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Abstract
Plasmonic metamaterials enable manipulation of light at subwavelength scales and exhibit unique optical functionalities. However, the realization of high-performance, large-range, and dynamically tunable optical absorbers based on plasmonic metamaterials remains challenging. Here, we propose and demonstrate a continuously tunable absorbers consisting of a zigzag array of bulk Dirac semimetals (BDS) meta-atoms and a metal reflector spaced by insulator layers. This structure exhibits a collective resonance formed by the electric dipole modes polarized along the long axis of each individual meta-atom, which allows us to precisely control this resonance frequency by fine-tuning the unit cell geometry and the Fermi energy levels of the BDS. In addition, the related physical mechanism behind this complete absorption can explained by employing coupled-mode theory (CMT) and mode-expansion theory (MET). Our results may arouse the investigations of the tunable metamaterials device based on the BDS.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Subwavelength-scale manufacturing opens up new avenues for the production of new structures, such as metamaterials, which can lead to field localization and peculiar light-matter interactions. Metamaterials, in particular, on which the surface plasmon-polaritons (SPPs) are generated via a resonant interaction between free electrons in a metal and electromagnetic waves, have emerged as the basis for many fascinating applications, such as chemical and biomedical sensors [1,2], infrared detectors [3,4] and absorbers [5–11].
So far, different configurations of metamaterials have been used to implement localized surface plasmon (LSP) absorbers with a large spectral shift, including nanorods [12], nanodisks [13], and rectangle structure [14] etc. More complex plasmonic absorbers based on specific physical mechanisms have been widely investigated [15–17]. In 2014, Wang et al. [18] theoretically studied a frequency continuous tunable perfect absorber based on metamaterials with an absorption intensity greater than 99% is achieved. Shrekenhamer et al. [19] reported an electronically tunable metamaterials absorber by combining the variable properties of liquid crystals with metamaterials. Zhang et al. [20] has investigated a polarization-independent metamaterials absorber with a tunable resonant frequency by using graphene wires. By adjusting the bias voltage of the graphene, the absorption peak frequency can be actively adjusted at a lower terahertz frequency without reducing the absorption. However, in practical applications, to precisely fabricate graphene in experiments is very difficult due to its single-atom-layer thickness. This limits their use in electromagnetic radiation protection and optics. In addition, the electromagnetic properties of absorbers using conventional materials strongly depend on the size, shape, and periodicity of the artificially engineered photonic materials, which makes the design very difficult and limits their development.
Recently, 3D Dirac semimetals—a 3D graphene analog, also known as the bulk Dirac semimetals (BDS)— has attracted great attention [21–25]. Notably, BDS films combine the properties of both metal and dielectric: at frequencies lower than Fermi energy, SPPs can propagate along the surface of BDS films, while at higher frequencies, the dielectric response becomes dominate [26]. Due to its metallic properties at terahertz frequencies, BDS can be considered a ‘Salisbury shield’ for absorbers [27], which preventing transmission and is more convenient than graphene in tunable absorber applications. In addition, the conductivity of the BDS can also be dynamically adjusted by changing the Fermi energy of the BDS by alkaline surface doping [28] or electrical bias [29–31]. In contrast, based on the zero-band gap in upper and lower band of Dirac cones, graphene possesses excellent optical properties and surface conductivity. However, this characteristic also limits its utility in applications, which may require strong light–matter interactions [32]. These features ensure that BDS can be considered as a new material for tuning frequencies and has broad potential in the evolving fields of absorbers, sensors, imaging and communications.
In this paper, we design a large-range, continuously tunable perfect terahertz absorber based on BDS-insulator-metal (BIM) stacked triple-layer structure. The effect of geometrical parameters on the absorption spectra is simulated by using the finite-difference time-domain (FDTD) method and is theoretically analyzed by the mode-expansion theory (MET). A large-range of absorption spectral can be realized by scaling the lateral geometrical parameters of the structure. More importantly, the resonance wavelength can be further controlled by fine-tuning the Fermi energy level of the BDS layer while maintaining high absorption performance. Consequently, our proposed structure provides a new perspective for the design of tunable absorbers and may be a promising application in fields related to photovoltaic technology.
