1. Introduction

Similar to an electromagnetic wave absorber working in the microwave band [1,2], THz band [3,4] and visible band [5,6], light absorber working in the infrared band is a kind of device that can be used to absorb infrared electromagnetic wave effectively. They have important application prospects in the aspects of radiation [7,8], sensing [9,10], detecting [11,12], imaging [13,14], filtering [15] and so on.

In the near infrared band (0.7-2.5μm), the metallic grating structures that were isolated by the dielectric layer on the metal substrate [16–19], the groove or cavity-type grating structures that were dug out of the metal material [20], the structures mixed with bar and cavity-type grating [21,22], the structures that were formed by pure metal material [23] and the pyramid structure constituted by stacked metal material and dielectric material [24] were used to construct absorbers.

In the mid infrared band (2.5-25μm), the combined metallic grating structures that were isolated by the dielectric layer on the metal substrate [8, 13, 25–28], and the sawtooth structure formed by stacked metal material and dielectric material [29] were used to construct absorbers.

In the far infrared band (25-500μm), two dimensional grating structure [30], composed of elliptical graphene sheets that were isolated by the dielectric layer on the metal substrate, were used to construct absorbers.

Because metal materials within the absorber may be damaged due to corrosion, and lose the absorption ability generally at high temperature, so it is urgent to find materials with high corrosion resistance and high temperature resistance.

SiC is a kind of important compound semiconductor material, which has the advantages of low density, high mechanical strength, high thermal conductivity, high thermal stability, low thermal expansion coefficient and good chemical inertia and so on. Since the first synthesis of SiC in 1994 [31], wide attention has been aroused in sensor, composite materials and absorption of electromagnetic waves [32].

Using SiC material, B. Neuner III and collaborators have constructed a kind of mid-infrared light absorber, its absorptivity was higher than 20% in the range of 9-15μm and the maximum can be close to 50% [33]. G. C. R. Devarapu and collaborators have designed a kind of one-dimensional photonic crystal using SiC material. The maximum absorptivity can be close to 100% in the range of the absorption spectrum of SiC [34]. The disadvantages of such two kinds of mid-infrared light absorbers are that the bandwidth corresponding to the high absorptivity is narrow. In order to overcome this shortcoming, here a kind of grating-type mid-infrared light absorber is designed using SiC and dielectric material.

The rest of this paper is arranged as follows: in the second section, introduce the structure model and calculation method, in the third section, we present the results and necessary discussion, and come to a conclusion in the fourth section.

2. Structure model and calculation method

The structure model of the mid-infrared light absorber based on the SiC material is shown in Fig. 1. The absorber is a grating structure which is extended along the horizontal direction. The unit is constituted by the metallic silver plate with width $\text{P}$ and the truncated pyramid structure with top width ${\text{W}}_{\text{1}}$ and bottom width ${\text{W}}_{\text{2}}$. The truncated pyramid structure is composed of many composite layers which are formed by the SiC flat plate with thickness ${\text{T}}_{\text{1}}$ and the dielectric flat plate with thickness ${\text{T}}_{\text{2}}$. The total number of the composite layers is expressed by $layer$. The thickness of the silver flat plate is ${\text{T}}_{\text{3}}=1.0\mu m$, it is large enough to block the transmission of light.

 

Fig. 1 Schematic diagram of the mid-infrared light absorber based on SiC material and the computational setting of the FDFD method. Here, $P$is the unit length, $W_{\text{1}}$ is the width of the top layer and $W_{\text{2}}$ is the width of the bottom layer in the composite layer, $T_{\text{1}}$ is the thickness of the SiC and $T_{\text{2}}$ is the thickness of the dielectric in the composite layer, $T_{\text{3}}$ is the thickness of the silver substrate. The shadow areas located on the top and bottom are the perfect matched layer(PML). The reflecting plane, TF/SF plane and transmission plane are marked by the dotted line respectively. The left and right boundaries are the periodic boundary condition (PBC). The breaks on the left and right boundary indicate that there is sufficient space between the TF/SF plane and the upper surface of the top layer in the composite layer.

