Xiangjun Li, Jie Yin, Jianjun Liu, Fangzhou Shu, Tingting Lang, Xufeng Jing, and Zhi Hong*
Abstract
Anapole metamaterials have attracted growing attention in recent years due to their unique nonradiating and nontrivial properties. Although anapole modes have been demonstrated in metamaterials with three-dimensional structures, the design and realization of planar anapole metamaterials in a wide frequency range is still a big challenge. Here we propose and experimentally demonstrate a planar anapole metamaterial consisting of dumbbell-shaped apertures on a stainless-steel sheet at terahertz frequencies. The planar metamaterial can generate a resonant transparency in the terahertz spectrum due to the excitation of the anapole mode. Particularly, the frequency of anapole-induced resonant transparency can be tuned easily in the range of 0.15–0.93 THz by simply varying one geometric parameter of the dumbbell apertures. We anticipate that the resonant transparency in planar anapole metamaterials can be potentially used in filters, sensors, or other photonic devices.1. INTRODUCTION
Metamaterials (MMs) have attracted considerable interest owing to their exotic electromagnetic properties and functionalities that do not exist in naturally occurring materials [1–5]. The desired electromagnetic response in MMs can be achieved by properly tailoring their meta-atoms or molecules by a few key multipole excitations, such as electric and magnetic dipoles. Recently, toroidal multipoles have attracted great attention because they are necessary for the complete multipole representation of an arbitrary radiating source along with the familiar electric and magnetic multipoles [6,7]. The toroidal dipole response in artificial MMs is usually weak and masked by more dominant electric and magnetic multipoles. Therefore, toroidal MMs are initially designed to amplify toroidal moments and suppress the competing electric and magnetic multipoles [8,9]. Fortunately, since the first experimental demonstration of toroidal dipole response in MMs in 2010 [10], there has been great progress in metallic or dielectric metamaterials from the microwave to visible wavelengths [11–18]. Toroidal dipoles offer a deeper insight into the multipolar response of subwavelength optical structures to many optical phenomena such as electromagnetically induced transparency (EIT) [16,19], unconventional optical activity [9,20], negative index of refraction [21], and bound states in the continuum (BIC) [22–25].
Recently, the anapole mode as a radiationless state with nontrivial oscillating current configuration has gained widespread attention, and it can be achieved by the destructive interference between the electrical and toroidal dipoles [26–30]. The nonradiating response of the anapole mode accompanied by enhanced near fields in single nanoparticles has found numerous applications such as in cloaking [31–33], harmonic generation [34–36], nanoscale lasers [37], and Raman scattering enhancement [38]. The anapole mode was first proposed and experimentally demonstrated in microwaves using metallic MMs with three-dimensional (3D) dumbbell apertures in 2013 [39]. By adjusting the quantity and rotation angle of metallic plates, anapole resonant electromagnetic transparency with a high factor was achieved. Recently, a quasiplanar plasmonic MM [40] from a combination of dumbbell apertures and vertical split-ring resonators (SRRs) was designed and fabricated, which exhibited an anapole response in the near-infrared (IR) spectra. However, the fabrication of 3D or quasiplanar structures of MMs is complicated, especially for the visible and terahertz (THz) frequency ranges. Therefore, designing planar anapole metamaterials is expected for realistic applications. Although there are some works discussing the anapole excitation in planar metamaterials in the microwave [41], THz [42–45], and optics [46–49] frequency ranges, the anapole-induced resonant transparency has not been observed. In addition, the tunability of anapole frequency is poor in previous works, and the design and realization of anapole resonance over a wide frequency range remains challenging.
In this paper, we describe the quantitative and experimental demonstration of anapole-induced total resonant transparency in a dumbbell apertured planar metamaterial at THz frequencies. The near-Lorentz transmission line of resonant electromagnetic transparency was achieved through destructive interference between the electric dipole and toroidal dipole as well as effective suppression of the magnetic quadrupole. By optimizing the structure parameters, robust anapole resonance with high transmittance was achieved over the frequency range of 0.15–0.93 THz by adjusting one geometric parameter. The proposed planar anapole metamaterials were fabricated on stainless-steel sheets using a laser micromachining technique, and the measured transmissions of the resonant transparency were in good agreement with the simulations.
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2. STRUCTURE OF THE PLANAR ANAPOLE METAMATERIAL AND SIMULATIONS
Figure 1.(a), (b) Schematic of a planar anapole metamaterial with dumbbell-shaped apertures, which is illuminated by a normally incident plane wave with the electric field along the y axis. The structure parameters are radius , width , separation between the two circular cuts , , , and the thickness of the stainless-steel sheet . (c) Simulated and Lorentz fitted transmission resonance at 0.26 THz for the planar metamaterial when , , and .