2. Design and materials
The structure under consideration is schematically depicted in Fig. 1. The geometrical parameters in a unit cell are defined as Px = 64 µm, Py = 38.4 µm, A = 32 µm, B = 12.8 µm, h = 7 µm, and t = 5 µm, with an orientation angle of θ = 18°. The thicknesses of BDS layer is 0.5 µm. This unit cell consists of a zigzag BDS array and a continuous metal film separated by a SiO2 spacer. One advantage of this design is that the absorption peak can be tuned to desired resonance frequency by scaling the elliptical geometry parameters (size and period) and fine-tuning the Fermi level of the BDS [33–35]. The bottom gold layer is used as a back reflector, which minimizes light transmission. In this way, perfect absorption can be obtained when the reflection close to zero [36]. The structure is illuminated by a normally-incident plane wave with electric field polarized along the x direction.
Fig. 1. (a) Schematic diagram of the proposed metamaterials structure. (b) Schematic of the BDS layer with a zigzag array.
The BDS film is modeled by the Kubo formalism in the random-phase approximation (RPA). If we only consider longitudinal operations, at the low-temperature limit T << EF, the local dynamic conductivity σ of BDS layer can be approximately written as:
The proposed structure is performed using Lumerical finite-difference time-domain (FDTD) Solutions. In our simulation, a unit cell that is periodic along the x and y axes is selected, and a perfectly matched layer (PML) is applied to the top and bottom of the unit cell. Broadband plane waves are launched to the unit cell along the z direction, and the reflection is collected with a power monitor placed behind the radiation source. Electric and magnetic field distribution cross-sections are detected by a 2D field profile monitors in x−y plane and x−z plane, respectively. The relative dielectric permittivity of the SiO2 is assumed 2.1025 [39]. The BDS is modeled as a conductive material with complex permittivity expressed as [27]:
Fig. 2. The real (a) and the imaginary (b) parts of the permittivity for BDS as a function of frequency with the different Fermi energy levels.
3. Results and discussions
Figure 3(a) presents the absorption spectra of the proposed structure. The red curve is obtained from the FDTD simulation. The setting of the parameters is consistent with Fig. 1. In order to ensure that the BDS exhibits metallic properties (Fermi energy > resonance frequency), the Fermi energy of BDS can be set to 100 meV. Since the bottom layer of the proposed structure is optically thick, the transmission T ($\omega$) is close to zero. Therefore, the simple formula $A = 1 - R - T \;(T = 0)$ can be used to calculate the absorption ($A$) of the structure, where R and $T$ represent reflection and transmission, respectively. The maximum absorption reaches over 99.5% at wavelength of 92.52 µm. In addition, since the structure we propose is a one-port single-mode resonator, it can be well described by CMT when frequencies around a particular resonance (${\omega _0}$) [40]. This theory can account for both enhancement and suppression of absorption. We briefly review this theory as follows [40,41]:
Fig. 3. (a) FDTD simulated (red curve) and CMT fitted (blue dots) absorption spectra for the proposed structure. Electric field intensity (z direction) profile of the upper (b) and lower (c) layers of the unit cell. (d) The magnetic field (y direction) profile for the absorber at the resonance frequency. p1 and p2 (White arrow line) indicate the electric dipole moments of the individual resonators. The dielectric spacer and the metallic film boundaries are indicated by the black-dotted line.
