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We develop the resonant mode coupling approximation to calculate the opticalspectra of a stack of two photonic crystal slabs. The method is based on aderivation of the input and output resonant vectors in each slab in terms ofthe Fourier modal method in the scattering matrix form. We show that using theresonant mode coupling approximation of the scattering matrices of the upperand 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 isrigorously derived by means of an effective Hamiltonian. We demonstrate thatthe proposed procedure dramatically decreases the computation time withoutsufficient loss of accuracy. We believe that the proposed technique can be apowerful tool for fast solving inverse scattering problems using stochasticoptimization methods such as genetic algorithms or machine learning.

Resonant mode coupling approximation for calculation of optical spectra of photonic crystal slabs