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Abstract
We proposed a bulk Dirac semimetal (BDS) based metamaterial that consists of two identical vertical BDS rods and two horizontal BDS rods with different lengths. Numerical simulation results show that the proposed structure can realize the tunable multiple plasmon-induced transparency (multi-PIT) effect. The multi-PIT effect is mainly attributed to the introduction of the bonding mode simply by manipulating the lengths of horizontal rods. By changing the Fermi energy of the BDS, the tunable multi-PIT spectrum and tunable multi-band group delay can be achieved. The multi-PIT peaks are also sensitive to the background refractive index and can lead high FOM values of 16, 50.9 and 10.6, respectively. The proposed structure is desirable for designing tunable THz sensors, modulators and slow light devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electromagnetically induced transparency (EIT) is a quantum effect and initially investigated in the atomic system [1,2]. Plasmon-induced transparency (PIT), an EIT-like optical effect based on metamaterial structure, has attracted growing attention in recent years. PIT effect possesses the characteristics of sharp and pronounced spectral response and large group delay which are desirable in metamaterial applications such as sensing [3–5] and slow light [6–12]. Various sophisticated models have been investigated in metamaterials [13–18] to generate PIT effect. As an attractive characteristic of PIT metamaterial, multiple PIT effect is more advantageous in practical applications and usually generated with complex structures [19–21]. However, most of the resonant antennas of multi-PIT are usually made of metal, and cannot be dynamically controlled after produced. Recently, bulk Dirac semimetal (BDS), a matter performs like “three-dimensional (3D) graphene”, has been considered in metamaterial construction [22–26]. The BDS also possesses the dynamical conductivity as the Fermi energy of BDS can be tuned by the method of via alkaline surface doping [27,28]. Different from graphene, the BDS is a bulk material, which is easier for fabrication, more stable and easier to couple with incident wave.
In this paper, we numerically investigate the generation and tunable property of the multiple plasmon-induced transparency in a BDS based THz metamaterial by using the finite-difference time-domain (FDTD) method. The unit cell of the proposed metamaterial consists of two identical vertical BDS rods and two horizontal rods with different lengths on a dielectric substrate, which performs a multi-PIT transmission spectrum when irradiated with THz plane wave. We first investigate the physical mechanism of the multi-PIT effect and get the conclusion that the multi-PIT effect is mainly attributed to the introduction of the bonding mode simply by manipulating the lengths of the horizontal BDS rods. Then we investigate the tunable properties of the multi-PIT spectrum and the slow light effect. By tuning the Fermi energy of BDS from 70 meV to 60 meV, the multi-PIT windows undergo an obvious red shift with the PIT peak intensities remaining unchanged, and large positive values of group delays indicating slow light are obtained and red shift with the multi-PIT windows. Additionally, we also investigate the spectral sensitivity of the structure with the Fermi energy of 70 meV. Large values of figure of merit (FOM) are acquired by the multi-PIT peaks, making the proposed structure desirable for multi-frequency sensing application.
2. Structure design and simulation method
Figure 1 illustrates the unit cell of the proposed metamaterial, which consists of two identical vertical BDS rods and two BDS rods with different lengths on a dielectric substrate with a refractive index of 1.5 [22]. The geometric parameters of the structure shown in Fig. 1 are ${p_x} = 120\mu m$, ${p_y} = 90\mu m$, ${a_1} = 34\mu m$, ${a_2} = 38\mu m$, $b = 84\mu m$, ${w_1} = 8\mu m$, ${w_2} = 10\mu m$ and $s = 15\mu m$. The gaps between each two BDS rods are kept as $g = 8\mu m$ and the thickness of the BDS rods are $0.2\mu m$. The dynamic conductivity of the BDS is expressed as [22]
For numerical investigation of the proposed BDS metamaterial, we use the finite-difference time-domain method (FDTD solutions, Lumerical Inc., Canada) to calculate the transmission and plasmonic properties. In the simulations, the substrate is assumed to be semi-infinite. We apply periodic boundary conditions in x and y directions, and perfectly matched layer (PML) absorbing boundary condition in the z directions which absorbs light waves with minimal reflections. The x polarized THz plane wave irradiates along the z direction from the air side.
3. Results and discussion
We assume the initial Fermi energy of BDS is 70 meV. Figure 2(a) shows the two transmission spectra of the proposed structure with different rod length ${a_1}$ (the gaps between each two BDS rods are kept as $g = 8\mu m$). The black solid line and the red dashed line correspond to the transmission spectra for ${a_1} = 34\mu m$ and ${a_1} = 38\mu m$, respectively. It can be observed that when the lengths of the two parallel rods are the same, i.e., ${a_1} = {a_2} = 38\mu m$, the unit cell of the proposed structure can be simplified as one vertical rod with one horizontal rod, only the dipole resonance of the parallel rod is excited, resulting in a broad resonance dip in the transmission spectrum. When the rod length ${a_1}$ is reduced to $34\mu m$, three transparency windows are generated at the frequencies of around 1.44 THz, 1.51 THz and 1.59 THz. The corresponding z-component electric field distributions are shown in Figs. 2(b), 2(c) and 2(d). We can see that the bonding mode on the two horizontal rods is excited all the time at the three frequencies. Moreover, two out-phase quadrupole modes on the vertical rods are excited at 1.44 THz, two in-phase quadrupole modes on the two vertical rods are excited at 1.51 THz and the resonance on the vertical rods at 1.59 THz are relatively weak.