The absorption $A$ can be obtained
In order to better understand the nature of our perfect absorber, the electric field distribution is shown in Figs. 3(b) and 3(c) for the top and bottom layers of dielectric spacer, respectively. When the localized surface plasmon resonance (LSPR) is excited, an anti-parallel electric dipole moment is formed in the upper and lower layers along the long axis of each individual meta-atom. In fact, due to the anti-parallel electric dipole moment resulting in a magnetic moment related to as magnetic resonance [42,43], which will result in an increase in the local magnetic field between the BDS and the metal layers, as shown in Fig. 3(d). Consequently, electromagnetic energy can be highly confined in the SiO2 spacer, and no electromagnetic waves are reflected back. These analyses prove that there is almost perfect absorber when the resonance is excited.
In addition, the effect of the geometrical parameters (orientation angle $\theta$ and spacer thickness h) on the absorption spectra are shown in Figs. 4(a) and 4(c). To validate our simulation results, we derived two analytical formulas that relate ${Q_a}$ and ${Q_r}$ to our proposed metamaterials structure details. ${Q_a}$ and ${Q_r}$ are two dimensionless parameters. These analyses can help design some structural design and fabrication.
Fig. 4. (a) and (c) Absorption spectra of the simulated structure as a function of the orientation angle $\theta$ and spacer thickness h, respectively. The geometries are the same as the one simulated in Fig. 1, except for the changing orientation angle and spacer thickness. (b) and (d) ${Q_r}$ and ${Q_a}$ of the simulated structure with changing orientation angle and spacer thickness obtained by analytical calculations (lines) based on Eqs. (7–9) and retrieved from FDTD simulated spectra (symbols), respectively.
Under normal incident plane wave illumination, the dominant component of the dipole moments are perpendicular to the incident field polarization Ex, as shown in Fig. 3(b) (White arrow line). Due to the anti-symmetric distribution of the components (P1y = −P2y), the out-coupling with the plane wave of Ey polarization is forbidden [44]. Therefore, only the x-direction component is nonzero (P1x = P2x). Herein, we use mode-expansion theory (MET) [45,46] to further calculate the previously mentioned CMT. The radiation quality factor of the system is expressed as:
The absorption quality factor of the system is expressed as:
In the FDTD simulation, we can easily obtain these two parameters ($A, {\omega _0}$) from the absorption spectrum. After that, we can use Eq. (6) to fit the absorption spectral line to obtain two important parameters ${Q_r}$ and ${Q_a}$. From the results of analytical calculations and FDTD simulations shown in Figs. 4(b) and 4(d), we can see an excellent consistency.
As shown in Fig. 4(a), the resonance frequency oscillates as the rotation angle $\theta$ increases, and the peak absorption decreases, which can be understood from Eqs. (7–9). As the rotation angle $\theta$ increases, $Q_{r}$ changes slowly and $Q_{a}$ drops sharply. The distinct $\theta$ dependences of two $Q$ factors are clearly shown in Fig. 4(b). Physically, the change in $Q_{r}$ is attributed to the near-field coupling between the BDS and the gold layer, while $Q_{a}$ depends on the lateral structural parameters. According to the CMT theory mentioned earlier, we can know that when $Q_{a} = Q_{r}$, the absorption can reach the maximum. As the rotation angle $\theta$ increases, the relative sizes of $Q_{a}$ and $Q_{r}$ increase, so the absorption intensity decreases.
Figure 4(c) shows the effect of another important parameter spacer thickness h on the absorption performance of the proposed system. When increasing the thickness of spacer, the resonant frequency of absorption peak tends to exhibit a red-shift, and the absorption decreases. This can be understood again by calculating the values of $Q_{r}$ and $Q_{a}$ by Eqs. (7–9). As h increases, $Q_{r}$ is almost inversely proportional to h, which can be attributed to changes in near-field coupling losses. $Q_{a}$ increases with h. The distinct h dependences of two Q factors are clearly shown in Fig. 4(d). To achieve maximum absorption performance, there exists a trade-off between nearfield coupling loss and the intrinsic losses in the absorber design.