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The dielectric constant of SiC material is [35]:

The finite-difference frequency-domain (FDFD) method [36] is used to carry out the numerical calculation in this paper. Based on the two-dimensional Yee's grid and the central difference method, Maxwell equations are discreted and a large sparse linear algebraic equation can be obtained:

Here $[A]$ is a coefficient matrix, $[x]$is a column vector associated with field distribution, $[b]$ is a column vector associated with source. Assuming a plane electromagnetic wave with wavelength $\lambda$ incident on the grating-type absorber as shown in Fig. 1 at an angle of $\alpha$ relative to the vertical direction, the field distribution can be obtained by solving the Eq. (3). Then the reflection coefficient $R$ and the transmission coefficient $T$ can be obtained according to the distribution of the energy flow density ($\overrightarrow{S}$) in the reflection plane and the transmission plane. Based on the energy conservation law, the absorptivity of the grating absorber can be obtained by $A=1-R-T$. When using the FDFD method, the grid resolution must be high enough, the PML must be thick enough, and the space regions must be large enough.

In order to validate the FDFD program of our own writing, the absorption spectra for the sawtooth anisotropic metamaterials (AMM) absorber as shown in the Fig. 1 of Ref [29]. is recalculated firstly using the same parameters. In the calculation, the spatial discrete distance is set to be $\Delta x$ = $\Delta y$ = 25nm. The grid scale along the horizontal direction depends on the unit length, for example, it is $121$when $P=3\mu m$. The grid scale along the vertical direction is set to be $6601$, and the layers of the PML are set to be 100. This setting will be used throughout this paper. The calculated results are shown in Fig. 2. One can see that our results are very consistent with the results shown in the Fig. 2(b) of Ref [29]. This fact indicates that our FDFD program is valid.

 

Fig. 2 Recalculated absorption spectra for the sawtooth AMM absorber [29] using our FDFD program. The blue line represents the absorptivity contour with$A=0.9$. Black dots on the map are read from the Fig. 2(b) of Ref [29].

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3. Results and discussion

Based on a large number of numerical calculations, the structure parameters of the absorber as shown in Fig. 1 are optimized. The contour plot of the dependence of the absorptivity on the incident wavelength and the incident angle is shown in Fig. 3. The optimized structural parameters are: $layer=20$, $P=3\mu m$, $W_1=0.8\mu m$, $W_2=2.7\mu m$, $T_1=0.3\mu m$, $T_2=1.2\mu m$ and $T_3=1\mu m$. One can see that, in the range of $10.5$-$12.5\mu m$ and $0$-${80}^{\circ }$, the contour map consists of many absorption bands which are closed together. In the short wavelength region, the absorption bands are slightly curved with the incident angle. In the long wavelength region, the absorption bands are almost irrelevant with the incident angle. The maximal absorptivity in each absorption band is greater than 80%.

 

Fig. 3 The contour plot of the absorptivity with the incident wavelength and incident angle. Here the structure parameters are $layer=20$, $P=3\mu m$, $W_1=0.8\mu m$, $W_2=2.7\mu m$, $T_1=0.3\mu m$, $T_2=1.2\mu m$ and $T_3=1.0\mu m$.

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The absorptivity shown in Fig. 3 can be explained by the material properties of SiC and the field distribution in the structure. Based on the Eq. (1), the dispersion curves of SiC material in mid-infrared band are shown in Fig. 4. In the range of $10.5$-$12.5\mu m$ (shadow area), the real part of the dielectric constant is less than zero, while the imaginary part is larger than zero. These features are very similar to many noble metals, such as Au and Ag, in the visible frequency band.

 

Fig. 4 The dependence of the real part and the imaginary part of the dielectric constant of SiC on the wavelength.

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When the TM wave incident at $\alpha =0^{\circ }$, with the optimized structure parameters, the distributions of the $Hz$ field corresponding to $\lambda =10.50\mu m$, $11.89\mu m$ and $12.50\mu m$ are shown in Figs. 5(a), 5(b) and 5(c) respectively. According to Figs. 4 and 5, we find that there are three kinds of absorption mechanism in action, they are the excitation of surface plasmon and magnetic polariton [37] as well as the loss of materials. In order to verify whether or not magnetic polariton is excitated, the distribution of the $Hz$ field and the corresponding $\overrightarrow{E}$field within the subregion of Fig. 5(c) are plotted in Fig. 6. The subregion is from −1.5$\mu m$ to 1.5$\mu m$ along the x direction and −35.0$\mu m$ to −32.0$\mu m$ along the y direction. From Fig. 6, one can see, in the SiC-dielectric-SiC structure, the electromagnetic field distribution is very consistent with that of the magnetic polariton shown in the Fig. 3(a) of Ref [37]. So we believe that the magnetic polaritons are excitated in our absorber.

