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Abstract
A bifunctional broadband absorber in the terahertz band based on patterned bulk Dirac semimetal (BDS) and strontium titanate (STO) is proposed. The properties of the absorber are investigated using the finite-difference time-domain (FDTD) method. The results show that the width of absorption can be modulated from 0.59 THz to 0.7 THz when the Fermi energy of the BDS is independently shifted from 40 meV to 50 meV. By tuning the temperature from 250 K to 400K, the center frequency of the broadband absorption spectrum can be changed from 1.311 THz to 1.505 THz, and the absorption bandwidth broadens from 0.66 THz to 0.81 THz. In addition, the simulation results show that the absorber is insensitive to electromagnetic wave polarization, and can still maintain a stable broadband absorption effect when the oblique incidence is within 40° for TE and TM modes. Based on the impedance matching theory, the physical mechanism of the broadband absorption is analyzed theoretically. This work can provide an alternative way to design high-performance multifunctional tunable terahertz devices.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, terahertz technology has been widely studied because of its broad application prospects in imaging, medical treatment, security inspection, communications and other fields [1,2]. In order to realize a compact and practical THz systems, a variety of devices such as sources, detectors, modulators, switches and absorbers are developed. Among them, the study of terahertz absorber has aroused interest of researchers. Due to the lack of natural materials suitable for the terahertz wave band, designing efficient terahertz absorbers becomes a challenge [3]. In 2008, Landy proposed a “perfect absorber” to achieve perfect absorption of incident electromagnetic waves [4]. Since then, narrow-band absorbers [5–8], multi-peak absorbers [9–12] and broadband absorbers [13–17] have been developed for different applications. Narrowband and multi-frequency absorbers can be used in sensing, filtering and other fields, and broadband absorbers can be used in terahertz switching and power harvesting fields. However, absorbers made of noble metals with fixed parameters and characteristics cannot be used in environment which requires different absorption bands. This situation limits the application and development of metamaterial absorbers.
In order to break this limitation, the study of tunable absorbers has attracted the attention of researchers. So far, a variety of tunable absorbers have been designed using materials such as graphene and vanadium dioxide [18–21]. The conductivity of vanadium dioxide is mainly tuned by temperature, and its tuning efficiency is relatively lower than others. Although graphene has excellent tunable properties, it is very difficult to be fabricated in experiments. BDS is a bulk material called “three-dimensional graphene”, and its conductivity can be adjusted by dynamically shifting the BDS Fermi energy which is tuned through alkaline doping and bias voltage [22–25]. Compared with monolayer graphene, BDS is less susceptible to interference from the environment, so devices designed with this material can have stable performance. Recently, strategy of using BDS to design tunable absorbers has become a new focus. For example, in 2020, Shi et al. designed a BDS-insulator-metal (BIM) stacked triple-layer structure to realized tunable frequency of the perfect absorption peak by shifting the Fermi energy of the BDS [26]. In 2020, Xiong et al. designed a bifunctional absorber with graphene and BDS. The absorbance bandwidth of the absorber can be independently or jointly tuned by changing the Fermi energy of graphene and BDS [27]. STO is a ferroelectric material with high permittivity and low dielectric loss. Moreover, the response of STO to THz wave is determined by the strong polar soft vibrational modes, and its relative permittivity can be modulated by temperature [28]. Due to the electrical-tunable characteristics of BDS and the temperature-tunable characteristics of STO, multiple properties of absorption can be adjusted independently or simultaneously by using BDS and STO. Recently, the bifunctional independently tuning properties of absorber using BDS and STO becomes a new design scheme. In 2020, Xiong et al. proposed a dual-tuning narrow-band absorber which is composed of a patterned BDS structure, an STO substrate and a gold film. The peak frequency of the absorber can be tuned from 1.94 THz to 2.53 THz by adjusting the temperature of STO from 250 to 400 K. Furthermore, by changing the Fermi energy ${E_F}$ of BDS from 10 meV to 60 meV, the peak frequency can also be modulated from 2.14 THz to 2.44 THz [29]. In the same year, they proposed a narrow-band absorber consisting rose-shaped BDS and an STO film. By adjusting the Fermi energy of the BDS from 10 to 80 meV, the peak absorptivity of device can be tuned from 70% to 99.9%, and the absorption frequency point shifts from 3.265 THz to 4.82 THz. When the temperature of the STO is increased from 200 K to 300 K, the absorption frequency can be changed from 2.665 THz to 3.69 THz [30]. It can be found that the previous studies mainly focused on the tuning frequency and amplitude of narrow-band absorber via BDS and STO. In fact, it is also necessary to achieve bandwidth and frequency tuning for broadband absorption.
