Bifurcation of bound states in the continuum in periodic structures

In lossless dielectric structures with a single periodic direction, a bound state in the continuum (BIC) is a special resonant mode with an infinite quality factor (Q factor). The Q factor of a resonant mode near a typical BIC satisfies Q∼1/(β-β _∗)², where β and β _∗ are the Bloch wavenumbers of the resonant mode and the BIC, respectively. However, for some special BICs with β _∗=0 (referred to as super-BICs by some authors), the Q factor satisfies Q ∼ 1/β⁶. Although super-BICs are usually obtained by merging a few BICs through tuning a structural parameter, they can be precisely characterized by a mathematical condition. In this Letter, we consider arbitrary perturbations to structures supporting a super-BIC. The perturbation is given by δF(r), where δ is the amplitude and F(r) is the perturbation profile. We show that for a typical F(r), the BICs in the perturbed structure exhibit a pitchfork bifurcation around the super-BIC. The number of BICs changes from one to three as δ passes through zero. However, for some special profiles F(r), there is no bifurcation, i.e., there is only a single BIC for δ around zero. In that case, the super-BIC is not associated with a merging process for which δ is the parameter.