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Abstract
Traditional absorbers are usually sandwich structures in which a metallic ground plane is employed to prevent the transmission. Such absorbers suffer from a major drawback that incident light can only irradiate from the front of the absorbers. In this paper, a novel absorber with bulk Dirac semimetal (BDS)-AlCuFe quasicrystals is proposed to realize bidirectional and dynamically tunable terahertz (THz) perfect absorption. The proposed structure consists of two layers of AlCuFe plates with rectangular apertures and a dielectric spacer. By adjusting transverse distance between the top and bottom rectangular apertures, perfect absorption could be realized under TM polarization. Simulation results show that perfect absorption can be obtained whether light irradiates from the front or back of the system, indicating a performance of bidirectional absorption. In addition, benefiting from the variable Fermi level of AlCuFe, the resonance frequency can be dynamically tuned in the THz range. Our work will stimulate more investigations on BDS-based bidirectional absorbers and optical modulators.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Absorption enhancement plays a key role in optical devices and it has attracted considerable interests in recent years. Especially, perfect optical absorption has become an important research field because of the possibility to attain a 100% absorption by restraining the light propagation channels. To date, various perfect absorbers, such as single-band [1–3], multi-band [4–6], broad-band [7–12], metasurface absorber [13] and coherent absorber [14,15] have been made by exploiting different technologies and approaches. However, most of absorbers have a common drawback that operation wavelength will be fixed once these structures are designed. So, the absorber has to be remanufactured when one wants to tune the resonance peak. Fortunately, this problem was solved by designing a graphene-based absorber due to the dynamic tuning of graphene surface conductivity [16–19]. Since then, a range of graphene-based dynamically tunable devices have been proposed in mid-infrared and THz region [20–25]. However, it is difficult to precisely fabricate graphene in experiments due to its single-atom-layer thickness. Hence, it is quite meaningful to find the easily prepared three–dimensional (3D) material with tunability of dielectric properties. Such 3D material-based devices will be the promising platform to realize a dynamically tunable absorber.
Recently, a novel state of quantum matter-3D BDS which is also called “3D graphene” has attracted great attentions due to enormous potential in manipulating light [26,27]. Comparing to one-atomic-layer graphene, 3D BDS retains the structural benefits of bulk metals, which is much easier to manufacture and more stable in fabrication facilities. Similar to graphene, the permittivity functions of 3D BDS can also be dynamically controlled by adjusting Fermi level EF through surface doping [28]. Furthermore, owing to crystalline symmetry protection in BDS films, ultrahigh carrier mobility of 9×106 cm2/(V·s) can be attained at 5 K [27,29]. It is notable that this carrier mobility is much higher than that of graphene (2×105 cm2/(V·s)). With these excellent characteristics, BDS can be regarded as a suitable candidate for the design of optical modulators, sensors and communications. In recent years, experimental works based on Cd3As2 and AlCuFe quasicrystals have been reported. In 2017, Zhu et al. demonstrated and fabricated a tunable mid-infrared optical switch based on Cd3As2 by employing molecular beam epitaxy (MBE) [30]. Nayak et al. employed the Bridgman technique to grow AlCuFe quasicrystals [31], and the 3D Dirac nature of AlCuFe quasicrystals was experimentally confirmed by optical conductivity measurements [32]. To date, many BDS-based devices have been studied [33–36]. For example, Wang et al. [37] theoretically demonstrated a tunable THz absorber based on BDS films with three different-shaped resonators (square-shaped, circular-patch and cross-shaped), which further extends the application of BDS in the THz region. In a recent paper, Sun et al. [38] designed and fabricated an electrically contacted saturable absorber composed of Cd3As2 thin film and a GaAs substrate. Meng et al. [39] showed that BDS thin-film exhibited strong and tunable saturable absorption effects at the near-IR. Although these pioneering works have reported BDS-based absorbers with different functions, the critical issue of absorption efficiency has not yet been discussed. Moreover, although it is easy to realize single-band, multi-band and broad-band absorbers, the majority of absorbers only exhibit unidirectional function. Due to the increasing demand for improving the capacity of energy storage, it is highly desirable to construct a single device with bidirectional absorption which cannot be realized in traditional absorbers because of the inherent structure drawback. Therefore, to realize an absorber with double absorptivity in a single BDS-based system is the motivation of the present study.
