Dual symmetry-protected bound states in the continuum enabled by toroidal dipoles in dielectric metamaterials

Bound states in the continuum (BICs) are a special kind of resonant states that remain localized even though they coexist with a continuous spectrum of radiating waves. They have already emerged as an important design principle for creating systems with high-quality ([Formula: see text] factor states to enhance light–matter interaction. Many approaches have been proposed to achieve BICs, but it is still of great challenge to design multiple BICs simultaneously, and especially working at terahertz (THz) frequencies. In this paper, we propose an all-dielectric metamaterial, consisting of four hollow cylinders in each unit cell. We show dual BICs exist in such a simple structure, and as breaking the symmetry via varying the inner radius of two diagonal cylinders, they will turn to quasi-BICs with high yet finite Q-factor. These quasi-BICs are manifested themselves as two new dips in the transmission spectrum, of which the resonance shapes can be well described by the Fano formula with a few fitting parameters. We find the evolution of their Q-factors still follows the simple linear relationship with respect to the inverse square of the asymmetry parameter. Based on the multipole decomposition method, two BICs are further investigated to show different multipole components for them. Interestingly, the higher frequency BIC is closely related to the excitation of toroidal dipole (TD), which will split into two TDs as breaking the symmetry. The proposed metamaterial provides an alternative platform to merge the physics of BICs, Fano, and TD, and to pave the way for potential device applications (since the states of extremely high-Q factor).