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.
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