Herein, we propose a AlCuFe-based bidirectional and dynamically tunable perfect absorber and systematically study three types of structures and corresponding absorption properties. The proposed absorber is composed of two layers of AlCuFe plates with rectangular apertures and a dielectric spacer. Based on this special structure, the proposed absorber is free substrate with 180° rotational symmetry in z-direction, which is the key point to achieve bidirectional absorption. Perfect absorption can be obtained by optimizing transverse distance between the top and bottom rectangular apertures. Simulation results show that the proposed absorber exhibits the same absorption effect when light irradiates from both sides of the system. Meanwhile, the physical mechanism of the proposed bidirectional total absorption (BTA) can be understood by examining electric field distributions at resonance frequency. Another important feature of the proposed system is that absorption spectra can be dynamically tuned by changing the Fermi level of AlCuFe. Overall, this design approach not only overcomes the limitation of irradiation direction for traditional absorbers and greatly improves the absorption efficiency, but also exhibits advantages in tunable spectral selectivity.
2. Materials and design
Figure 1(a) shows 3D schematic of the BTA structure without substrate and Fig. 1(b) is amplifying view of unit cell used in the simulation. The BTA structure consists of two layers of BDS plates with rectangular apertures and a dielectric spacer. The thickness of BDS is set to 0.4 µm, and ambient medium is supposed to be air. The top and bottom BDS plates are separated by the dielectric spacer with refractive index n = 1.8 and thickness t = 26 µm. The geometric parameters are fixed as follows unless otherwise specified: L = 40 µm, w = 10 µm, S = 82 µm. In our simulations, periodic boundary conditions are applied along x and y directions with periodicity Px = 120 µm, Py = 54 µm. While, perfectly matched layers are utilized along the propagation direction of the electromagnetic waves (z direction) to absorb all light approaching the boundaries. The finite-difference time-domain (FDTD) method is employed to calculate transmission, reflection and electric-field distributions, which are then used to elucidate resonance mechanism and scrutinize absorption effect. The mesh size inside the BDS layer is set to 0.04 µm along the z axis and 0.5 µm along the x and y axes. In addition, a simulation time of 100 ps is set to ensure the validity of the simulation.
Fig. 1. (a) Schematic of the BTA structure. Each unit cell is composed of two layers of BDS plates with rectangular apertures and a dielectric spacer, which repeats in the x and y directions forming arrays with periodicity Px and Py. (b) The magnified unit cell of the BTA structure.
3. Results and discussions
3.1 The first type of structure (single layer 3D BDS)
In 2016, Kotov et al. demonstrated that in a BDS film the metallic response manifests in the existence of surface plasmon polaritons (SPPs) [26]. On the basis of this background, we consider three types of structures to expound the absorption mechanisms of the BDS-based absorbers. In addition, we also investigate the effect of geometric parameters on absorption spectra. Initially, a patterned structure consisting of a BDS plate with rectangular apertures is proposed. The incident plane is parallel to x-z plane, and the polarization angle θ is defined, as shown in Fig. 2(b). Thus, θ = 0° and θ = 90° corresponds to TM wave and TE wave, respectively. Under the TM wave, w is parallel to the electric component of incident light, then surface charge oscillations occur along the sides of the apertures. To give an intuitive evidence, the electric-field distribution is presented in Fig. 2(c). Clearly, the distribution of the electric field is mainly concentrated at both sides of the apertures. The red and blue spectra represent the opposite charges in the electric-field distribution. Great enhancement of electric field indicates that larger charge accumulates at the sides of aperture arrays. This characteristic of electric-field distribution shows the excitation of electric dipole resonance in this structure. Thus, each aperture element has the function of providing electric dipole response.
Fig. 2. (a) Schematic of the single layer structure. The structure consists of a BDS plate with rectangular apertures, which repeats in x and y directions forming arrays with periodicity Px and Py. (b) Top view of the single layer structure. (c) The electric-field (Ez) (in the plane of y = 0) distribution at resonance frequency. (d) The ratio of extinction cross section to geometric area as a function of frequency (L = 40 µm, w = 10 µm, and Fermi energy EF = 55 meV). The resonance frequency ωp as a function of width w (e) and Fermi level EF (f).
In order to investigate the absorption properties of BDS with such a structure, we calculate its extinction cross section. Under the irradiation of light, the polarizability of the structure exhibits a resonance which can be expressed as [40]:
For further investigations, we calculate the parameters ωp as a function of width w and Fermi level EF as shown in Figs. 2(e) and 2(f), respectively. We note that ωp experiences a redshift with w varying from 10 µm to 80 µm. However, in Fig. 2(f), ωp presents the contrary tendency with the increase of EF when w is fixed. This is similar to the relation between resonance frequency and Fermi energy in graphene SPPs [20]. A more detailed explanation will be given in the section of 3.5. It can be inferred from Fig. 2(e) that fitting parameter ωp bears an intrinsic dependence on the geometric parameters. In addition, previous studies have shown that ωp is also related to electronic properties of atomic structure [41]. These calculated results provide a better understand for the resonance property of BDS and bring a reference for the optimization of parameters.
