Mixed bound states in the continuum: Disclosing BIC’s content via bulk normal modes

We present a nonperturbative theory of bound states in the continuum (BICs) based on the analytical theory of infinite-grating eigenmodes in the case of a planar grating waveguide, that is, 1D photonic crystal slab. We describe a mixed BIC mainly formed by a coherent mixture of two photonic-crystal normal modes in a vicinity of their avoided crossing where both of them have a nonzero coupling with a radiation-loss channel. We reveal the universal properties of the mixed BIC associated with the spatial parity symmetry breaking and self-similar spectral behavior of the bulk normal modes near $\Gamma$-point. We show that the mechanism of the mixed-BIC formation constitutes a special kind of the generic Friedrich–Wintgen mechanism. A cutoff from the radiation-loss channel and extremely high-Q narrow resonance are achieved due to the destructive interference of the two crossing normal modes. On the contrary, a conventional symmetry-protected BIC is formed mostly by a single photonic-crystal normal mode which has vanishing coupling Fourier coefficient with every available radiation-loss channel. Implementation of the mixed BICs in various photonic-crystals structures could lead to interesting applications.