  Double-resonant extremely asymmetrical scattering (DEAS) is a strongly
resonant type of Bragg scattering in two joint or separated uniform gratings
with different phases. It is characterised by a very strong increase of the
scattered and incident wave amplitudes inside and between the gratings at a
resonant phase shift between the gratings. DEAS is realised when the first
diffracted order satisfying the Bragg condition propagates parallel to the
grating boundaries, and the joint or separated gratings interact by means of
the diffractional divergence of the scattered waves from one grating into
another. This Letter develops a theory of non-steady-state DEAS of bulk TE
electromagnetic waves in holographic gratings, and investigates the process of
relaxation of the incident and scattered wave amplitudes to their steady-state
values inside and outside the gratings. Typical relaxation times are
determined. Physical explanation of the predicted effects is presented.
