Transient-field representation in terms of steady-improper solutions

The transient-excitation problem of an open dielectric slab by the integral transform method is solved. The solution is represented by an expansion in discrete spectrum functions (so-called steady-improper or nonmodal complex oscillations) increasing in space when moving away from a slab surface. The physical interpretation of the improper complex oscillations is proposed. The space-time existence region of the solution is defined. The oscillation expansions are shown to describe a transient process in the structure.