Analytical normalization of resonant states in photonic crystal slabs and periodic arrays of nanoantennas at oblique incidence

We present an analytical formulation for the normalization of resonant states at oblique incidence in oneand two-dimensional periodic structures with top and bottom boundaries to homogeneous space, such as photonic crystal slabs and arrays of nanoantennas. The normalization is validated by comparing the resonant state expansion using one and two resonant states with numerically exact results. The predicted changes of resonance frequency and linewidth due to perturbations of refractive index or geometry can be used to study resonantly enhanced refractive index sensing as well as the influence of disorder. In addition, the normalization is essential for the calculation of the Purcell factor.