3. EXCITATION OF THE ANAPOLE RESONANCE
Figure 2.(a) Surface current in the x-y plane, (b) magnetic field in the x-z plane, and (c) electric field in the x-y plane at the resonance of 0.26 THz for the planar metamaterial. The black arrows represent the direction of the surface current and magnetic field in (a) and (b), respectively. (d) Schematic of the excitation of toroidal dipole and electric dipole in the unit cell; represents the head-to-tail magnetic moment, and j represents the surface current.
Figure 3.(a) Five leading scattered powers of multipole decomposition for the planar metamaterial, where , , , QE, and QM are electric dipole, magnetic dipole, toroidal dipole, electric quadrupole, and magnetic quadrupole, respectively. (b) Phase of Cartesian and . The orange dots represent the phase difference between them. The grey dotted line indicates the location of the corresponding resonant transparency at 0.26 THz.
It is worth mentioning that an optical anapole was achieved in a 3D dumbbell-SRR metallic MM [40]. The destructive interference between and can occur when the MM is made of single dumbbell apertures without SRRs, but the scattered power of the QM is close to that of the , which greatly increases the radiative loss of the resonance. In order to suppress the excitation of the QM, an SRR positioned vertically to the dumbbell aperture was introduced. As a result, the scattered power of the QM was reduced to approximately 1/3 of the ; however, the resonant transparency was not achieved, which may be due to the large material loss. For the simple dumbbell metamaterial we designed for the THz band, the scattered power of QM is effectively suppressed to only 1/10 of , much smaller than that in the quasiplanar structure at the optical band, leading to the enhancement of anapole resonant transparency. This result can be explained by the large difference in the intrinsic ohmic resistance of metal at the optic and THz bands. As the ohmic resistance of the metal in the THz band is much smaller than that in the optic regime, the incident electric field induced pair of counter-rotating surface currents along the two circular cuts of the dumbbell aperture shown in Fig. 2 is greatly enlarged, resulting in the enhancement of the excitation of the , i.e., relative suppression of the QM.
4. ANAPOLE RESONANCE IN A WIDE FREQUENCY RANGE
Figure 4.Transmission spectra of planar metamaterials and corresponding scattered powers of the and at resonance (a), (b) with respect to when and ; (c), (d) with respect to W, when and ; and (e), (f) with respect to , when and . The phase difference between and remains constant at .
Figures 4(c) and 4(d) plot the transmission spectra and scattered powers for the metamaterial at select values of , which are similar to the results shown for select values. As increases from 200 to 300 μm, the transmission peak of the resonance increases quickly and reaches a maximum when anapole resonance is achieved at , while the resonance frequency decreases steadily.
However, the resonance characteristics of the metamaterial with respect to are quite different when and are fixed at 100 and 300 μm. As shown in Figs. 4(e) and 4(f), the resonance frequency shifts from 0.15 to 0.31 THz when increases from 15 to 150 μm, but the resonance peak remains higher than 0.95. It is interesting to note that and not only increase quickly with the increase of but also remain equal in strength and opposite in phase at all times [see Fig. 4(f)]; hence, complete destructive interference occurs in the entire range, leading to anapole-induced total resonant transparency. That is, the anapole-induced resonant transparency can be tuned in the range of 0.15–0.31 THz by simply changing the width of the dumbbell aperture .
Figure 5.Three anapole resonance bands produced by varying when and are fixed. In the case of band A: and ; band B: and ; and band C: and .
5. EXPERIMENTAL RESULTS
Figure 6.Measured (solid line) and simulated (dotted line) transmission spectra of four anapole metamaterials with different values of , 54, 78, and 95 μm, respectively. Inset: microscopic top view of a fabricated planar anapole metamaterial with , , and .
6. CONCLUSION
In conclusion, we quantitatively and experimentally demonstrated the total resonant transparency in a planar anapole metamaterial. The metamaterial consists of dumbbell apertures on a stainless-steel sheet, which was easily fabricated using a laser micromachining technique. The near-Lorentz transmission line of resonant electromagnetic transparency was achieved by destructive interference between the electric dipole and the toroidal dipole, with concurrent suppression of the magnetic quadrupole. Thus, a simple method for achieving robust anapole-induced resonant transparency with high transmittance in the frequency range of 0.15–0.93 THz is provided. The measured transmission results were in good agreement with the simulations. Such planar anapole metamaterials with low ohmic loss at THz frequencies can be potentially used in filters, sensors, or other photonic devices.
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