In this paper, a tunable broadband terahertz absorber based on BDS and STO materials is proposed. By using FDTD, the absorption properties of the absorber are studied theoretically. Specifically, it was found that, when tuning the Fermi energy of BDS, the absorption bandwidth can be changed. And when the STO temperature is tuned, the broadband absorption center frequency and bandwidth can be adjusted. Besides, the effect of incident angle and polarization angle on absorption performance are also investigated. The absorber provides a new strategy for dual-tunable function of broadband absorption, and has potential applications in the field of photovoltaic equipment, stealth equipment in military applications and filters.
2. Geometric structure and numerical model
The unit structure of the terahertz absorber is shown in Fig. 1. As shown in Fig. 1(a), each unit is composed of four layers which are patterned BDS, STO film, polydimethylsiloxane (PDMS) and gold film from top to bottom. We can see that the units of the BDS are connected, so the Fermi energy can be changed by bias voltage. And the thickness of BDS, STO film, PDMS and gold film are 1 ${\mathrm{\mu}}{\textrm{m}}$, 0.1 ${\mathrm{\mu}}{\textrm{m}}$, 30 ${\mathrm{\mu}}{\textrm{m}}$ and 0.2 ${\mathrm{\mu}}{\textrm{m}}$, respectively. Figure 1(b) is the unit top view where special geometric parameters of patterned BDS are given (w=3 ${\mathrm{\mu}}{\textrm{m}}$, R1=33 ${\mathrm{\mu}}{\textrm{m}}$, R2=15 ${\mathrm{\mu}}{\textrm{m}}$, R3=27 ${\mathrm{\mu}}{\textrm{m}}, \theta = 40^\circ , \Phi = 60^\circ )$. The relative permittivity of PDMS is 2.35 and the loss tangent is 0.06 [31]. The conductivity of the gold film is $4.56 \times {10^7}S\textrm{ }{m^{ - 1}}$ [32].
Fig. 1. (a) Three-dimensional diagram of the unit cell and (b) top view of the proposed absorber base on periodic array.
The properties of the designed absorber are studied theoretically by using FDTD algorithm. When simulating, the boundary condition in the x and y direction is set to be the periodic boundary, while the boundary condition in z direction is set to be a perfect matching layer. The terahertz plane wave with the x-polarization direction is incident on the surface of the absorber. The absorption rate can be calculated by the following formula $A(\omega )= 1 - R(\omega )- T(\omega )$. $R(\omega )$ is the reflectance of the absorber calculated by the formula $R(\omega )= {|{{S_{11}}(\omega )} |^2}$ and $T(\omega )$ is the transmittance of the absorber calculated by the formula $T(\omega )= {|{{S_{21}}(\omega )} |^2}$. Since the thickness of the gold film of the absorber is greater than the skin depth of the terahertz wave, the transmittance $T(\omega )$ is set to be zero. So, the absorption formula is changed to $A(\omega )= 1 - R(\omega )= 1 - {|{{S_{11}}(\omega )} |^2}$.
According to random-phase approximation theory [33,34], in 0.1 $-$ 10 THz region the conductivity $(\sigma )$ of BDS can be expressed as follows:
As a thermally control material, the properties of STO are shown in the following formula [37–39]
The change of real and imaginary parts of the STO permittivity with frequency and temperature is shown in Figs. 3(a) and 3(b). It can be observed that, the real and imaginary parts of the permittivity increase with increasing frequency, but decrease with increasing temperature.
Fig. 3. (a) Real and (b)Imaginary parts of the permittivity for STO under temperatures from 250 K to 400 K.
3. Results and discussions
The initial value of the Fermi energy of BDS and the STO temperature is set to be 45 meV and 300 K, respectively. In the case of x-polarized vertical incidence, the absorption and reflection spectrum obtained by simulation in 0.5 $-$ 2.5 THz are shown in Fig. 4(a) using black and red solid line, respectively. Obviously, there are two absorption peaks at 1.14 THz and 1.5 THz, which are defined as peak I and peak II. The absorption rates of the two peaks are 96% and 100%, respectively. And the two absorption peaks combine together to form a broadband absorption spectrum. The absorption bandwidth above 80% absorption can be obtained as 0.65 THz [40]. Figure 4(b) shows the relationship between the absorption and the plane wave polarization angle. It can be observed that the absorption is independent of angle. Namely, the absorber is insensitive to the polarization of incident wave.
