  We present a new paradigm in the field of photonic crystals and
metamaterials, applying the resonant-state expansion (RSE) to planar
photonic-crystal structures. The RSE allows us to understand and quantify
optical resonances in photonic-crystal structures in terms of the analytic
resonant states of a homogeneous planar waveguide. The RSE provides an
efficient and reliable tool for accurate calculation of a complete set of the
resonant states of a photonic-crystal slab, which is required for the correct
description and a better understanding of its optical spectra. For the proof of
principle, numerical verification of the RSE, and demonstration of its
unprecedented accuracy and convergence, an infinite planar photonic crystal
slab periodic in one dimension is taken as an example. To illustrate the power
of the present approach, we consider the mode evolution with the amplitude of
the periodic modulation, revealing the role of the guided modes in the
formation of bound states in the continuum.
