Bound states in the continuum in a dielectric metamaterial with symmetry breaking in two dimensions

Bound states in the continuum ( BICs ) , since their ultra-high quality ( Q )-factor to extremely enhance light matter interactions, have attracted extensive interest very recently. As a typical category, symmetry-protected BICs are predictive and easily manipulated by using structure's symmetry. However, most of the studies focus only on the structures with symmetry breaking in one dimension, in which one BIC will emerge and exhibit an inverse square relationship to asymmetry parameter. The structures with symmetry breaking in two dimensions remain rather unexplored. We here propose a dielectric metamaterial made of a square lattice of disks with a small hole. As moving the hole away from the center, the in-plane inversion symmetry can be broken either in one dimension or in two dimensions. As usual, a symmetry-protected BIC dominated by magnetic dipole ( MD ) occurs in the fi rst case. In the second case, symmetry-protected dual BICs arise, consisting of the usual MD- dominated BIC and a new electric dipole ( ED )-dominated BIC that is in cross-polarization to incident wave. The new BIC possesses an even higher Q-factor, which can also be continuously tuned via the position of the hole. Besides the structural modulation, we show the polarization angle of incident wave will act as another degree of freedom for designing symmetry breaking in two dimensions, where the similar symmetry-protected dual BICs are observed as well. Our work provides an alternative scheme for engineering multiple BICs and improving Q-factor, which may pave the way for practical device applications.