Due to having the ability to support surface plasmons from terahertz to optical regime, graphene has attracted increasing interests for the application of terahertz and optical devices, such as polarizers,^[1] photodetectors,^[2] modulators,^[3–6] and absorbers.^[7–10] Especially, the tunability of its carrier mobility and conductivity, the performance of graphene-based devices can be controlled by chemical doping or electrostatic doping to change the Fermi level without changing the structure of the device. As one of the most important devices, absorbers with different geometries of graphene have been designed including disks and independent ribbon,^[11–14] square patch,^[15] stack,^[16] multi-layered structure,^[17,18] and cross-shaped structure.^[19,20] In order to increase the absorbance bandwidth, the graphene patterns-based absorbers have been proposed.^[21–23] Although the fractional bandwidth of these absorbers based on multi-layered structure can be enhanced, most of the mentioned graphene-based absorbers suffer from some drawbacks, such as the difficulty in fabrication technique, angle dependence, and polarization sensitivity of the incident electromagnetic waves. However, despite recent making some progress in absorbers, these absorbers are designed in the terahertz and optical regions. Furthermore, far-infrared absorbers are rarely reported. As an indispensable frequency band of far-infrared electromagnetic wave, a wide-angle and polarization insensitive broadband far-infrared absorber with single-layer simple patterned graphene still remains worth to be further investigated.

In this study, a periodically semicircle-patterned graphene sheet absorber is proposed to achieve over 90% broadband far-infrared absorption a wide-incident-angle. By introducing gradient width of the semicircle-patterned graphene unit, the continuous plasmon resonances of the far-infrared absorber are directly excited. The bandwidth of 90% absorbance is 4.29 THz from 6.76 THz to 11.05 THz. The absorbance is more than 90% even the incident angles reach 50° for both TE- and TM-polarization modes. The broadband absorption spectra of the far-infrared absorber are insensitive to the polarizations and the incident angles. By tuning the chemical potential via electrostatic doping of the semicircle-patterned graphene sheet, the peak absorption can be continuously controlled from 10% to 100%. This design scheme offers a new perspective on the design of graphene-based tunable far-infrared devices. The proposed absorber has promising applications in far-infrared detecting, sensing, imaging and stealth.

Figure 1 shows the geometry and unit cell of the proposed far-infrared absorber by depositing the periodically planar arrays of semicircle disk-patterned graphene on polymide substrate. A thin ion gel layer is coated on the top of the semicircle disk-patterned graphene sheet and contacted to the top electrode to control the graphene conductivity via DC voltage. The Au ground plane can be used as another electrode. Figure 1(b) shows the unit cell of the far-infrared absorber, which is composed of four semicircle disks patterned graphene with the same radius and a gold ground plate, separated by a lossless polymide layer. p is the periods in x and y directions, h is the thickness of the dielectric spacer, r is the radius of semicircle disk patterned graphene. We assume the lossless dielectric spacer is polyimide with the permittivity of ε = 3.5. The conductivity of the gold ground plate is σ_gold = 4.56× 10⁷ S/m with the thickness of 0.2 μm. The initial values of the structure parameters are set to be p = 4 μm, h = 4.6 μm, t = 10 nm, and r = 1.2 μm. The thickness of the graphene sheet is set to 1 nm for easy simulation.^[24] The semi-circle graphene patterns can be fabricated by large-scale synthesis, transfer and etching techniques, and the electron beam lithography can be employed to produce semi-circle patterns on graphene layer. The chemical vapor deposition method is one of the beneficial methods for fabricating this multilayer structure.

Fig. 1.

	Figure Option ViewDownloadNew Window
	Fig. 1. (a) Schematic diagram of the proposed far-infrared absorber and (b) top-view of the semicircle disk-patterned graphene unit cell.

In our proposed structure, the lateral-view of the semicircle disk-patterned graphene likes a graphene ribbon with a gradient along width direction. When the graphene ribbon has a width (W) and is excited by a normal incident electrical vector, it will produce significant plasmon resonance, which appears in Ref. [21]

In order to study the absorption properties of the periodically semicircle-patterned graphene sheet absorber, we simulate the absorption (A), transmittance (T), reflectance (R) spectra, and the real and imaginary part of the normalized input impedance under normal incidence, when the graphene Fermi energy level is assumed to be E_f = 0.6 eV.

