Method of eigenvectors for numerical studies of multilayer gratings

A new approach to numerical studies of lamellar multilayer gratings is developed. It stands out against the existing modal and differential methods by its applicability to thick multilayer gratings with a small grating period, and also to the case of grazing incidence of radiation. The diffraction properties of multilayer gratings are calculated for x rays with the angles of incidence down to zero. Reflection curves are calculated for multilayer gratings with the grating periods down to 5 nm and the number of bilayers up to 1000. The diffraction pictures are developed for all the range of x-ray radiation (soft and hard x rays). It is directly demonstrated that the multilayer grating can be regarded as a two-dimensional crystal. Numerical calculations based on the newly proposed method were used for the interpretation of experimental data on the performance of the Ni/C multiplayer grating.