As mentioned above, SPPs can be excited in the first type of structure when incident light is polarized along x axis. The SPPs waves have the form E(r, w, t) = E0 exp(ikspp(ω)x-kz|z|), where kspp = 2πneff / λinc is wave vector in the propagation direction. The corresponding effective refractive index neff is plotted in Fig. 3. Simultaneously, the electric-field (Ez) distribution is also presented and it reveals that most of the field energy is concentrated at the both sides of rectangular aperture, as shown in the inset of Fig. 3. It can be seen that neff presents a sharp decrease with frequency changing from 0.1 to 0.4 THz. Interestingly, neff shows a slow decrease with frequency changing from 0.4 to 1.7 THz. This trend is related to the permittivity of BDS. To further reveal the physical mechanism of this phenomenon, we plot conductivity and permittivity of BDS in details in Figs. 4(c) and 4(d).
Fig. 3. The calculated effective refractive index as a function of frequency. Inset shows the electric field (Ez) distribution of the SPPs related to the x-z cross section (in the plane of y = 0).
Fig. 4. Real (a) and imaginary (b) parts of the dynamic conductivity for BDS at zero temperature in units e2/ħ as a function of the normalized frequency ħω/EF. The parameters are set as g = 40, εc = 3, τ = 4.5 × 10−13 s. Real (c) and imaginary (d) parts of the BDS permittivity.
Since BDS can be considered as 3D graphene, it can also be described by conductivity σ. At long-wavelength limit, Kubo formalism is used to govern the complex-valued conductivity of BDS in random-phase approximation theory (RPA). Then, the conductivity of BDS can be written as [26]:
3.2 The second type of structure (traditional absorber structure)
For the first type of structure in Fig. 2(a), it should be emphasized that the maximum absorptivity is only 50% which will be discussed in the following analysis. For this kind of system in Fig. 2(a), the absorption (marked as A) is related to self-consistent amplitude η written as A = −2η2−2η. In our simulation, the structure is a film with symmetric environments, which results in the same refractive index for the top and bottom sides of structure. Thus, the corresponding Fresnel reflection and transmission coefficients are written as r = η and t = 1+η, respectively. Apparently, A gets its maximum of 0.5 when r = −1/2, t = 1/2, η = −1/2. Therefore, Amax = 0.5 is the limit of absorption for structure in Fig. 2(a). However, in asymmetric environments, the maximum absorption can be effectively improved by employing a back mirror or Bragg mirror to block the transmission channel. Inspired by this, we propose the second type of structure, consisting of a BDS-insulator-BDS structure where only the top BDS layer is patterned. The two BDS layers are separated by a dielectric spacer with refractive index n = 1.8 and thickness t = 26 µm. The thickness of top and bottom BDS layers both are set to 0.4 µm. Because of the existence of bottom continuous plate, it is presumed that the second type of structure does not allow any transmission. Figure 5(a) depicts the schematic of such a BDS-insulator-BDS structure. After introducing the ground plane, electric dipole response [37] in the aperture is strongly coupled with the bottom BDS layer, leading to opposite charges oscillation in the bottom plate, as shown in Fig. 5(c). Due to this strong resonance, electromagnetic energy is highly confined in the BDS-insulator-BDS structure. Thus, the perfect absorption is attained, as shown in Fig. 5(b). Such an absorber is similar to a traditional absorber with sandwich structure and we can tune the thickness of the dielectric spacer to realize the impedance matching. However, because of the existence of the bottom continuous plate, the source can only irradiate from the top surface of the system. That is to say, such an absorber cannot absorb electromagnetic energy irradiated from bottom surface of the system and absorption efficiency is extremely limited.
Fig. 5. (a) A bottom BDS ground plane is introduced into the system based on the structure in Fig. 2(a). (b) Simulated reflection, transmission and absorption spectra for this structure. (c) The electric-field (Ez) (in the plane of y = 0) distribution of the unit cell. The EF of BDS is initially assumed to be 55 meV.
