  We develop the resonant mode coupling approximation to calculate the optical
spectra of a stack of two photonic crystal slabs. The method is based on a
derivation of the input and output resonant vectors in each slab in terms of
the Fourier modal method in the scattering matrix form. We show that using the
resonant mode coupling approximation of the scattering matrices of the upper
and lower slabs, one can construct the total scattering matrix of the stack.
The formation of the resonant output and input vectors of the stacked system is
rigorously derived by means of an effective Hamiltonian. We demonstrate that
the proposed procedure dramatically decreases the computation time without
sufficient loss of accuracy. We believe that the proposed technique can be a
powerful tool for fast solving inverse scattering problems using stochastic
optimization methods such as genetic algorithms or machine learning.
