In this section, we discuss the relationship of wavelength-dependent absorption of the proposed absorber. Using (3), Figure 2 (a) shows the absorption results of the proposed MXene fractal-shaped absorber when considering TE/TM mode of excitation. Whereas, using (4), temperature dependent photothermal efficiency is calculated and presented in the part (b) of Figure. 2. Here, we are representing MXene, having a thickness of 40 nm described in ref. [54]. For the absorption and photothermal conversion analysis, the operating wavelength is considered from 750 to 3300 nm. It is clearly observed that the aggregative absorption rate remains above 90% in the wide spectrum of the infrared regime of the operating wavelength. The given spectra cover the near-infrared, short-infrared and some portion of the far-infrared regime of the electromagnetic spectra. Therefore, the proposed absorber is used for several applications – such as, NIR absorbers are useful for photovoltaic solar cell, photothermal therapy to kill cancer cells, infrared imaging and infrared sensors for night vision. Whereas, short-infrared absorber is useful in semiconductor industry for inspection and detection of defects, medical imaging, and security and surveillance. Moreover, photothermal conversion efficiency is calculated for different operating temperature ranging from 500 K to 1300 K within the 750-3300 nm operating window. For \(\:{\eta\:}_{avg}\) calculation, we have set the parameters as; C = 1000, T = 300 K to 700 K, Tambient = 273 K, Is = 1000 W. m-2, and Aavg is the aggregative absorption exists in the operating window. From the bar plot, it can be seen that photothermal efficiency value remain above 90% for the operating temperature of 500 K and 700 K and remains 85% at 1100 K due to high absorption characteristics of the proposed device. Hence the proposed device shows its potential for the photothermal-based applications under the high temperature environment.
To better understand the absorption mechanism of the proposed FSWMA, the effective permittivity, permeability, impedance and refractive index of the absorber were analyzed using the amplitudes and phases of the S-parameters for the normal incidence of the light [46]. The impedance of the absorber is an important parameter to evaluate the absorption feature of the proposed WMA absorber and can be defined as \(\:Z=\sqrt{{\mu\:}/\epsilon\:}\). Notably, at resonance, the impedance of the absorber matches with the free-space impedance and unity absorption is attained for the perfect matching condition. The impedance, refractive index, effective permittivity, and permeability values of the material used in the designed absorber are extracted by using [46].
$$\:Z=\:\sqrt{\frac{{\left(1+{S}_{11}\right)}^{2}-{S}_{21}^{2}}{{\left(1-{S}_{11}\right)}^{2}-{S}_{21}^{2}}}$$
4
$$\:n=\frac{-i{ln}\left({e}^{i{k}_{0}d}\right)}{{k}_{0}d}$$
5
where k0 and d represent the wavenumber and thickness of the absorber, respectively. In Eq. (5), \(\:{\varvec{e}}^{\varvec{i}{\varvec{k}}_{0}\varvec{d}}=\varvec{X}\pm\:\varvec{i}\sqrt{1-{\varvec{X}}^{2}}\) where \(\:\varvec{X}=1/2{\varvec{S}}_{21}\left(1-{{\varvec{S}}_{11}}^{2}+{{\varvec{S}}_{21}}^{2}\right)\). The remaining parameters, effective permittivity and effective permeability are calculated as
$$\:{\varvec{\epsilon\:}}_{\varvec{r}}=\frac{\varvec{n}}{\varvec{Z}}$$
6
$$\:{\varvec{\mu\:}}_{\varvec{r}}=\varvec{n}\varvec{Z}$$
7
Figure 3 shows the extracted parameters of the proposed FSWMA. To understand the absorption mechanism, we present the analysis related to the impedance of the proposed absorber for the normal incidence of light. Figure 3(a) show the normalized impedance of the absorber. It is noticed at 1500 nm that both the real part of the normalized impedance is unity and imaginary part of the normalized impedance is zero which corresponds to the perfect. However, the impedance fluctuates above and below the unity for the remaining operating regime, as well as the imaginary part of impendence swings above and below the unity. The unity real impedance and zero imaginary impedance allows the incoming electromagnetic waves to completely penetrate inside the substrate of the proposed FSWMA. Figure 3(b) shows the effective refractive index of the proposed metamaterial absorber. It is observed that the real part of the refractive index remains negative from 1782 to 3300 nm. The negative index medium is used negative reflection/refraction and backward wave propagation. However, the imaginary refractive index remains positive for the entire operating wavelength, as shown by solid red line. Part c and d of Fig. 3 show real and imaginary parts of the permittivity and permeability, respectively. It is noticed that the real part of permittivity and permeability is negative from 1782 to 3330 nm which lead to the negative refraction.
