Analytical Perspective for Bound States in the Continuum in Photonic Crystal Slabs

We investigate the formation of photonic bound states in the continuum (BICs) in photonic crystal slabs from an analytical perspective. Unlike the stationary at-$\mathrm{\ensuremath{\Gamma}}$ BICs which originate from the geometric symmetry, the tunable off-$\mathrm{\ensuremath{\Gamma}}$ BICs are due to the weighted destructive via the continuum interference in the vicinity of accidental symmetry when the majority of the radiation is precanceled. The symmetric compatible nature of the off-$\mathrm{\ensuremath{\Gamma}}$ BICs leads to a trapping of light that can be tuned through continuously varying the wave vector. With the analytical approach, we explain a reported experiment and predict the existence of a new BIC at an unrevealed symmetry.