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Abstract
In this paper, we propose a tunable and polarization-independent absorber based on a bulk Dirac semimetal (BDS) metasurface at terahertz frequencies with a high absorption. The numerical results show that the full width at half maximum is ${\bigtriangleup} f = 9.1\times 10^{-2}$ THz. The absorption is maintained at above 95% when the Fermi level is in the range from 65 meV to 85 meV and the resonance frequency is in the range from 2.46 THz to 3.16 THz. For both polarizations, the absorption peak is maintained at above 80% for incident angles up to $60^{\circ }$. Based on our method, various BDS-based tunable absorbers can be designed for terahertz, infrared, and visible frequencies. This significantly enhances the usefulness of these absorbers in a wide range of applications such as sensing systems and optoelectronic devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials are artificial electromagnetic materials that are composed of periodic unit cells that possess exceptional physical properties not found in traditional materials. A variety of metasurface devices have been designed including the first quarter-wave plate [1,2], polarization converters [3,4], sensors [5–7], lenses [8,9], and absorbers [10–12]. Many of them have been widely used in practical applications such as antenna technology [13] and optoelectronic device [14]. A perfect absorber is obtained by minimizing the reflection and eliminating transmission. In 2008, Landy et al. reported a perfect absorber based on metamaterials [15]. Since then, metamaterial-based absorbers have been widely studied and various structures have been proposed to improve the performance characteristics of the metamaterial-based absorbers. The recent advances in metamaterial-based absorbers such as high absorption efficiency, wide angle incidence [16], single frequency to multi-frequency [17], and multi-frequency to wide-band [18], have improved the prospects of these types of absorbers to be an important component in radio frequency identification technology, stealth technology, electromagnetic protection, electromagnetic compatibility and shielding. However, these absorbers have drawbacks such as instability, and quality. This limits their usefulness in electromagnetic radiation protection and aircraft stealth where long-term stability and high absorption are necessary. In addition, the electromagnetic properties of metasurfaces-based absorbers using traditional materials mainly depend on the shape of the artificially designed structural unit and its physical size, which make it very difficult to design and limit its development.
In the past few years, two-dimensional (2D) materials have been used to enhance the stability and absorption of the absorber. Graphene is one of the most popular 2D materials which has shown excellent prospect in metasurface applications. The optical response of graphene is characterized by its surface conductivity $\sigma$ that is significantly related to its $E_F$, which can be dynamically tuned by applying a bias voltage [19–25]. In 2017, Da et al. [26] proposed the design of a tunable absorber based on a patterned graphene metasurface by two ways: one is to tune the surface resistance of graphene to maintain the absorption and the other is to use the stack of graphene as the absorbing layer to change the resonance frequency. Meng et al. [27] proposed a dual-band absorber with a patterned H-shaped graphene array which controls the number of absorption spectra by changing the refractive index of the dielectric and the Fermi level $E_{F}$ in the mid-infrared region. Although graphene exhibits tunable optical properties that enable the dynamic manipulation of light, its coupling with incident electromagnetic waves is not sufficient for practice use. Very recently, bulk Dirac semimetal (BDS) such as AlCuFe, ${\textrm{Cd}_3\textrm{As}_2}$ [28] have been reported, which are considered as “three-dimensional (3D) graphene” and exhibit excellent properties with a high mobility of $9 \times 10^{6}$cm$^{2}$V$^{-1}$s$^{-1}$ at 5K [29,30]. The mobility can be dynamically adjusted by changing the Fermi level $E_{F}$ similar to the case of graphene. Other BDS-based metasurfaces have also been reported such as polarization converter, and plasmon-induced transparency [31–35]. Liu et al. proposed a narrowband absorber by utilizing the metallic property of BDS at THz frequencies and the total quality factor Q reaches 94.6 in 2018 [36]. In 2019, Dai et al. investigated a broadband terahertz cross-polarization conversion based on BDSs that can be tuned by changing the Fermi level of the BDSs, and the polarization conversion rate mostly remains above 80% [37].