3.3 The third type of structure (bidirectional absorption structure)
The limitation of absorptivity for the second type of structure motivates us to achieve a double absorptivity in a single system. The designed structure is schematically depicted in Fig. 1(a). In this structure, there is a lateral displacement S = 82 µm along the x-direction between the bottom and top apertures. This structure with three layers can be produced by atomic layer deposition method in experiments [43]. Only the TM wave is simulated for which electric dipole can be excited by x component of the electric field. For simplicity, the surface roughness effect is not taken into account in our simulation.
To gain the operating principle and performance of the proposed BTA, we present the simulated reflection, transmission and absorption spectra for incident light illuminating from the front side in Fig. 6(a), and the 3D sketch diagram is also shown in inset. It can be clearly seen that an absorption peak with absorptivity of 98% locates at the frequency of 1.73 THz. This absorption mechanism can be revealed by examining the electric-field distributions (Ez) at the resonance frequency. Figures 6(d)–6(f) show the corresponding electric-field distributions for S = 82 µm, S = 0 µm and S = 60 µm, respectively. According to Fig. 6(d), the bottom aperture locates at the antinodes of the wave, which results in an inefficient out-coupling between the free-space radiation and the SPPs in the spacer. In this situation, the electric dipole resonance in the bottom aperture cannot be obtained, indicating a low transmission. Thus, most of the electromagnetic energy is confined to the system. To demonstrate the mechanism more clearly, we also present the simulated reflection, transmission and absorption spectra for S = 0 µm in Fig. 6(b). It can be seen from the pink curve that the absorption spectrum shows a poor absorptivity of 56%, which is much lower than that of S = 82 µm (98%). Comparing with Fig. 6(d), the Ez for S = 0 µm in Fig. 6(e) shows remarkable differences. We can see that when S = 0 µm, the bottom aperture locates at the nodes of the wave from Fig. 6(e), and strong localized resonance is achieved because the incident wave can transmit through the top apertures to the bottom film. Then, the strong dipole response is excited in the bottom apertures. Owing to this, a high transmission is obtained, resulting in a low absorption. Similarly, as shown in Fig. 6(f), the condition of S = 60 µm is the same as the condition of S = 0 µm, except for the transmitted phase difference. As can be seen from the electric-field distributions that transmitted phase difference in the bottom aperture is close to π for these two conditions. Above results indicate that the location of the bottom aperture plays a critical role for achieving perfect absorption.
Fig. 6. (a) Simulated reflection, transmission and absorption spectra when incident light illuminates from the front side for S = 82 µm. (b) Simulated reflection, transmission and absorption spectra for S = 0 µm. (c) Simulated reflection, transmission and absorption spectra when the incident light illuminates from the back side for S = 82 µm. The electric-field (Ez) (in the plane of x-z) distributions of the unit cell under the condition of S = 82 µm (d), S = 0 µm (e), and S = 60 µm (f), respectively.
The performance of the BTA based on BDS will be demonstrated and evaluated in this section. A bidirectional response means that the absorber is able to harvest the electromagnetic energy that illuminates surface of the device from both sides. Therefore, by designing a bidirectional structure, the absorption efficiency of the device could be significantly improved. It is well established that the traditional absorber is absence of 180° rotational symmetry due to the existence of the bottom continuous metallic plate in the structural plane. As displayed in Fig. 5, light can only irradiate from the front side of the system, while the energy cannot transmit the system when light irradiates from the back side. Here, we realize a bidirectional absorber by introducing a same pattern as the top layer in the bottom layer, which breaks the absence of rotational symmetry along the incidence direction of the electromagnetic wave (z direction). In order to validate that the structure we proposed possesses the capacity of double absorptivity, in Fig. 6(c), we plot reflection, transmission and absorption spectra when incident light illuminates from back side of the system. We can note that a perfect absorption peak located at the frequency of 1.73 THz is obtained, which is consistent with the case of light illuminating from front side. Hence, it can be inferred that the designed absorber could realize perfect absorption when incident light illuminates from both front and back sides. Overall, the 180° rotational symmetry of our proposed structure is a key factor to realize the bidirectional absorber, which leads to the different absorption characteristic from that of traditional absorber. As a result, the proposed system provides a new avenue for the design of new-style absorbers with double absorption capacity in a single device, which will greatly improve the absorption efficiency.
