2024 , Volume 29, № 5, p.17-29

Rigorous coupled-wave analysis is a widely used method to determine the diffraction efficiency of periodic structures. The computational complexity that arises when implementing algorithms for rigorous coupled-wave analysis is characterized by the time required for the calculation and the amount of RAM used by the computer. The calculated time, in turn, depends on the selected parameters of the number of plane waves (modes), the sum of which determines the electromagnetic field, and the number of lattice plates into which the periodic structure is divided. This paper proposes three techniques for reducing the time required to calculate a single value or series of diffraction efficiency values obtained using rigorous algorithms for coupled wave analysis. The first technique uses the properties of Toeplitz matrices, which are the matrices of Fourier coefficients when expanding the dielectric constant of each lattice plate into a series. The second technique reduces computational complexity by reducing the number of variables in the Fourier coefficient function. The third technique uses parallel computing to calculate a set of Fourier coefficient matrices and a set of diffraction efficiency values. Using examples of problems of constructing the dependences of the diffraction efficiency of two-layer double-relief sawtooth microstructures with antireflection coatings on the angle of incidence of radiation and temperature, it is shown that the use of the properties of Toeplitz matrices can significantly reduce the calculation time. The second technique insignificantly reduces the calculation time. Parallel computing significantly reduces computation time, while using more RAM. By combining the proposed techniques, a working algorithm that meets the user’s requirements for the estimated time and available RAM of the computer is proposed.