In this paper, we propose a tunable and polarization-independent absorber based on BDS metasurfaces at terahertz frequencies with a high absorption. The proposed absorber is a triple-layer structure consisting of a patterned BDS film at the top, a dielectric layer in the middle, and a metal reflector at the bottom. Subsequently, we studied the performances of the proposed absorber, including the influence of the structural parameters, the Fermi level $E_{F}$ of the BDS on its absorption and resonance frequency. In addition, we also studied the electric and magnetic field distributions. The numerical results show that the peak absorbance is maintained at above 95%, while $E_{F}$ is between 65 meV and 95 meV and the resonance frequency is in the range from 2.46 THz to 3.16 THz. For both polarizations, the peak absorbance is maintained at above 85% for incident angles up to $60^\circ$. The design enables the development of various BDS-based tunable absorbers at other terahertz, infrared, and visible frequencies. This allows the absorber to be used in a wide range of applications in sensing systems and optoelectronic devices. One of the most important contributions of this study is the realization of an ultrathin structure in the design, and it makes the proposed device operate satisfactorily over a wide incident angle range.
2. Structure and materials
Figure 1 shows a schematic diagram of the proposed tunable BDS-based absorber which is a three-layer structure composed of a patterned Dirac semimetal layer at the top, a dielectric layer in the middle, and a metal reflector at the bottom.
Fig. 1. Schematic of the 3$\times$3 unit structure of the proposed absorber which is composed of a patterned Dirac semimetal film, the dielectric layer and a metal reflector. The incident electric field is along the $x$-axis and the magnetic field is along the $y$-axis.
$P$ represents the period of the unit cell in both the $x$- and $y$-directions. In order to eliminate the transmission of the device, a good conductor such as gold or silver is used to form the bottom metallic layer. The thickness $t_1$ of the metallic layer is $0.2$ µm, which is greater than the skin depth of the incident wave and is used as a fully reflective substrate. In our simulation, We choose gold with a conductivity of $4.56\times 10^7$ S/m as the bottom metallic layer, which is able to completely reflect the terahertz-frequency light. The dielectric constant $\varepsilon _r$ of the intermediate dielectric layer is set to 4.3. The patterned BDS film is a thin disk with four circles symmetrically cut off at the edges. The redius of the thin disk is $R=2$ µm and its thickness is 20 nm. Assuming that the center of the unit cell is the coordinate origin, and the centers of the four cut circles are located at symmetric positions at the edge of the thin disk on the top layer with their origin coordinates at ($2$ µm , 0), (-$2$ µm , 0) , (0 , -$2$ µm) , (0 , $2$ µm). The radii $r$ of each of the cut circles is $0.4$ µm.
In the simulation, to emulate the model of the BDS, the complex conductivity of the BDS is calculated using the Kubo formalism in random-phase approximation (RPA) theory at the long-wavelength limit of $q\ll k_F$ (local response approximation). The dynamic conductivity of the Dirac semimetals at the low-temperature limit of $T\ll E_F$ can be written as follows [30]:
In our simulation, we choose AlCuFe quasicrystals as the BDS film. The real and imaginary parts of the dynamic conductivity of the BDS are normalized to 1 nm of the thickness is observed in Fig. 2. From Fig. 2, we infer that the conductivity of the BDS can be dynamically adjusted by its $E_F$. The real component is linear when $\hbar \omega /E_{F}>2$, and it is neglligible when $\hbar \omega /E_{F}<2$ (Fig. 2(a)). The proposed absorber works in the terahertz range from 100 GHz to 10 THz, i.e, $\hbar \omega /E_{F}\leq 0.551$ for $E_F=75$ meV. The real component is zero in the terahertz range. The permittivity of the BDS using the two-band model is expressed as [38]:
here, $\varepsilon _{b}=1$ and $\varepsilon _0$ is the permittivity of vacuum.Fig. 2. (a) Real (left) and (b) imaginary (right) parts of the dynamic conductivity for the BDS (normalized to 1nm of the thickness) at zero temperature in units of $e^{2}/\hbar$ as a function of the normalized frequency $\Omega = \hbar \omega / E_{F}$ for different $E_F$ (60 meV, 75 meV, and 90 meV). The other parameters are $\mu = 3\times 10^{4}$ cm$^{2}$V$^{-1}$s$^{-1}$, $\tau = 4.5\times 10^{-13}$ s, and $\varepsilon _{c}=3$.