Fig. 4. (a) Absorption and reflection spectrum under x-polarized plane wave (b) Absorption maps of this absorber by changing the plane wave polarization angle
Next, we investigate the effect of Fermi energy of the BDS on absorption, and the specific results are shown in Fig. 5(a). We can see that there two peaks and a dip in the three simulation curves. When temperature is set to be 300 K, and shifting the Fermi energy of BDS from 40 meV to 50 meV, the frequency of peak I $({f_1},{f_2},{f_3})$ almost does not change, while peak II shifts significantly from $1.43\textrm{ THz }({f_1}^\prime )$ to $1.58\textrm{ THz }({f_3}^\prime )$. Although the absorption rate at the dips drops significantly, it still remains above $80\textrm{\%}$.
Fig. 5. The broadband absorption spectrum with (a) different Fermi energy of the BDS material and (b) different temperatures of STO (c) The bandwidth with different Fermi energy of BDS (d) The center frequency and absorption bandwidth with different temperatures.
As shown in Fig. 5(b), when the BDS Fermi energy remains at 45 meV, and the temperature is tuned from 250 K to 400 K, absorption peak I shifts from $1.14\textrm{ THz }({f_4})$ to $1.35\textrm{ THz }({f_7})$ and the peak II shifts from $1.51\textrm{ THz }({f_4}^\prime )$ to $1.76\textrm{ THz }({f_7}^\prime )$. Here we define the center frequency of the absorption as ${f_c} = {{({f_ - } + {f_ + })} / 2}$, where the ${f_ - }$ and ${f_ + }$ are the low-frequency and high-frequency edges of 80% absorptance, respectively. Therefore, from Fig. 5(b), we can see when the temperature changes from 250 K to 400 K, the center frequency has a blue shift and the absorption bandwidth increases.
In order to reflect the tuning above directly and figuratively, the effects of Fermi energy and temperature on bandwidth and center frequency are shown in Fig. 5(c) and Fig. 5(d), respectively. From Fig. 5(c), it can be found that, with increasing the Fermi energy, the absorption bandwidth increases continuously from 0.59 THz to 0.7 THz. In Fig. 5(d), we can see that as the temperature increases, the center frequency shifts from 1.311 THz to 1.505 THz, and the absorption bandwidth broadens from 0.66 THz to 0.81 THz.
In order to study theoretically the physical mechanism of the tuning of broadband absorption, impedance matching theory was used [41,42]. Since the bottom layer is a gold film with a thickness greater than the skin depth of the terahertz wave, the transmittance of the absorber $T(\omega )$ is 0. Then specific formula for impedance matching is:
Fig. 6. (a1) Real part and (a2) imaginary part of normalized impedance Z with different Fermi energy of the BDS. (b1) Real part and (b2) imaginary part of normalized impedance Z with different temperatures of STO.
When the Fermi energy is 45 meV, Figs. 6(b1) and 6(b2) show the variation of normalized impedance with temperature from 250 K to 400 K. We can see that, at ${f_4}\textrm{ },{f_5}\textrm{ },{f_6},{f_7}, {f_4}^\prime \textrm{ },{f_5}^\prime \textrm{ },{f_6}^\prime ,{f_7}^\prime$, the real parts of impedance are close to 1 and the imaginary parts of them are almost 0, which means that the impedance of the absorber matches well with that of free space.
