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Abstract
The toroidal dipole is implemented by abundant and bio-friendly water with a high dielectric constant in the microwave range. A Fano resonance, with high Q-factor up to 152, resulting from enhanced fancy toroidal dipole could be stimulated at 1.65 GHz. Analysis of the induced current and near- and far-field shows that energy can be concentrated in distilled water, and the intriguing toroidal dipole plays a decisive role in resonance. Under different size parameters and conductivity of water-based metamaterial, the toroidal excitation and its influence on transmission characteristics are discussed. The toroidal dipole excited in distilled water might be of great significance for designing ultra-sensitive sensors, absorbers, and slow-light devices.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Toroidal dipole, with special charge-current configuration that the currents flowing along the meridians of the torus, possesses the property of local field concentration. It was presented by Zel’dovich to explain the parity violation in 1958 [1] and firstly experimentally demonstrated in microwave range by N. I. Zheludev et al. using sub-wavelength metamaterial in 2010 [2]. Utilizing the designable nature of molecular structures, toroidal dipole can be extremely enhanced to the detectable level even much higher than the traditional electric and magnetic dipole. The strengthened toroidal and suppressed electric dipole in metamaterial could be introduced in ultrasensitive sensing [3–6], analogue electromagnetic induced transparency [7–9], absorber [10,11], circular dichroism [12], and so on [13–23]. In particular, Fano resonance based on the strong confined field property of toroidal metamaterial has attracted great attention of scientific researchers [24–27]. Subsequently, all-dielectric metamaterial is of great interest to avoid the dissipation loss of metallic structures [28–33]. In addition, all-dielectric toroidal dipole can concentrate energy inside the structure, which is more conducive to the energy confinement. Ceramic materials with high dielectric constant are usually used in all-dielectric metamaterial at microwave range [34,35]. However, ceramic is generally brittle, and can only be processed into simple structures, which is not conducive to structural diversity.
Water, a bio-friendly, low-cost, and abundant material, is easy to obtain and has huge potential and broad application prospect. The dielectric constant of water is dependent on temperature [36,37], making it a good choice for studying electromagnetic phenomena and designing tunable metamaterials [38]. Another advantage of water with high permittivity in microwave range is strong plasticity. Introducing 3D printing technology, the structure of water-based metamaterial can be flexible, complex, and feasible [39]. It greatly enriches the diversity of water-based metamaterials. In recent years, some toroidal dipole metamaterials have taken advantage of these properties of water. In 2017, I. V. Stenishchev et al. demonstrated experimentally for the first time that toroidal metamaterial can also be realized by water-based material [40]. Two kinds of water-based metamaterial were proposed and implemented toroidal dipole response at microwave frequency. In 2021, E. Takou et al. proposed two thermally tunable metamaterials to study the temperature tolerance of anapole, a state of resonance in which toroidal dipole destructive interferes with electric dipole [41]. The enhanced toroidal of water-based structures have been experimentally verified at different temperatures of water. While, the high Q-factor Fano resonance achieved by water-based toroidal metamaterial at microwave range is rare.
In this paper, a water-based Fano resonances toroidal metamaterial has been presented and verified in microwave frequency. The subwavelength structure which introduces distill water with high permittivity and excellent plasticity could achieve high Q-factor Fano resonance. According to scattered power of multipoles and parameter analysis, toroidal dipole makes the most important contributions at the resonance frequency. From near-field distribution, it can be known that the energy is mainly concentrated in the interior of the structure, which is favorable for the enhancement of light-matter interaction. It may offer a new path for the application of water-based toroidal metamaterials in tunable ultra-sensitive sensors and slow-light devices.
2. Design and fabrication
Electromagnetic properties of presented water-based toroidal metamaterial are simulated with Computer Simulation Technology (CST). The structures are arranged periodically along the x and y directions, and the z axis is an open boundary. When linearly y-polarized electromagnetic wave normally irradiates the metamaterial, the enhanced toroidal dipole in disc-shaped distilled water could be excited and produced strong Fano resonance.