Fig. 2. (a) The transmission spectra of the proposed metamaterial with a1=34 μm (black solid line) and a2=38 µm (red dashed line). The z-component of electric field distributions at the frequencies of (b) 1.44 THz, (c) 1.51 THz, (d) 1.59 THz corresponding to the transmission spectrum for a1=34 µm.
To further explore the generation of the multiple PIT windows, we investigate the performance of the proposed structure with only the two parallel rods ${a_1} = 34\mu m$ and ${a_2} = 38\mu m$. The transmission spectrum is shown in Fig. 3(a), in which two transmission dips and a transparency peak are generated. The z-component electric field distributions at the dip and peak frequencies are shown in Figs. 3(b), 3(c) and 3(d), from which we can conclude that the reduction of rod length ${a_1}$ from $38\mu m$ to $34\mu m$ will cause the bright-bright mode coupling of the two horizontal BDS rods [22,30,31], and result in a transparency window at the frequency of 1.58 THz. Thus, similar to the case shown in Fig. 3, the transparency window around 1.59 THz in Fig. 2(a) is mainly attributed to the bright-bright mode coupling between the two horizontal BDS rods. Then the quadrupole resonances on the vertical BDS rods are excited by the bonding mode of the horizontal BDS rods, and the hybrid mode of vertical quadrupole mode and the horizontal bonding mode serve as the dark mode, resulting in the two transparency windows around the frequencies of 1.44 THz and 1.51 THz in the multi-PIT spectra in Fig. 2.
Fig. 3. (a) The transmission spectrum of the structure with only the two parallel rods a1=34 µm and a2=38 µm, the inset show the unit cell of the corresponding structure. The z-component of electric field distributions at the frequencies of (b) 1.51 THz, (c) 1.58 THz, (d) 1.62 THz.
The optical properties of BDS can be modulated due to its dynamical conductivity, which can be achieved by changing the Fermi energy via alkaline surface doping [27,28]. When changing the Fermi energy, the electron density in BDS is changed, resulting in the change of the resonant frequency. Figures 4(a), 4(b) and 4(c) show the transmission spectra of the proposed structure under different Fermi energies. It is clear that by a small decrease in the Fermi energy, the multiple PIT effect can easily undergo a red shift with the PIT peak intensities remaining unchanged. Moreover, the PIT effect is always accompanied by the strong dispersion of the transmission phase, which leads to slow light effect. Here we investigate the slow light effect by introducing the group delay, which can be expressed as [32]
where $\varphi$ is the transmission phase shift and $\omega$ is the angular frequency. The transmission phase shift and group delay of the proposed structure with different Fermi energies are shown in Figs. 5(a) and 5(b), respectively. Large positive group delays indicating slow light are obtained around the PIT windows, and the tunable multiple pass bands of group delay can be achieved by changing the Fermi energy.Fig. 4. Transmission spectra with different Fermi energies of (a) 70 meV, (b) 65 meV and (c) 60 meV.
Fig. 5. (a) The simulated transmission phase shift and (b) group delay of the multi-PIT metamaterial with the decreasing of the Fermi energy of BDS.
In addition, PIT effect also has the potential in sensing application since the transparency peak is sharp and sensitive to the change of the refractive index of the surrounding medium. Figures 6(a), 6(b) and 6(c) show the PIT spectra with different refractive indices, where ${E_F} = 70meV$. As the refractive index increasing from 1 to 1.4, the PIT spectrum undergoes an obvious red shift. Here we introduce figure of merit (FOM) [25], which is defined as the sensitivity value divided by the full-width at half-maximum (FWHM), to evaluate the sensing ability of the proposed multiple PIT structure.
Fig. 6. The simulated transmission spectra with different background index of (a) 1.0, (b) 1.2 and (c) 1.4.
4. Conclusions
In summary, we have numerically investigated the tunable multi-PIT effect in a BDS based THz metamaterial by using the finite-difference time-domain (FDTD) method. The proposed metamaterial possesses multi-PIT transmission spectrum in the THz region. The generation of the multi-PIT effect is mainly attributed to the introduction of the bonding mode simply by manipulating the lengths of the horizontal BDS rods. The tunable multi-PIT windows and large positive values of group delays can be achieved by tuning the Fermi energy of BDS. Moreover, Large values of FOM can be acquired by the multi-PIT peaks, which is desirable for multi-frequency biosensing. We believe that the proposed structure can be used for designing tunable THz sensors, modulators and slow light devices.
Funding
National Natural Science Foundation of China (NSFC) (11474041); Scientific and Technological Developing Scheme of Jilin Province (20180101281JC); “135” Research Project of Education Bureau of Jilin Province (JJKH20190579KJ); “111” Project of China (D17017).
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