Figure 2(a) illustrates the absorption, transmittance, reflectance spectra in TE- and TM-polarized modes under far-infrared electromagnetic wave normal incidence. As expected, a broadband polarization-insensitive far-infrared absorption is achieved for both TE and TM polarizations. From the absorption, transmittance, reflectance spectra, one can see that the over 90% absorbance bandwidth reaches 4.29 THz from 6.76 THz to 11.05 THz with a central frequency of 8.905 THz for both polarizations. This indicates that the proposed absorber has the characteristics of polarization insensitive, high absorption, and broad absorbance bandwidth. Figure 2(b) displays the real and imaginary parts of the normalized input impedance of the proposed far-infrared absorber. Because maximum absorption of the absorber occurs the impedance matching condition, which is the imaginary part of the normalized input impedance of the proposed far-infrared absorber near zero. To achieve the broad far-infrared absorbance bandwidth, the input impedance imaginary part of the proposed far-infrared absorber should be adjusted to near zero. From Fig. 2(b), we observe that the imaginary part of the proposed far-infrared absorber is near 0 from 6.76 THz to 11.05 THz. It indicates that the effective impedance of the proposed absorber matches with the free space impedance.

Fig. 2.

	Figure Option ViewDownloadNew Window
	Fig. 2. (a) Absorption (A), transmittance (T), and reflectance (R) of the proposed far-infrared absorber with TE and TM modes under normal incidence, respectively, (b) the real and imaginary parts of the normalized input impedance according to the absorption spectra.

To investigate the absorption properties of the proposed far-infrared absorber, we analyze the absorption spectra as a function of the structural parameters h, r, and graphene Fermi levels E_f. As the dielectric layer thickness (h) of the proposed absorber increases from 4.0 μm to 5.0 μm, the absorption bandwidth exhibits slightly redshift while the dielectric layer thickness has little influence absorbance in the absorption frequency bandwidth, as shown in Fig. 3(a). As depicted in Fig. 3(b), the radius (r) of the semicircle disk patterned graphene has a significant influence on the absorbance when the parameter r varies from 1.0 μm to 1.25 μm. In order to obtain a perfect far-infrared absorber with the above 90% absorption and broad bandwidth from 6.76 THz to 11.05 THz, we set the parameter r = 1.2 μm. The absorption spectra of the proposed absorber under different graphene Fermi levels are plotted in Fig. 3(c). Figure 3(c) illustrates that the graphene Fermi level has a great influence on the absorption and bandwidth of the absorber. Furthermore, as the graphene Fermi levels increases from 0.2 eV to 0.7 eV, figure 3(c) clearly shows that the absorbance greatly increases from 49% to 95% and over 90% absorbance bandwidth changes from 0 THz to 4.29 THz. In the present article, we choose the geometric parameters of the proposed absorber as h = 4.6 μm and r = 1.2 μm to obtain a broad absorbance bandwidth and a high absorption.

Fig. 3.

	Figure Option ViewDownloadNew Window
	Fig. 3. Absorption spectra of the proposed far-infrared absorber with different dielectric layer thicknesses h (a), different radii r (b), and the different graphene Fermi levels Ef (c).

Figures 4(a) and 4(b) show the electric field distributions of the patterned graphene for both polarizations at the first resonant frequency of 7.78 THz. At low resonant frequency f = 7.78 THz, the energy is concentrated on the transverse two of semicircular patterned graphene for the TE polarization, while for the TM polarization, the energy is concentrated on the two of semicircular patterned graphene in the longitudinal direction.

Fig. 4.

	Figure Option ViewDownloadNew Window
	Fig. 4. Electric field distribution of (a) TE-mode and (b) TM-mode at f = 7.78 THz, electric field distribution of (c) TE-mode and (d) TM-mode at f = 10.76 THz.

Figures 4(c) and 4(d) show the electric field distributions of the patterned graphene for both polarizations at the second resonant frequency of 10.76 THz. At high resonant frequency f = 10.76 THz, the energy is concentrated on the longitudinal two of semicircular patterned graphene for the TE polarization, while the energy is concentrated on the transverse two of semicircular patterned graphene for the TM polarization. It is clearly observed that the energy is mainly concentrated on the edge of the graphene pattern, which means surface plasmon resonances are strongly bounded to the patterned graphene edges.

Figure 5 gives the absorption spectra of different planar array directions of semicircle disk-patterned graphene and polarization modes.

Fig. 5.

	Figure Option ViewDownloadNew Window
	Fig. 5. Absorption spectra of different planar array directions of semicircle disk-patterned graphene and both polarizations.

