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In this work, we design and numerically investigate dual quasi-bound states in the continuum (quasi-BICs) in all-dielectric metamaterial consisting of a silicon stair-like resonator by breaking the symmetry in the direction perpendicular to the metamaterials. By introducing this unique degree of freedom beyond the in-plane symmetry, one can observe the evolution from BICs to quasi-BICs and efficiently control the Q-factors and frequencies of quasi-BICs. The charge density distribution, far-field radiations and near-field distributions demonstrate the dominant electric quadrupole responses in such two quasi-BICs. Further, we examine actively tunable response of such two quasi-BICs with respect to a change in the Fermi energy of graphene layer, indicating the potential applications in designing quasi-BIC-based modulators, filters and sensors.

Dual quasi-bound states in the continuum in graphene/dielectric hybrid metamaterial from out-of-plane symmetry protection