Non-steady-state double-resonant extremely asymmetrical scattering of   waves in periodic gratings
  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. 
Dmitri K. Gramotnev and Timo A. Nieminen