  Extremely asymmetrical scattering (EAS) is a highly resonant type of Bragg
scattering with a strong resonant increase of the scattered wave amplitude
inside and outside the grating. EAS is realized when the scattered wave
propagates parallel to the grating boundaries. We present a rigorous algorithm
for the analysis of non-steady-state EAS, and investigate the relaxation of the
incident and scattered wave amplitudes to their steady-state values.
Non-steady-state EAS of bulk TE electromagnetic waves is analyzed in narrow and
wide, slanted, holographic gratings. Typical relaxation times are determined
and compared with previous rough estimations. Physical explanation of the
predicted effects is presented.