 

Fig. 5 The distributions of the $Hz$ field corresponding to the incident TM wave at$\lambda =10.50\mu m$(a), $11.89\mu m$(b) and$12.50\mu m$ (c) with the optimized structure parameters.

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Fig. 6 The distributions of the $Hz$ field and the corresponding $\overrightarrow{E}$field within the subregion of Fig. 5(c). The red arrows on the map indicate $\overrightarrow{E}$field.

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At the wavelength of $10.50\mu m$, as shown in Fig. 4, the real part of the dielectric constant of SiC is a smaller negative value, the imaginary part is a smaller positive value. This means that the metal properties of SiC are weaker, and the material loss is small. Then, electromagnetic wave can travel through the pyramid structure, as shown in Fig. 5(a). However, due to the excitation of surface plasmon and the magnetic polariton, the strength of the field decreases gradually. When electromagnetic wave reaches the bottom metallic silver surface, localized surface plasmons are formed and the energy is further bound on the upper surface of the silver.

When the wavelength increases to $11.89\mu m$, one can see from Fig. 4, due to the growth of the real part of the dielectric constant of SiC in the negative direction, the metal properties of SiC are enhancing. At the same time, with the growth of the imaginary part of the dielectric constant of SiC in the positive direction, the loss of the SiC material is increasing gradually. Moreover, due to the excitation of surface plasmon and the magnetic polariton, as well as the gradual increased losses, electromagnetic waves travel down the pyramid structure with the gradual decay of the field strength, which causes that the electromagnetic wave can hardly reach the upper surface of the bottom metallic silver, as shown in Fig. 5(b).

When the wavelength increases to $12.50\mu m$, one can see from Fig. 4 that, the real part of the relative dielectric constant of SiC has reached to a minimum value −221, and the imaginary part has reached to a maximum value 142, therefore, SiC shows strongest metallic properties and the maximum loss. Thus, as shown in Fig. 5(c), electromagnetic wave cannot penetrate SiC almostly. In addition to the excitation of surface plasmon and the magnetic polariton, as well as the strongest losses, the electromagnetic wave is strongly absorbed.

Assuming the TM wave incident at $\alpha =0^{\circ }$, here we study the dependence of the absorptivity on the geometric structure parameters. When the number of the composite layers, the period of the grating, the top width and the bottom width of the truncated pyramid structure, the thickness of the SiC layer and the thickness of the dielectric layer changed separately, while keeping the other five optimized parameters unchanged, the dependence of the absorptivity on the incidence wavelength with these parameters are shown in Fig. 7.

 

Fig. 7 The dependence of absorptivity on the incidence wavelength, when the number of composite layers (a), the period of the grating (b), the top width (c) and the bottom width (d) of the truncated pyramid structure, the thickness of the SiC layer (e) and the dielectric layer (f) change separately, while keep the other five parameters unchanged. Here we assume that the TM wave incident at $\alpha =0^{\circ }$.

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Comparing the plots in Fig. 7, we can see that the number of composite layers has a relatively great influence on the absorptivity. Figure 7(a) shows that the absorptivity will significantly decrease when the number of composite layers is small. When this number reaches to 20, the absorption tends to be stably fluctuating in the range of 0.8 to 1. Considering the complexity of the fabrication, the absorber studied in this paper contains only 20 composite layers.

The period of the grating has a great influence on the absorptivity. From Fig. 7(b), one can see, when the period is reduced to $P=1.5\mu m$ by 50% relative to the optimal value$P=3\mu m$, the absorption curve will be decreased in the wavelength range of $11.0$-$11.5\mu m$ and form a valley. When the period is increased 50% relative to the optimal value$P=3\mu m$, reaching to $P=4.5\mu m$, the absorptivity curve will be decreased too in several bands and form several valleys.