The proposed water-based toroidal metamaterial is shown in Fig. 1(a), in which the light gray part is the resin disc-shaped cavity structure, which is fabricated by 3D printing technology. Resin with dielectric constant of 1 and negligible loss is a common material for 3D printing. Because of the flexibility of the processing technology, it not only greatly reduces the difficulty of model implementation, but also provides more possibilities for the diversity of metamaterial design. The structural parameters of unit cell in Fig. 1(b) are: period P = 52 mm, overall thickness of unit cell h = 7 mm, thickness of water h1 = 4 mm, radius of disc-shaped cavity r = 25 mm. And, cavities are connected by interconnected pores with width w = 6 mm and length L = 1 mm.
Fig. 1. Schematic diagram of toroidal metamaterial. (a) Schematic view of water-based metamaterial composed of disc metamolecules. (b) Unit cell with geometrical parameters. (c) The experimental environment and the photograph of 3D printing sub-wavelength structure with resinous material.
Considering the feasibility of sample fabrication and measurement, the entire water-based metamaterial is composed of 10*10 unit cells arranged periodically in the x- and y-axis, as shown in inset of Fig. 1(c). The blue part is distilled water injected into the disc-shaped cavities from a row of square holes left on one side of the water-based metamaterial. When the frequency is below 4 GHz, the resin disc-shaped cavity structure is almost lossless and the relative dielectric constant of distilled water is approximately 78 at room temperature of 20°C. The Sharp Fano resonance caused by fancy toroidal dipole has been experimentally verified with Agilent PNA E8362B (a vector network analyzer) and double ridged horn antenna in anechoic chamber, as revealed in Fig. 1(c).
3. Analysis and discussion
Fano resonance with asymmetric line shape usually results from the interference between narrow discrete state with less energy radiation, and broad spectral line, a wide spectrum of radiation formed by the electromagnetic wave that directly passes through the structure. The transmission spectrum of water-based toroidal metamaterial structure is displayed in Fig. 2, in which the simulation and experimental results are represented by the red solid and black dashed line respectively. From simulation curve, an obvious asymmetric sharp Fano resonance with peak value of 0.995 in toroidal dipole metamaterial could be excited by linearly polarized electromagnetic wave at 1.65 GHz. The fitting result of Fano resonance could be calculated by Eq. (1) and displayed in inset of Fig. 2.
Fig. 2. Simulated (red solid line) and measured (black dashed line) transmission spectra of the toroidal metamaterial. The fitting result of Fano resonance (blue dot in inset).
The electromagnetic response of the 3D printing metamaterial has been qualitatively analyzed through induced current, electric and magnetic field, so as to have a deeper understanding of the physical mechanism in toroidal dipole resonance. According to Fig. 3(a), the induced current in the middle of the water disk is obviously stronger than the sides at 1.63 GHz, accompanied by high radiation loss derived from strong electric dipole. Most of the incident wave power has been scattered, which could be proved by the weak near-field distribution in Fig. 3(b), (c), and (d). So, the transmission spectrum down to the valley at 1.63 GHz. The induced current, as revealed in Fig. 3(e), generated in water at 1.65 GHz is stimulated by the normally incident electromagnetic wave. Two current loops with opposite flowing directions can be formed in water-based structure. Therefore, vortex magnetic field displayed in Fig. 3(f) could be stimulated to implement enhanced toroidal dipole along y-axis. The majority electric and magnetic field, displayed in Fig. 3(g) and (h), are concentrated within distilled water at Fano peak, which can greatly reduce the radiation loss.
Fig. 3. The distribution of current and field of water-based metamaterial at 1.63 GHz and 1.65 GHz. (a), (e) The current in dielectric materials. (b), (f) The magnetic field distribution. (c), (g) The electric field intensity in the x-z plane and (d), (h) The magnetic field intensity in the x-y plane.
The existence of toroidal dipole could be verified by the field distribution of all-dielectric metamaterial. For investigate the role of each multipole at the vicinity of sharp Fano resonant peak, the scattered power of multipoles has been calculated by Cartesian multipole decompositions.
In the above Eqs. (2)–(6), P, M and T represent the electric, magnetic and toroidal dipole moment. $Q_{\alpha ,\beta }^{(e )}$ and $Q_{\alpha ,\beta }^{(m )}$ are electric quadrupole and magnetic quadrupole moments. And j is the current density, r and c stands for the displacement vector and the speed of light, ω represents the angular frequency.
