Resonant mode coupling method for the description of oscillating dipoles emission inside stacked photonic nanostructures.

Resonant modes are important characteristics of the optical properties of photonic crystals since they are responsible for the features in the transmission and reflection spectra, as well as the emissivity of quantum emitters inside such structures. We present a resonant modes expansion method applied to a problem of radiating dipoles inside of a photonic crystal. In stacked photonic crystal slabs there is a coupling between resonances of distinct subsystems and Fabry-Perot resonances. We propose a technique to calculate coefficients of resonant mode expansion based on the scattering matrix formalism of the Fourier modal method (FMM). The method appears to be convenient since it does not require rigorous normalization of resonant fields or application of perfectly matched layers. Then we demonstrate the agreement between the resonant modes expansion results and exact FMM solutions.