4. Application
In general, the resonance wavelength of the proposed absorber can be adjusted in two ways, one is to adjust the structural parameters, and the other is to adjust the Fermi level of BDS. However, the adjustment of conventional structural parameters and Fermi energy often causes slight detuning [36], resulting in a decrease in peak absorption. Here, we deliberately chose the zigzag metamaterials array to achieve a large range, high performance absorber by adjusting the scaling factor S. In FDTD simulations, structural parameters are determined by particle swarm optimization in the software package. Spectral properties are presented as a function of scaling factor S, which is a geometric parameter related to the period, the long and short axes lengths of the ellipse. When S is increased from 0.6 to 1.2, the resonance positions continuously changes in the spectral range of 72.2 µm to 130.3 µm, and the average absorption reaches 98.5%. This high performance absorption result is shown in Fig. 5(a). The decrease in absorption for wider range is attributed to the relative decrease of intrinsic loss rate caused by the lateral structural parameters.
Fig. 5. (a) Absorption spectra of the different scaling parameters S of the structure shown in Fig. 1. Resonance wavelength is controlled by scaling the unit cell lateral dimensions. The geometrical parameters are Px = 64 µm, Py = 38.4 µm, A = 32 µm, and B = 12.8 µm, with the fixed structure parameters h = 9 µm, t = 5 µm, Ef = 100 meV, and orientation angle θ = 18°. (b) Absorption spectrum of the structure shown in Fig. 1 as a function of the BDS Fermi energy. (c) Resonance wavelength (blue line) and peak absorption (red line) as a function of the Fermi level of the BDS layer.
One of the central features of our zigzag metamaterials structure is the tunability of the spectral resonance wavelength. Therefore, for certain structural parameters, the adjustable performance of the metamaterials depends on the size of the BDS Fermi energy. In general, the adjustment of Fermi energy results in a decrease in absorption because the change in Fermi energy results in a change in the permittivity of the material, as shown in Fig. 2. For the proposed structure, since the influence of BDS Fermi energy on the resonance frequency is much greater than the absorption, we can precisely control the resonance wavelength by appropriately adjusting the Fermi energy. As shown in Figs. 5(b) and 5(c), the Fermi energy of BDS increase from 80 to 105, the resonance wavelength has a redshift from 95.7 µm to 99.6 µm, and the absorption efficiency remains unchanged.
Due to the flexibility of our metamaterials design, it can be applied to a variety of advanced electronic equipment and optics. To illustrate this concept, first, select the appropriate scaling factor S for manufacturing, and then fine-tuning the BDS Fermi energy to achieve precise control of the resonance wavelength and maintain high absorption. Similarly, for a wider range of spectral regions, the peak of the absorber can be maximized by varying the thickness of the spacer layer.
In the preceding discussions, all results were based on normal incident light. In practical applications, the proposed absorber should ensure high absorption over a relatively wide range of incident angles. We fix the parallel component of the wave vector of the incident plane wave to the x direction (the electric field parallel to the plane of incidence), but change the angle of incidence of the input beam. The absorption peak of the proposed structure varies with the incident light wavelength and the angle of incidence, as shown in Fig. 6. We noticed that when the incident angle changes from 0° to 30°, the resonant wavelength of the absorber exhibits a slight red shift, and the absorption hardly changes. The results show that the proposed absorber is less affected by the incident angle within a certain range, and can maintain strong magnetic resonance under oblique incidence. The characteristics of the proposed absorber may be important for many practical applications.
5. Conclusion
In summary, we have demonstrated a novel zigzag BDS metamaterial-based perfect absorber with absorption near 100% in the terahertz range. We also numerically and theoretically analyzed the change in absorption peaks for different angle of rotation and the thickness of the spacer. More importantly, we can achieve precise control of the absorption peak over a wide range by scaling the scale factor S and fine-tuning the BDS Fermi energy. Additionally, the proposed absorber can tolerate oblique incidence of the incident source. Thus, the proposed structure can be used in applications related to absorbers, color filters, and optoelectronic devices in the terahertz range.
Funding
National Natural Science Foundation of China (61505052, 61775055).
Disclosures
The authors declare no conflicts of interest.
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