A graphene-based tunable ultra-narrowband mid-infrared TE-polarization absorber is proposed. The simulation results show that, the absorption peak can be tuned from 5.43896µm to 5.41418µm, by tuning the Fermi level of graphene from 0.2eV to 1.0eV. The simulation results also show that the absorption bandwidth is less than 1.0nm and the absorption rate is more than 0.99 for TE-polarization (electric field is parallel to grating grooves) in the tuning wavelength range. The ultra-narrowband absorption mechanism is originated from the low power loss in the guided-mode resonance. The tuning function is mainly attributed to the change of the real part of the graphene’s permittivity. This tunable ultra-narrowband mid-infrared absorber has potential applications in the tunable filtering and tunable coherent emission of thermal source.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Perfect absorbers with engineered nanostructures have attracted a great deal of research interest due to their extensive applications in sensing , wavelength selective thermal emission , solar energy , cloaking  and photo-detection . A variety of absorbers have been proposed and demonstrated at different frequencies including microwave [6,7], terahertz [8,9], infrared [10,11], and visible regions [12–14]. However, the fixed absorption peaks of these absorbers will make their function invalid when the application requirements of absorption peaks change. In addition, fabrication of a new absorber to achieve another resonant absorption peak is not a cost-effective option. Thus, to conveniently meet the dynamic demand of different absorption peaks, it is very necessary to develop tunable absorbers.
Graphene, which consists of a single atomic layer of carbon with a 2-dimensional hexagonal lattice structure, has attracted intense scientific interests due to its unprecedented properties such as high electron mobility, high optical transparency, flexibility, and tunable conductivity [15–20], One of the most interesting properties of graphene is that the conductivity can be tuned by applying the bias voltage upon graphene. Such characteristic of the voltage-control conductivity has enabled graphene act as a core component in designing various devices such as modulators [21,22], switches [23,24], tunable filters [25,26], and tunable absorbers [27,28]. To date, many graphene-based tunable absorbers have been presented, their operating bandwidths range from a single narrow-band to multiband and broadband [29–31]. However, a tunable absorber with absorption bandwidth less than 1.0nm has not been reported. On the other hand, it is noticed that some efforts have been made to achieve the ultra-narrowband absorbers because they can be applied as high temporal coherent thermal resources or high figure-of-merit sensors [32–35]. Therefore, considering the advantages of graphene and the ultra-narrowband absorbers, a graphene-based tunable ultra-narrowband absorber will be very desirable.
In this paper, we report a graphene-based tunable ultra-narrowband mid-infrared TE-polarization absorber. The tunable wavelength range of absorption peaks can reach 24.8nm by increasing the graphene’s Fermi energy from 0.2eV to 1.0eV. In addition, the full width half maximums (FWHMs) under different are less than 1.0nm. This tunable ultra-narrowband mid-infrared absorber has potential applications in the tunable filtering and tunable coherent emission of thermal source.
Figure 1 shows the proposed structure. The top layer is a dielectric grating which can be described by period , ridge width , and height . The grating filled factor can be defined as . Under the dielectric grating, there are two dielectric film layers separated by graphene. The thicknesses of these dielectric film layers are and . The substrate material is metal to efficiently block light from transmission. A TE-polarization plane electromagnetic wave is incident upon the proposed structure at an angle of (). The absorption characteristics of this proposed structure are evaluated with the rigorous coupled-wave analysis (RCWA) , and the absorption can be attained with where and are the reflection and transmission, respectively. In addition, the metallic substrate is much larger than the penetration depth of incident electromagnetic waves so that can be treated as zero. Thus, the absorption can be simplified with . Calcium fluoride is used as dielectric material in the proposed structure, and the refractive index of calcium fluoride in the mid-infrared regime is described with formula :
The surface conductivity of graphene permittivity can be can be derived from the Kubo formula  and can be given by:
3. Results and discussion
Figure 2 shows the absorption spectra with different at normal incidence, and the optimized structure parameters are , , , , and . As illustrated in Fig. 2(a), by increasing the graphene’s Fermi level from 0.2eV to 1.0eV, the absorption peaks blue-shift from to , and the tunable range of absorption peaks is 24.8nm. In addition, under different , the absorption rate is still larger than 0.99. From Figs. 2(b)-2(d), the full width half maximums (FWHMs) under the different are less than 1.0nm which is at least two orders lower than those of mid-infrared absorbers reported in [39–42]. The results indicate that the absorption peaks of the proposed structure can be tuned with ultra-narrow bandwidth by adjusting the graphene’s Fermi level. Such tunable ultra-narrowband absorber can be used as a filter or coherent emission resource.