3. Results and discussion
To understand the mechanism and performance of the proposed absorber shown in Fig. 1, we numerically investigate the absorption using the frequency-domain solver of CST Microwave Studio (Fig. 3). In the first simulation, the parameters are set as follows: $P=4.3$ µm, $t_1=0.2$ µm, $t_2=3$ µm, $R=2$ µm, $r=0.4$ µm, and $E_F=75$ meV. To emulate the BDS model, we calculated its conductivity by Eqs. (1) and (2) of the corresponding working frequency and import the data into the CST Microwave Studio package. The open boundary conditions were used in the z-direction the $z$-direction, while periodic boundary conditions are applied in the $x$- and $y$-directions to replicate an infinite array of the structure. By default, the periodic structure is illuminated by a normal incident plane wave. The simulation result is shown in Fig. 3(a).
Fig. 3. (a) Simulated absorption at $E_F=75$ meV in TE mode(red curve) and TM mode(blue curve), and the resonance frequency of the proposed absorber is $f=2.860$ THz. (b) Simulated absorption at different Fermi levels $E_F$ from $E_F=60$ meV to $E_F=100$ meV of BDS, (c)and at different polarization angles.
The absorption is obtained using the $A=1-R(\omega )-T(\omega )$, where the reflection is given by $R(\omega )=|S_{11}|^{2}$, and the transmission is given by $T(\omega )=|S_{21}|^{2}$. Here, $\omega$ denotes the angular frequency, $S_{11}$ and $S_{21}$ denote the reflection and transmission coefficients of the absorber respectively. The proposed absorber uses a metal substrate with a thickness greater than the skin depth of the incident wave to eliminate the transmission $S_{21}$ of electromagnetic waves. Therefore, the absorption expression reduces to $A=1-R(\omega )$. Good impedance matching plays a significant role for an absorber. In general, the equivalent surface impedance $Z_1$ of the device can be made equal to the free space impedance $Z_0$ by changing the structural parameters, medium parameters, etc. The reflection is expressed as:
According the definition of S parameters [39], we can get where $S_{11}$ and $S_{21}$ are the complex reflection and transmission coefficients, respectively. In the actual calculation, we use the S parameters from CST software in the simulation to calculate the impedance value $Z_1$. When the equivalent surface impedance is equal to the free space impedance, i.e., $Z_{1}=Z_{0}\approx 377\ \Omega$, the reflection coefficient is $R = 0$ at the resonance frequency and the incident electromagnetic wave can enter the structure without reflection.According to the result in Fig. 3(a), the proposed absorber can be considered as a perfect absorber whose resonance frequency is $f = 2.860$ THz and the full width at half maximum (FWHM) is ${\bigtriangleup} f = 9.1\times 10^{-2}$ THz. The smaller FWHM indicates that absorption can be quickly minimized at frequencies that do not require high absorption. The absorption bandwidth is approximately 0.0227 THz and the absorption is above 95% when $E_F=75$ meV. The red and blue curves are substantially coincident, indicating that perfect absorption is achieved at both TE and TM modes due to the high symmetry of the structure. To better illustrate that the polarization independent, we simulated the relationship between polarization angles and absorption. We can infer that the absorption of at different polarization angles which is shown in Fig. 3(c) are almost coincident, so we can consider the designed absorber to be polarization-independent. In order to explore the relationship between the $E_F$ of the BDS and the resonance frequency, we simulate the absorption at different Fermi levels $E_F$ as shown in Fig. 3(b). As $E_F$ of the BDS gradually increases from 60 meV to 75 meV, the absorption peak of the resonance frequency increases from 88% to 100% . As the increment of $E_F$ , the conductivity increases which can be seen in Fig. 2 and enhance the conductive performance of the BDS, which induce an effective current path of BDS film and gold substrate, and excites a strong magnetic response. When the magnetic resonance dominates, the loss of the incident wave is caused by the dielectric layer. The energy of the incident wave is converted into other forms of energy by the ohmic loss of the metal and the dielectric loss of the dielectric layer, then increase its absorption. Moreover the resonance frequency increases from 2.285 THz to 2.860 THz, i.e., it is blue-shifted. The absorption of the absorber is maintained at above 95% when $E_F$ increases from 65 meV to 85 meV and the resonance frequency increases from 2.46 THz to 3.16 THz. The results show that the $E_F$ has a significant effect on the performance of the absorber, and its changes directly affect the electrical and magnetic resonances. When the $E_F$ is at 75 meV, the electromagnetic resonance is stronger than its at other Fermi level $E_F$. The electromagnetic waves penetrating the structure are completely consumed, and the absorber has a perfect impedance matching at the resonance frequency.
