  Extremely asymmetrical scattering (EAS) is an unusual type of Bragg
scattering in slanted periodic gratings with the scattered wave (the +1
diffracted order) propagating parallel to the grating boundaries. Here, a
unique and strong sensitivity of EAS to small stepwise variations of mean
structural parameters at the grating boundaries is predicted theoretically (by
means of approximate and rigorous analyses) for bulk TE electromagnetic waves
and slab optical modes of arbitrary polarization in holographic (for bulk
waves) and corrugation (for slab modes) gratings. The predicted effects are
explained using one of the main physical reasons for EAS--the diffractional
divergence of the scattered wave (similar to divergence of a laser beam). The
approximate method of analysis is based on this understanding of the role of
the divergence of the scattered wave, while the rigorous analysis uses the
enhanced T-matrix algorithm. The effect of small and large stepwise variations
of the mean permittivity at the grating boundaries is analysed. Two distinctly
different and unusual patterns of EAS are predicted in the cases of wide and
narrow (compared to a critical width) gratings. Comparison between the
approximate and rigorous theories is carried out.
