Fourier modal method for calculating neutron scattering from surface-relief and bulk diffraction gratings

We report a rigorous method for calculating the interaction of neutron waves with a periodic potential structure. In earlier work, several assumptions and simplifications were used in methods describing the diffraction of neutron waves from relief gratings. The approach presented here is based on the Fourier modal method widely used in electromagnetic wave optics, which has been adapted for the case of a neutron wave. It allows consideration of the mutual influence of waves of different diffraction orders and has no restrictions on either the range of energies under consideration or the shape of the structure profile. The developed theory makes it possible to accurately interpret the results of experiments on neutron scattering on surface-relief and bulk periodic structures.