Equations (7)–(9) represent the scattered power of electric, magnetic and toroidal dipole. Equations (10) and (11) are the far-field scattered power of electric and magnetic quadrupoles.
In Fig. 4, only three strongest multipoles have significant influence on the transmission spectrum, and the power of other multipoles is just so small that can be ignored. The scattered power of toroidal dipole IT rises rapidly. Meanwhile, the IP with the strongest spectrum range is strongly suppressed. The radiation loss of water-based metamaterial attains the maximum value when the parasitic magnetic quadrupole reaches the top and electric dipole has not down to the bottom in the vicinity of Fano dip. Hence, the transmission spectrum shows a valley at 1.63 GHz. Whereafter, the scattered power of electric dipole sharply drops down to the minimum, and toroidal dipole plays the key role among all the multipoles which is enhanced to be several orders of magnitude higher than traditional electric dipole. Because of the property of toroidal dipole, the energy has been concentrated around the water-based structure instead of scattered. So, the incident wave can pass through the structure almost lossless, and the transmission peak can reach 0.995 at 1.65 GHz. While, the magnetic quadrupole derived from the reverse flow current suppresses the ultra-high Q-factor of the structure.
Fig. 4. The scattered power of multipoles stimulated by normal incident wave in water-based metamaterial.
The relationship between enhanced toroidal dipole and the transmission characteristic of the proposed water-based metamaterial has been analyzed under different structural parameters. Figure 5(a) shows the effect of different disc spacing L on transmittance. When L increases from 1 to 3 mm, the transmission peak has a slight blue shift indicated in the enlarged illustration. With the growth of spacing, the coupling between structural units weakens gradually, and the toroidal dipole in the structure decreases obviously. Therefore, the field strength is decreased significantly, which can be reflected by the trend in Q-factor of the transmission curve in Fig. 5(b).
Fig. 5. As the length L increases (a) the blue shift of transmission curve and (b) the relationship between Q-factor and toroidal dipole.
Figure 6(a) displays the transmission curve of water-based toroidal metamaterial under different width of element connection w. Obviously, the change of w has little effect on the transmission spectrum of metamaterials. So, the structure is tolerant of this term due to the insensitivity to width. The variation of transmission spectrum with the change of water thickness h1 is shown in Fig. 6(b). When h1 increases from 3 to 5 mm, the Fano peak displays an obvious red shift as a result of the increase of effective refractive index.
Fig. 6. Transmission spectra of sub-wavelength structure with different (a) width w and (b) thickness of the water h1.
In the simulation, the conductivity of distilled water has been set to 10−4S/m, which can be regarded as a medium in a non-conductive state. Two pairs of reverse induced currents generated in water form magnetic dipoles connected head-to-tail, which constitutes an enhanced toroidal dipole. In Fig. 7, conductivity is increased from 10−4S/m to 10−1S/m to analyze the important effect of conductivity on toroidal scattered power and transmission curve. When conductivity increases, the scattered power of toroidal dipole drops significantly and the transmittance decreases, which proves that transmission peak is produced by toroidal dipole resonance.
Fig. 7. The influence of water conductivity on (a) transmission peak and (b) the variation of scattered power in toroidal dipole.
4. Conclusions
In short, a toroidal metamaterial consisted of disc-shaped distilled water with high permittivity is proposed based on fantastic electromagnetic properties of toroidal dipole. Through optimization parameters, a sharp Fano resonance with amplitude up to 0.995 could be excited at 1.65 GHz. By analyzing the current density, electromagnetic field distribution and scattered power in far-field, it could be known that the novel toroidal dipole is the leading role at the Fano resonance peak. The effects of different parameters and conductivity of water on transmission characteristics are analyzed. The intriguing water-based toroidal structure may provide a new path for the ultra-sensitive sensors, slow-light devices, and so on.
Funding
National Natural Science Foundation of China (61741104); Science and Technology Program of Guizhou Province (ZK[2021]306); Guizhou Education Department Youth Science and Technology Talents Growth Project (KY[2017]031, KY[2020]007).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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