Implementation of the extinction theorem in a problem of Airy pulse scattering by a dielectric layer

A problem of Airy pulse transformation by a plane-parallel layer is considered. Solving of this problem is made by the Volterra integral equation method in two stages. Finding of an electrical field inside a layer is implemented on the first stage. The fields of reflected as well as transmitted pulses are calculated on the second stage. The virtual structure of the pulse field inside the layer consists of some terms one of which extinctions the initial pulse according to the Ewald-Oseen extinction theorem.