Study On High-Q Dual-band Toroidal Metamaterials

Toroidal dipole is a kind of basic electromagnetic dipole like the electric/magnetic dipole. Because of the weaker coupling with incident electromagnetic waves, the toroidal moment is usually neglected in the standard multipole expansion. However, using metamaterials the detectable toroidal dipoles can be designed. In this way, some toroidal metamaterials have been proposed to realize some peculiar effects.In this paper, firstly, by using the numerical simulation method of electromagnetic waves, a dual-band high-Q toroidal metamaterial at microwave frequencies is proposed theoretically. The meta-molecule is composed of two meta-atoms with same shape but different size. The simulation results show that two peaks appear clearly on the transmission spectra of the metamaterials. Increasing the fold number of the meta-molecule, the two peaks are blue-shifted, and their Q values are significantly increased. Detailed studies show each peak comes from the simultaneously excited electromagnetic modes(electric dipole and toroidal dipoles) of each meta-atom in each meta-molecule. The electric fields of the emitted radiation of the two kinds of dipoles are anti-phase, and thus destructively interfere. This suppresses the radiation losses, which leads to the peaks with high Q values. Increasing the fold number of meta-molecule leads to the meta-molecule with a higher rotational symmetry, which leads to good confinement of electromagnetic energy inside the meta-molecule. This contributes to the higher Q value. In addition, the impact of the molecules structural parameters on the spectra are studied. The tunable properties of the metamaterial are also be studied by inserting dielectric with adjustable dielectric constant into the gap of each meta-atom. The solw-light effect of the metamaterial has also been studied by calculating the corresponding group delay.Next, another high Q value toroidal metamaterial but with single response at microwave frequency is proposed theoretically and experimentally. We found only one dip appears clearly on the transmission spectrum. As increasing the fold number of the metamaterial molecule, the dip is blue-shifted, and the dip's Q value increases greatly. Detailed studies show the dip is related to the simultaneously excited electric and toroidal dipoles of each molecule. The emitted electric fields of the two dipoles destructively interfere. This suppresses the radiation losses, which leads to the dip with high Q value. Fold number of the meta-molecule increasing also leads to better confinement of the electromagnetic energy inside each meta-molecule, which leads to the dip with higher Q value. The impact of the meta-molecule structure parameters on the transmission spectra has been studied. And the slow-light effect of the metamaterial is also studied.Our studies may suggest other options to design high Q value metamaterials. The results are significant in physics; Meanwhile, they are of applied value in microwave field. The proposed metamaterials can be designed as high-performance filter, modulator and so on.