequency, relative absorption bandwidth, and quality factor for different Fermi levels.
Further, we investigated the effect of the metamaterial dielectric substrate’s refractive index on the proposed absorbers’ absorption profiles. To this end, we performed a sweeping analysis of refractive indices within the 1.5-4 range. Next, the conductivity scaling is kept at N=2 and the chemical potential is $\xi$=0.6 eV for both Penrose models 1 and 2. In Figs. 8(a) and 8(b), we illustrate the absorption intensity as a function of frequency and refractive index. For this analysis, we ran a sweeping analysis for 200 points within the 1.5-4 range of interest. In Figs. 8(c) and 8(d), we present the 2D plots of our analysis in which the absorption profiles for both models are depicted versus frequency for refractive indices of 1.5, 2.5, and 3.4.
Fig. 8. Absorption intensity as a function of frequency and varying substrate’s refractive index n, for (a) Penrose model 1 and (b) Penrose model 2. Absorption versus frequency for substrate refractive indices of 1.5, 2.5, and 3.4 for (c) Penrose model 1 and (d) Penrose model 2.
The results show that as we increase the refractive index from 1.5 to 4, we start to see additional spectral peaks in the absorption profiles of both models. In addition, the increase in the refractive index increases the absorption intensity in both models. However, this enhancement is much higher in Penrose model 2 when compared to model 1. Since Penrose model 2 incorporates a higher graphene-based surface area, leading to more plasmon-enhanced resonances, we can observe higher enhancement rates in the absorption intensity of Penrose model 2 compared with model 1. Further, to investigate the impact of polarization (i.e., TE or TM) on the field profiles in the proposed metamaterial absorbers, we illustrate the absorption profiles for Penrose models 1 and 2 when TE and TM polarizations were applied. In Fig. 9, we illustrate the absorption intensity profiles when the chemical potential is varied between 0.1 and 1 eV for both models and under both polarizations. In these analyses, we kept the thickness of the graphene as N=2 layers and the substrate’s refractive index as n=3.4. Figures 9(a) and 9(c) show the results for Penrose model 1 under TE and TM polarizations, respectively. Similarly, Figs. 9(b) and 9(d) present the results for Penrose model 2 under the TE and TM polarizations, respectively. For the sake of clarification, we also illustrate the 2D plots for these analyses in Fig. 8. We can observe that in both Penrose models 1 and 2 under TE and TM polarizations, an increase in the chemical potential results in an increase in absorption. Model 1 shows lower absorption intensity under both TE and TM polarizations, as seen in Figs. 10(a) and 10(c). A comparison between Figs. 10(b) and 10(d) shows that in model 2, when the chemical potential is 0.6 eV, TE polarization achieves a higher absorption intensity. It can be observed that at 3.65 THz, 6.11 THz, and 8.61 THz, where absorption is higher than 70%, absorption intensity reaches 71%, 87%, and 73%, respectively for TM mode. In the case of TE mode, the absorption intensity reaches 82%, 90%, and 72%, respectively. The results show that the difference between TE and TM polarization is not that significant, with only slightly higher absorption intensities for TE mode, which is why we chose to work with TE mode throughout this work. We may still say Penrose model 2 is more sensitive to polarization type than model 1.
Fig. 9. Comparison of absorption intensity as a function of frequency and varying graphene’s chemical potential $\xi$, for (a) TE mode in Penrose model 1, (b) TE mode in Penrose model 2, (c) TM mode in Penrose model 1, and (d) TM mode in Penrose model 2.
Fig. 10. Comparison of absorption versus frequency for graphene’s chemical potential $\xi$ at 1 eV, 0.6 eV, and 0.1 eV, for (a) TE mode in Penrose model 1, (b) TE mode in Penrose model 2, (c) TM mode in Penrose model 1, and (d) TM mode in Penrose model 2.
5. S-parameter analysis
In the following section, we present the results for S-parameter [72] calculations and the effective metamaterial parameters, including effective permittivity $\varepsilon _{eff}$, effective permeability $\mu _{eff}$, effective impedance $Z_{eff}$, and effective refractive index $n_{eff}$. The S-parameter $S_{11}$ is the complex reflection and $S_{21}$ stands for transmission coefficient. Equations (2)–(4) provide the formulations of these effective parameters.
Fig. 12. Effective parameters analyses for Penrose models 1 and 2 (a) effective refractive index $n_{eff}$, (b) effective impedance $z_{eff}$, (c) effective permittivity $\varepsilon _{eff}$, and (d) effective permeability $\mu _{eff}$.
Table 2. Summary of some of the most recent works on graphene-enhanced metamaterial absorbers
6. Summary and conclusions
In this work, we proposed two Penrose tiling-inspired metamaterial absorbers based on a dual-layer graphene structure within the 0.2-20 THz range. These metamaterial absorbers can be tuned based on the Fermi level of graphene, the thickness of the graphene, polarization, relative absorption bandwidth, and the refractive index of the substrate. We demonstrated that Penrose model 2 outperformed Penrose model 1 in all of our analyses by achieving higher absorption profiles and reaching a perfect absorption of 99.99% at 8.58 THz. In addition, our results show that as graphene’s Fermi level increases from 0.1 to 1 eV, the absorption bandwidth increases from 0.45 to 0.82 THz in Penrose model 2. Furthermore, the same model’s relative absorption bandwidth increases from 5.2% to 9.4%. The quality factor, however, decreases as the Fermi level increases. In order to analyze the behavior of the proposed structures within the visible and near-infrared spectrum (0.3 µm −1.1 µm), we also performed the S-parameter analysis for the proposed metamaterial absorbers. We found out that within that frequency range, the two proposed structures perform identically; therefore, the design parameters show no significant role within that spectral range. In contrast, these structures are highly tunable and show distinct design-based enhancements as we move to the 0.2-20 THz region. These highly tunable metamaterial absorbers, which enhance light-matter interactions through geometric and material selections, could find potential applications in infrared absorbers, THz sensors, and modulators.
Acknowledgments
The authors would like to express their gratitude to Prof. Mathieu Francoeur for the valuable feedback on the manuscript’s findings.
Disclosures
The authors declare no conflicts of interest.
Data Availability
The data supporting this study’s findings are available from the corresponding author upon reasonable request.
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