Here, we further discuss the angle-dependent absorption when light falls on the metasurface. Figure 5 shows the absorptivity of the proposed absorber for different polarization of the excited light. It observed that the change in polarization does not affect the absorptivity. Therefore, the proposed absorber shows polarization-independent characteristics due to the symmetric nature of the unit cell structure. As a result, the LSPR remains unaltered due to the change in the polarization of the incidence light. Therefore, the absorptivity remains the same.
Figure 6 shows the absorption results for the obliquity of incidence of light. Here, we take the angle of incidence from 0\(\:^\circ\:\) to 60\(\:^\circ\:\) and a step size of 15\(\:^\circ\:\). Figure 6(a) for the TE mode of excitation, reveals that the angle of excitation has profound effects on the absorption due to the anisotropic nature of the proposed absorber. The corresponding plot shows a blueshift in the absorption bands that exist in the visible and near-infrared regimes of the spectra with the increase in the obliquity of the incidence. Furthermore, considering the absorption band in the near-infrared regime, the increase in the absorptivity value is noticed as the obliquity of incidence increases. However, the absorption band is reduced with the increase of obliquity of incidence. The blue shift in the absorption spectra is observed. On the contrary, for TM mode, the absorptivity reduces with the increase of the incidence angle. However, the blue shift in the absorption spectra is noticed unchanged.
Nanostructure fabrication and design process may reduce performance of the device. Therefore, the devices with high manufacturing tolerance are more desirable. In this section, we present the parametric analysis of the proposed device and vary the different parameters of the unit cell and reveal the performance of the device for ± 10–15% tolerance rate. Figure 7 shows the absorption by varying the parametric values of the absorber under investigation. Figure 7(a) shows the absorptivity for the different thicknesses of the substrate of the absorber while keeping the unit cell period P = 320 nm. The absorptivity is analyzed by varying the thickness of the SiO2 substrate from 272 to 368 nm. Please note that the absorptivity almost remains same by altering the substrate thickness as obvious in Fig. 7(b) shows the absorption by varying the unit cell period from P = 255 to 345 nm. It is noticed that wideband high absorption of above 80% is observed for P = 180 nm from 1050 to 1800 nm. It is noticed that absorptivity is increased with the increase of the period of the unit cell, however, the absorption band is reduced. For P = 220 nm, the high absorption value such as above 80% is attained from 1000 to 1550 nm and is shown by the solid blue line. Figure 7(c) shows the absorption for different thickness of the Ni layer in the absorbing device. It is can be observed from the figure that impact of the thickness of the Ni remains less ineffectual on the absorption. Henceforth, the device has high manufacturing tolerance.
Table 1 presents the comparison summary of the proposed absorber with several state-of-the-art works while considering some performance metrics. The proposed absorber features a simple design and is low-cost compared to reported studies where gold or other expensive metals have been used. The proposed absorber performs wideband operation with significant absorption in the visible and near-infrared regions. The narrowband operation of the proposed absorber may support sensing and wideband absorption characteristics would be beneficial in solar applications.
Table 1
Performance comparison of proposed absorber with reported works
Geometry | Material | Bandwidth Absorption > 90% | Angular Stability Absorption > 50% | Photothermal efficiency \(\:\varvec{\eta\:}\)/ T(K) |
Nano disks [21] | W and SiO2 | 295– 2500nm (2205 nm) | TE (θ = 60°) TM (θ = 60°) | Not discussed |
1D multilayered [26] | W and SiO2 | 400–1750nm (1350 nm) | TE (θ = 60°) TM (θ = 50°) | 91.2% (Tabs = 1273 K) |
Nano-disk [37] | TiO2, SiO2 and TiN | 288.5 -2157.5 nm (1869 nm) | TE (θ = 60°) TM (θ = 60°) | 92.83% (Tabs = 1273 K) |
1D multilayered [55] | W and SiO2 | 300–2000 nm (1700 nm) | --- | 90.02% (Tabs = 373 K) |
Octagonal prism array [56] | W and SiO2 | 373–1656 nm (1283 nm) | TE (θ = 50°) TM (θ = 50°) | 94.72% (Tabs = 1073 K) |
Present Work Fractal shaped | MXene, SiO2, Ag | 436–528 nm (92 nm) 1090–1750 nm (660 nm) | TE (θ = 60°) TM (θ = 50°) | 92.2% at 500 K |