3.4 Numerical optimization of the bidirectional absorber
Although above designed structure exhibits excellent absorption performance, the effect of L on the resonance frequency and absorptivity is also a key factor that should be considered. Figure 7(a) shows the dependence of the reflection spectra on the value of L when other parameters are fixed. We can see that the reflection gradually decreases and resonance frequency exhibits a redshift as L increases from 25 µm to 40 µm in steps of 5 µm. Similarly, transmission spectra also show the same trend with the increase of L. When L is relatively small, the ability to confine light is weak. Thus, both transmission and reflection are large and absorption is small. Conversely, when L is relatively large, transmission, reflection and absorption show the contrary results. When both reflection and transmission are minimal, the maximal absorption is obtained. Accordingly, a high absorption can be attained by appropriately tailoring geometric parameter L, which allows the incident light to be effectively coupled to the BTA structure. In addition, the effect of S on the phase of transmitted light is also investigated. As mentioned in Fig. 6, the location of the bottom aperture has a great influence on the transmission. To get a deep insight on this mechanism, the calculated phase of the transmitted light as a function of S/Px is presented in Fig. 7(c). The phase gradually decreases when S/Px changes from 0 to 0.416. Interestingly, when S/Px reaches to 0.5, the phase begins to increase. Then, the phase begins to decrease again. Combined with preceding discussions in Fig. 6, this simulation result clearly shows that the bottom aperture also plays a significantly important role in the phase of the transmitted light.
Fig. 7. Reflection (a) and transmission (b) spectra for different L, respectively. (c) Calculated phase of the transmitted light as a function of S/Px.
3.5 Active tunability and sensing of the bidirectional absorber
Resonance frequency is an important indicator in practical applications, which is the heart of sensors and other optical devices. Especially, most absorbers need to achieve adjustable resonance peaks for application requirements. To analyze the tunable properties of the resonance frequency, the absorption spectra with various EF of BDS are simulated in Fig. 8(a), where L and w are fixed at 40 µm and 10 µm, respectively. The results show that as EF increases from 45 meV to 75 meV, the resonance frequency experiences a blueshift from 1.64 to 1.85 THz. Notably, although the resonance frequency is changed, the absorptivity remains almost independent with the change of EF. As a consequence, dynamic adjustment of resonance frequency is realized. For revealing the underlying physical mechanism of this tunability, perturbation theory is introduced. According to this, the change of resonance frequency caused by material perturbation of the BDS films can be written as [44–46]:
Fig. 8. (a) Absorption spectra for different EF of the BDS. (b) Dependence of the resonance frequency on different refractive indices of the surrounding medium when other parameters are fixed.
Finally, in order to demonstrate the sensing performance in this bidirectional absorber, we perform additional simulations to show the dependence of absorption spectra on different refractive indices of the surrounding medium. The Fermi energy is set to EF = 55 meV and other parameters remain fixed. As can be seen in Fig. 8(b), the absorption peak of the bidirectional perfect absorber (BPA) is dependent on the refractive index (RI) of the surrounding medium. As RI increases gradually, the resonance frequency occurs a redshift. Through the study of RI above, we further investigate the sensing property of BPA-based sensor, and we use the figure of merit (FOM) to evaluate the performance of the RI sensor:
where FWHM, Δf and Δn are the half full width of the absorption, frequency shift and RI variation of the surrounding medium, respectively. In our simulation, the calculated FOM is about 3, which is very similar to that of other researchers’ work [47]. Therefore, the proposed BPA system can be used as a device for sensing and detecting RI changes of a tested agent.4. Conclusion
In summary, we have proposed a novel AlCuFe quasicrystals-based absorber and systematically studied three types of structures and corresponding absorption properties. As a bulk material, BDS possesses excellent structure advantage over 2D graphene and is more convenient to be made as devices. Simulation and fitting results show that the ratio of extinction cross section of BDS exhibits a desirable value, indicating that BDS material can act as a potential absorption material. The proposed BTA structure consists of two layers of BDS plates with rectangular apertures arrays separated by a dielectric spacer. Simulations demonstrate that perfect absorption could be effectively realized by optimizing transverse distance between the top and bottom rectangular apertures under TM polarization. Importantly, the absorption spectrum is identical for incident light illuminating from both front and back of the absorber due to the 180° rotational symmetry of the structure in z direction. What’s more, by changing the Fermi level, the absorption spectra of our proposed absorber can be dynamically tuned and the absorptivity still remains high. Therefore, the proposed bidirectional absorber made of 3D BDS can realize double absorptivity and dynamically tunable frequency in a single system. It is believed that this architecture strategy will have a considerable effect and open a new avenue for fabricating ultrahigh-performance BDS-based THz absorbers.
Funding
National Natural Science Foundation of China (11847230, 51671086, 61505052, 61775055); Scientific Research Foundation of Hunan Provincial Education Department (18C0204, 18C0214); China Postdoctoral Science Foundation (2018M642967).
Disclosures
The authors declare no conflicts of interest.
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