  The resonant-state expansion (RSE) provides a precise and computationally
cheap tool to find resonant states in complex systems using the optical modes
of a simpler system as a basis. We apply the RSE to a photonic crystal slab in
order to identify and analyze its bound states in the continuum (BICs). We show
that the RSE is a useful and reliable method for not only finding the BICs but
also for differentiating between accidental and symmetry-protected BICs, as
well as for understanding their formation from the basis modes and evolution
with structural and material parameters of the system. The high efficiency of
the RSE allows us to track the properties of BICs and other high-quality
optical modes, covering the full parameter space of the system in a reasonable
time frame.