To further investigate the performance of the absorber, we studied the effect of the period $P$ on the absorption. As shown in Fig. 4(a), when the period $P$ increases from 4 µm to 5 µm with steps of 0.2 µm, the resonance frequency increases from 2.59 THz to 3.02 THz, i.e., it is blue-shifted. According to the analysis of the results obtained by parameter sweep, when the period $P$ is set to 4.3 µm, and the other parameters are fixed, the absorption reaches 99.9%, which can be considered as complete absorption. We also studied the relationship between absorption and the thickness $t_{2}$ of the dielectric layer, the radii $r$ of the cut circle, and the radii $R$ of the thin disk, as shown in Figs. 4(b)-(d). The results show that the resonance frequency shifts to the left with the increase in $t_{2}$ (i.e., it exhibits a red-shift) and the absorption is the highest when $t_{2}=3$ µm. The path phase of electromagnetic wave propagating in the dielectric layer is
here, the phase of the incident electromagnetic wave is $\varphi _p$, $\theta$ is the incident angel, the dielectric constant of the dielectric layer is $\varepsilon _r$. The structure is illuminated by a normal incident plane wave, the values of $\varphi _p$ and $\theta$ can be considered fixed. Therefore, the resonant frequency is inversely proportional to the thickness of the medium, when the thickness of the dielectric layer increases, and the resonance frequency will red shift. The radii $r$ of the cut circle has no obvious relationship with the resonance frequency (Fig. 4(c)) and the absorption is maintained at above 99% when $r = 0.2$ µm and $r = 0.4$ µm. Different from $r$, the resonance frequency is decreases with the increases in the radii $R$ of the thin disk which is inferred from Fig. 4(d).Fig. 4. Simulated absorption of the proposed absorber at (a) different periods $P$ from 4$\mu m$ to 5$\mu m$,(b) different thicknesses $t_2$ of the dielectric layer, (c) different radii $r$ of the cut circle, (d) different radii $R$ of the thin disk.
We further studied the effect of the permittivity of the dielectric layer on the absorption. In Fig. 5(a), when the permittivity increases from 2 to 10 with steps of 2, the absorption peak exhibits a red-shift, while the absorption is almost unchanged. It is shown that the imaginary part of the complex permittivity which is inferred from Eqs. (4) does not change with the change in permittivity $\varepsilon$ and as a result, the absorption of the absorber does not change. This indicates that the change in the permittivity of the dielectric layer is independent of the absorption. According to the S-parameters obtained from the simulation, the absorption when the incident angle $\theta$ is tuned from $0^{\circ }$ to $75^{\circ }$ with steps of $15^{\circ }$ is shown in Fig. 5(b). We note that the absorption is maintained at above 95% when $\theta$ increases from $0^{\circ }$ to $45^{\circ }$ with no significant drop. The absorption is maintained above 95%, and there is no significant drop. The absorption at the resonance frequency is above 88% even when $\theta =60^\circ$. The absorption frequency remains stable and no offset occurs when $\theta$ above $45^\circ$. The simulation proves that the proposed absorber is less affected by the incident angle $\theta$, indicating that the electromagnetic resonance can still be maintained under oblique incidence. The excellent performance of the proposed absorber significantly enhances its usefulness in applications such as multi-spectral imaging.