To get the ultra-narrowband absorption mechanism, Fig. 3 shows the electric field within two unit cells at the absorption peak (). The parameters used are the same with those in Fig. 2(b). From Fig. 3 we can see an obvious standing wave profile in X direction which indicates the guided-mode resonance in the dielectric material layers and graphene. In addition, as shown in Fig. 3, the electric field is mainly distributed in the lossless dielectric material so that the low power loss will occur in the resonance . Furthermore, such low power loss, which results in a high quality factor, eventually produces an ultra-narrow bandwidth in our absorber. Therefore, we can ascribe the ultra-narrowband absorption of our absorber to the low power loss in the guided-mode resonance.
To reveal the tuning mechanism of the ultra-narrowband absorber, we plot the real and imaginary parts of graphene permittivity as a function of wavelength in Fig. 4. As illustrated in Fig. 4, the real and imaginary parts of graphene permittivity slightly change in the wavelength range from and under the same . In contrast, the real and imaginary parts obviously jump when the graphene’s Fermi level varies from 0.2eV to 1.0eV under the same wavelength. Furthermore, from Fig. 4, we can see the change of the real part under different Fermi levels is much larger than that of the imaginary part. Thus, the spectral shift may be mainly originated from the change of real part of graphene permittivity. According to the perturbation theory of Fabry-Perot cavity in Z direction, the spectral shift can be expressed withFig. 2.
To further verify the contribution of the real and imaginary parts of graphene permittivity, we calculate the absorption spectra with some special graphene permittivity. According to Eq. (3), the permittivities at with and are and , respectively. To clearly evaluate the independent contribution of the real and imaginary parts, the real and imaginary parts of graphene permittivity with are modified separately. All parameters employed in the following part of this paper are the same with those used in Fig. 2(b) if they are not specified. Figure 5 shows the absorption spectra with the special graphene permittivity. The blue solid curve in Fig. 5 is the absorption spectrum with whose real part is equal to that with . In addition, the black solid curve in Fig. 5 is the absorption spectrum with whose imaginary part is equal to that with . To compare the spectral shift, the absorption spectrum with also shows in Fig. 5 with the red dashed curve. As shown in Fig. 5, the spectral shift of the blue solid curves is 25.0nm. However, the black solid curve and red dashed curve are almost overlapping so that the spectral shift of the black solid curve is almost negligible. To directly show the contribution of the real part of permittivity, we plot the absorption spectrum shown as green dashed curve with whose imaginary part is 0. The green dashed curve and blue solid curve are also almost overlapping. Thus, Fig. 5 shows that the spectral shift originated from the change of real part of graphene permittivity is much larger than that originated from the change of imaginary part. We can conclude that the spectral shift is mainly attributed to the change of the real part of the graphene’s permittivity.