Figure 6 displays the simulated power loss density and surface current distributions of the proposed absorber for TE polarization at two resonant frequencies of 7.78 THz and 10.76 THz, where figures 6(a) and 6(b) are the power loss density distributions at 7.78 THz and 10.76 THz, and figures 6(c) and 6(d) are the surface current distributions at 7.78 THz and 10.76 THz, respectively.

Fig. 6.

	Figure Option ViewDownloadNew Window
	Fig. 6. Surface loss density (a) at f = 7.78 THz and (b) f = 10.76 THz, respectively; and surface current (c) at f = 7.78 THz and (d) f = 10.76 THz, respectively.

It can be noted that the proposed far-infrared absorber exhibits tight power loss density and surface current confinement around the semicircle disk-patterned graphene sheet, leading to strong far-infrared electromagnetic wave trapping and absorption. The power loss density and surface current confinement characteristics are consistent with the absorbance spectra depicted in Fig. 2. The stronger the power loss density and surface current confinement is, the higher the absorption ration of the far-infrared absorber becomes. Moreover, most of the power loss density and surface current are confined to the edge of the semicircle disk-patterned graphene due to the localized surface plasmon resonance of the patterned grapheme sheet. Specifically, the extremely confined power loss density and surface current of the TE polarization are distributed between two adjacent unit cells in y direction at low resonant frequency of 7.78 THz and x direction at high resonant frequency 10.76 THz, respectively. The physical mechanism of this phenomenon is that the electric dipole resonances between two adjacent unit cells in y and x directions are excited by the two resonant frequencies of TE polarization incident far-infrared wave, respectively. Table 1 depicts the properties of our proposed absorber and some previously reported graphene absorber. According to Table 1, one sees that the designed structure has relatively good absorption bandwidth.

Table 1.

Table 1.

Table 1. Performance comparison of our proposed absorber with some reported graphene-based absorbers. . Reference Bandwidth > 90%/THz Graphene type Polarization [11] 2.2 multilayer graphene disks and ribbons sensitive [27] 2.8 multiple oval graphene discs insensitive [28] 8.7 graphene pattern and gold pattern insensitive Our results 4.29 graphene semicircle disk insensitive

Table 1. Performance comparison of our proposed absorber with some reported graphene-based absorbers. .

Finally, the absorption behavior dependence on the polarization angle and the incident angle is further studied. Since the semicircle-patterned graphene is axisymmetrical, the polarization sensitivity of the proposed absorber can be eliminated. The dependence of the absorption spectrum on the azimuth at normal incidence is shown in Fig. 7(a). One can see that the far-infrared absorber is polarization insensitive for both TE- and TM-modes with the incident angle ranging from 0° to 360° under normal incidence electromagnetic wave. Figures 7(b) and 7(c) depict the absorption spectra as functions of operating frequency and the oblique incident angle (0°–60°) for TE- and TM-polarized modes, respectively. It can be noted that the far-infrared absorber has stable absorption bandwidth (4.29 THz) under the incident angle changing from 0° to 50° for both TE- and TM-polarizations. Since the absorption characteristics are related to the confined surface plasmon resonance, and the bandwidth of the far-infrared absorber is mainly determined by the semicircle-patterned graphene sheet, and less dependent on the incident angle. It can also be noted that the peak absorbance decreases slightly when the incident angle is near to 50° for both TE- and TM-polarizations at some frequencies in the absorption bandwidth, and the absorbance is still above 90%. Therefore, the broadband absorption of the polarization-insensitive far-infrared absorber remains more than 90% with bandwidth 4.29 THz from 6.76 THz to 11.05 THz for both TE- and TM-polarized modes at oblique incident angle of 0°–50°.

Fig. 7.

	Figure Option ViewDownloadNew Window
	Fig. 7. Absorption spectra under (a) different azimuth angles, (b) TE-polarized mode, (c) TM-polarized mode.

We have presented a tunable polarization-insensitive broadband far-infrared absorber based on four semicircle disk-patterned graphenes. For normal incidence, the bandwidth of 90% absorption of the polarization insensitivity absorber has reached up to 4.29 THz. When the incident angle varies from 0° to 50°, the bandwidth of 90% absorption remains more than 4.29 THz. The bandwidth and absorption can be adjusted flexibly by controlling the chemical potentials of graphene. The proposed absorber has great application prospect in sensing, detection, imaging and optoelectronic devices.