Fig. 5. Simulated absorption of the proposed absorber at (a) different permittivities $\varepsilon$ and (b) different incident angles $\theta$.
In order to understand the absorbing mechanism of absorber, we simulate the electric and magnetic field distributions at the resonance frequency of 2.86 THz when $E_F$ = 75 meV. The results are presented in Fig. 6. The $x$- polarized wave is normally incident, which means that the incident electric field is along the $x$- direction and the magnetic field is along the $y$- direction as depicted in Fig. 1. The electric field distributions (in the cross section of $x$o$y$ plane) in the TE and TM modes of the BDS film on the top layer are shown in Figs. 6(a) and 6(b), respectively. We note that each structural unit is an independent resonant unit, and a strong resonance occurs at the edge of the cut circle of the thin disk. Due to the high symmetry of the structure, a perfect absorption of the TE and the TM modes is achieved at the resonance frequency. As observed in Fig. 6(c), the electric field in the cross section of yoz plane ($x = 0.3\ \mu$m ) is mainly distributed in the cut circles of the BDS film and the upper part of the dielectric layer. We also simulated the magnetic field distributions in the cross section of $y$o$z$ plane in TE mode and the results are shown in Fig. 6(d). We can infer that the incident electromagnetic field and structure can be effectively coupled at the resonance frequency. The magnetic resonance dominates and causes the loss of the dielectric layer to the incident electromagnetic wave, which is confined in the dielectric layer. The energy of the incident wave is converted into thermal energy or other forms of energy by the ohmic loss of the metal and the dielectric loss of the dielectric layer, and this increases the absorption of the proposed absorber.
Fig. 6. Electric field distribution at $f=2.86$ THz in (a) TE mode and (b) TM mode. (c) Electric field distribution and (d) magnetic field distribution in the cross section of $y$o$z$ plane in TE mode.
The proposed absorber can effectively reduce the electromagnetic radiation of electronic equipment and has certain practical applications in electromagnetic protection and information security.
4. Conclusion
In conclusion, we propose a theoretical model of a tunable absorber based on a BDS material at terahertz frequencies and demonstrate an efficient way to obtain a tunable narrowband absorber with perfect absorption in the terahetrz range. The model is formed by a BDS film with a patterned thin disk, a dielectric layer, and a fully reflective gold mirror. Thanks to the symmetry of the structure, perfect absorption is achieved for both TE and TM polarizations. In this study, both the absorption performance and the physical mechanism of absorption are investigated. The FWHM is ${\bigtriangleup} f = 9.1\times 10^{-2}$ THz when $E_F$= 75 meV. The absorption is above 95% when the $E_F$ of the BDS is in the range from 65 meV to 85 meV and the resonance frequency is in the range from 2.46 THz to 3.16 THz. We also observe that the absorption is sensitive to the geometrical parameters such as the period and height of the dielectric layer. We can achieve good performance of the absorber as needed in practice by adjusting these parameters properly. In addition, the proposed absorber is insensitive to wide-angle incident waves. Compared to traditional materials, the BDS-based metasurface is tunable and thinner. Our findings improve the applicability of the absorber in terahertz sensors, multi-spectral imaging and optical filters, etc.
Funding
Natural Science Foundation of Guangxi Province (2017GXNSFAA198048); National Natural Science Foundation of China (61640409); Innovation Project of GUET Graduate Education (No. 2017YJCX18, No. 2018YJCX32).
Acknowledgments
The authors would like to acknowledge the Guangxi Provincial Natural Science Foundation under contact No. 2017GXNSFAA198048, National Science Foundation Council of China under contact No. 61640409 and the research fund from Innovation Project of GUET Graduate Education under contact No. 2017YJCX18, No. 2018YJCX32, for their support.
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