Joint application of the finite element method and the scattering matrix method for solving diffraction problems on multilayer reflection gratings

A hybrid numerical technique based on a combination of the finite element method (FEM) and the scattering matrix method is applied to a wave diffraction problem on multilayer gratings. The grating represents a composite structure consisting of two main subdomains. The first one comprises a diffraction grating with a given groove shape. The second subdomain includes a set of homogenous dielectric layers, which form a multilayer reflection coating. The scattering matrix components of the diffraction grating are obtained by FEM and further transferred to the scattering matrix of the second subdomain. By means of the scattering matrix method the matching of the solutions at the interface of two subdomains is performed. The suggested hybrid method is applied to one-dimensional multilayer gratings with different groove shapes. The computational cost and the convergence rate of the proposed method are estimated. The results are compared with those, obtained by other numerical methods.