The width of the top layer of the truncated pyramid structure has a obvious influence on the absorptivity. It is finding that this width is not as smaller as better. One can see from Fig. 7(c), although the absorptivity will be improved in the wavelength range of $11.5$-$12.5\mu m$ with the top width $W_1=0.25\mu m$, but the width of the valley in the wavelength range of $11.0$-$11.5\mu m$ is significantly widened.

The bottom width of the truncated pyramid structure also has a great influence on the absorptivity, and this width cannot be too narrow. One can see from Fig. 7(d), wth the bottom width $W_2=2.8\mu m$ which is approached to the period of the grating$P=3\mu m$, the changes of the absorptivity curve are very small with respect to the optimized absorption curve. When the bottom width is reduced to $W_2=2.4\mu m$, it will form several valleys at $10.8\mu m$, $11.2\mu m$ and $12.1\mu m$.

The thickness of the SiC layer has a more influence on the absorptivity than the thickness of the dielectric layer, and cannot be too thin. One can see from Fig. 7(e), with the thickness$T_1=0.2\mu m$, new valley on the absorptivity curve will appear at $11.7\mu m$ and $12.2\mu m$. When the thickness of the SiC layer is further decreased to $T_1=0.15\mu m$, although the absorptivity improved in the range of $10.5$-$11.4\mu m$, it is significantly decreased in the range of $11.4$-$12.2\mu m$.

While the thickness of the dielectric layer has a little influence on the absorptivity. From Fig. 7(f), one can see that, respect to the optimized value $T_2=1.2\mu m$, when the thickness decreases $0.1\mu m$ or increases $0.1\mu m$, in the interested wavelength range, although the position of the peak and valley on the absorptivity curve vary, the magnitude of change of the absorptivity is small.

These geometry effects on the absorptance can be explained by the field distribution in the structure. In order to avoid a long and massive statement, here we only take three points on the Fig. 7(c) as examples to explain the underlying absorption mechanism.

Keeping the other five optimized parameters unchanged, with $\lambda =12.24\mu m$and $\alpha =0^{\circ }$, the distribution of the $Hz$ field corresponding to $W_1=0.25\mu m$(red dot on Fig. 7(c)), $0.80\mu m$ (green dot on Fig. 7(c)) and $1.00\mu m$ (blue dot on Fig. 7(c)) are shown in Figs. 8(a), 8(b), and 8(c) respectively. From Fig. 8, one can see that, relative to the optimized value $0.80\mu m$, when $W_1=0.25\mu m$, not only the localized regions are less, but also the field intensity in these regions is weaker, so the total absorptivity became small. When $W_1=1.00\mu m$, although the field intensity in the upper region is stronger, the field intensity in lower region is weaker, so the total absorptivity became small too.

 

Fig. 8 The distributions of the $Hz$ field corresponding to the top layer width $W_1=0.25\mu m$(a), $0.80\mu m$ (b) and $1.00\mu m$ (c) of the truncated pyramid structure while keeping the other five optimized parameters unchanged.

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4. Conclusions

Utilizing SiC material, a mid-infrared light absorber with a grating-type structure is designed. Its absorption properties are studied using FDFD method. Optimized structural parameters are: $layer=20$, $P=3\mu m$, $W_1=0.8\mu m$, $W_2=2.7\mu m$, $T_1=0.3\mu m$, $T_2=1.2\mu m$and $T_3=1\mu m$. With these parameters, the absorptivity of higher than 80% is obtained in the rang of $10.5$-$12.5\mu m$ and $0$-${80}^{\circ }$. By analyzing the field distribution, we find that the absorption mechanisms are the excitation of surface plasmon and magnetic polariton as well as loss of materials. The number of the composite layers has a greatest influence on the absorption properties, the period of the grating, the widths of the top and bottom layer, the thickness of the SiC layer has more influence on the absorption properties, while the thickness of the dielectric layer has less influence on the absorption properties. The underlying mechanism of the geometry effects on the absorptance is explained by three examples. This work is expected to guide the design, fabrication and application of the mid-infrared grating-type light absorber.