Dynamical theory: Application to spin-echo resolved grazing incidence scattering from periodic structures

Neutron spin-echo resolved grazing incidence scattering (SERGIS) measurements performed on a silicon diffraction grating with a rectangular profile were shown in our previous publications to be well explained by dynamical theory calculations. The theory is based on a Bloch wave expansion of the neutron wavefunction in the periodic layer of the grating, which includes all multiple scattering within that layer. Calculations show that the spin-echo polarization should be very sensitive to the scattering geometry (i.e., incident angle, sample alignment and beam divergence) and the sample specifications (i.e., grating period, groove depth). To test these predictions, SERGIS measurements have been performed on a set of gratings with different specifications in various scattering geometries. In all cases, simulations based on the dynamical theory, with all the parameters set to their known values, are in good agreement with the collected data.