In our graphene-based tunable ultra-narrowband mid-infrared absorber, both gold and graphene have imaginary parts of permittivity which can result in absorption. In order to clarify the contribution of gold and graphene on the perfect absorption in our absorber, the power loss of gold and graphene will be evaluated. The power loss for a nonmagnetic dispersive medium can be described by43]. We calculate the power loss of gold and graphene at the absorption peak which is shown in Fig. 2(b) with . We define and as the electric field in gold and graphene, respectively. Based on the data of extracted from Fig. 3, we can achieveEq. (6), we can see that the power loss of gold is about 4 times as large as that of graphene. We also calculate the power loss of gold and graphene at the absorption peak which is shown in Fig. 2(d) with . By employing the same method, we can get . From the above discussion, we can see that the contribution of gold and graphene on perfect absorption is in the same order of magnitude in our absorber when the graphene’s Fermi level is tuned from 0.2eV to 1.0eV.
Next, we investigate the influence of the geometric parameters on the absorption characteristic. In addition, without loss of generality, the graphene's Fermi energy is set as 0.2eV. We simulate the absorption spectra with different filled factors, grating heights, and dielectric layer thicknesses in Fig. 6. As shown in Fig. 6(a), the absorption will decrease if the filled factor deviates from 0.5, but it is still larger than 0.9 in the filled factor range from 0.3 to 0.7. As seen in Fig. 6(b), the absorption peak will red-shift with the increasing grating height. The absorption rate is above 0.98 in the grating height range from and . Figure 6(c) shows that the absorption peaks will red-shift if the dielectric layer thickness increases. The absorption rate is above 0.9 when range from and . In addition, we can see the similar results in Fig. 6(d) with those in Fig. 6(c).
To show the influence of refractive indices of the dielectric material to our absorber, the absorption spectra with different refractive indices are shown in Fig. 7. The refractive index of dielectric material is defined with . Other parameters employed in the simulation process are the same with those used in Fig. 2(b). As seen in Fig. 7, the absorption peaks with near-perfect absorption will red-shift if increases. The red-shift phenomenon in Fig. 7 can be explained with the guided-mode resonance mechanism shown in Fig. 3. As the refractive index of the dielectric material increases, the resonance peaks shift to longer wavelengths to support the guided mode in the dielectric material and graphene. The absorption peaks of TE1 mode at and are also shown in Fig. 7. The mode profiles of TE0 and TE1 mode with are inserted in Fig. 7. In addition, Fig. 7 indicates that the absorption peaks can be shifted by replacing the dielectric material.
To investigate how the absorption is affected by the incident angles, the absorption spectra with different incident angles are simulated in Fig. 8. As shown in Fig. 8, the absorption peaks red-shift with the increasing incident angles. In addition, the absorption peaks of TE1 and TE2 modes can be seen when increases in the interesting wavelength range. The mode profiles of different absorption peaks with are inserted in Fig. 8.
We notice that the absorption bandwidth is less than 1.0nm which indicates our absorber has high temporal coherence if it is applied as a thermal emitter resource . However, the spatial coherence is another important feature to a thermal emitter resource. To investigate the spatial coherence, we plot the angle-resolved absorption at the incident wavelength of in Fig. 9(a). Figure 9(a) shows that the absorption at is larger than 0.99. The angular width of FWHM with is used to describe the angle-resolved absorption characteristics. To clearly show the angle-resolved absorption characteristics, Fig. 9(b) is plotted to show the zoom-in pattern around . In Fig. 9(b), at is less than which means that our absorber is a highly directional thermal emitter. The corresponding spatial coherence length is as large as which is much larger than the corresponding wavelength. Thus, our absorber has both high temporal coherence and high spatial coherence.
We report a graphene-based tunable ultra-narrowband mid-infrared TE-polarization absorber in this paper. The absorption peak can be tuned by tuning the graphene Fermi level. Furthermore, the absorption bandwidth is less than 1.0nm and the absorption rate is more than 0.99 in the tuning wavelength range. The ultra-narrowband absorption mechanism is originated from the low power loss in the guided-mode resonance. The tuning function is mainly attributed to the change of the real part of the graphene’s permittivity. This tunable ultra-narrowband mid-infrared absorber has potential applications in the tunable filtering and tunable coherent emission of thermal source.
Anhui Provincial Natural Science Foundation (No. 1508085MF136).
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