In order to get a further understand about the physical mechanism of broadband absorption, the electric field distribution at resonant frequency is studied. As shown in Fig. 4(a), when the Fermi energy of BDS and the STO temperature is set to be 45 meV and 300 K, the resonant frequencies are 1.22 THz and 1.62 THz, respectively. When the 1.22 THz TE plane wave is incident, the electric field distribution is shown in Fig. 7(a), we can see the local plasmon resonance is mainly concentrated at the edges of the top and bottom outer arcs. Figure 7(b) shows the electric field distribution at 1.62 THz. It can be observed that local plasmon resonance exists not only in the outer arc, but also in the arc and center of the middle sector structure. Figure 7(c) and Fig. 7(d) illustrate the electric field distribution of the absorber at 1.22 THz and 1.62 THz under the incidence of the TM plane wave. It can be found that the electric field distribution is the 90-degree rotation of the electric field distribution under the incident of TE plane wave. This phenomenon further verifies the conclusion of polarization insensitivity in Fig. 4(b). In addition, the local plasmon resonance of the BDS will cause energy loss, and the loss can be calculated by the Eq. (9)
where E is the electric field inside BDS, V is the volume of BDS, and ${\varepsilon ^{\prime\prime} }$ is the imaginary of BDS permittivity. In the terahertz band, since the imaginary ${\varepsilon ^{\prime\prime} }$ of the BDS is very large, the terahertz wave will produce large losses in the local plasmon resonance region, resulting in two absorption peaks at 1.22 THz and 1.62 THz. And the combination of two absorption peaks causes a broadband absorption.Fig. 7. Electric field distribution at (a)1.22 THz and (b)1.62 THz under x-polarized plane wave, Electric field distribution at (c)1.22 THz and (d)1.62 THz under y-polarized plane wave
In practical applications, the stability of the absorber under oblique incidence of terahertz wave is important. This section discusses the relationship between absorption rate and incident angle. Here we set the STO temperature and the BDS Fermi energy to be 300 K and 45 meV, respectively. When the oblique incidence angle of the TE and TM polarized plane waves increases from 0° to 60°, the absorption results are given in Figs. 8(a) and 8(b), respectively. For TE polarization, as the angle increases from 0° to 40°, the absorber can maintain a stable absorption bandwidth. However, the absorption bandwidth is reduced significantly when the incident angle reaches 50°. For TM polarization, it can be observed that with the increase of the oblique incidence angle, although the broadband absorption blue-shifts gradually, absorption rate can still maintain about 80%. Therefore, the device can achieve broadband absorption within large oblique incident angle.
Fig. 8. Absorption of the bifunctional broadband absorber under different oblique incident angles for (a) TE and (b) TM polarizations.
In fact, as a new material, BDS have been used widely in tunable absorber [26,27]. For comparison, the typical cases reported are shown in Table 1.
Table 1. Comparison of the absorber in this article with published BDS-based tunable absorbers in THz band.
In Refs. [26,43], the absorbers can achieve only the frequency tuning of the narrowband absorption by changing the BDS Fermi energy. In Refs. [29,30], the absorbers realize both absorption rate and frequency tuning of the narrowband absorption peak through the combination of STO and BDS. In case of tunable broadband absorber base on BDS, Ref. [27] proposes an absorber based on graphene and BDS to achieve tuning of absorption bandwidth. The absorber in Ref. [44] also realizes the tuning of the absorption bandwidth and center frequency, but the absorption bandwidth and center frequency will change simultaneously when the BDS Fermi energy is tuned. This limits the flexibility of the absorber. However, our design is composed of temperature-tunable STO and electronically-tunable BDS. Due to the independent and joint tuning of the two materials, more flexible tuning of the frequency and bandwidth of broadband absorption can be achieved. And the absorption rate can still maintain above 80% during the tuning process. In addition, when the center frequency is tuned by changing the STO temperature, the absorption peak intensity is almost unchanged. Therefore, the absorber has a stable center frequency tuning function.
4. Conclusion
In summary, a thermally and electrically controlling broadband absorber is proposed in the terahertz band. At temperature of 300 K, the absorption bandwidth of the absorber can be changed from 0.59 THz to 0.7 THz by shifting the Fermi energy of the patterned BDS from 40 meV to 50 meV. When the Fermi energy of BDS is fix at 45 meV, the center frequency can be changed from 1.325 THz to 1.555 THz and the absorption bandwidth is changed from 0.66 THz to 0.81 THz by increasing the STO temperature from 250 K to 400 K. The tuning mechanism of absorber is analyzed by impedance matching theory. It is found that when the impedance of absorber matches the free space impedance well, resonance occurs and absorption enhances. Through electric field distribution analysis at absorption peak frequencies, we can see where the resonance of electric field occurs. In addition, the absorber is insensitive to the polarization of the incident wave. And this design can achieve stable broadband absorption within an oblique incidence angle of 40° for both the TE and TM polarizations. The bifunctional absorber can be applied to many optical control fields and provide a way for future terahertz absorber design.
Funding
Heilongjiang University (YJSCX2020-162HLJU); Natural Science Foundation of Heilongjiang Province (F2018027, LH2020E106, LH2020F041).
Disclosures
The authors declare no conflicts of interest.
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