Exactly solvable model of resonant tunnelling of electromagnetic waves through gradient barriers in an inhomogeneous plasma are considered. Interrelations of permitivity profile of an inhomogeneous plasma and the amplitude of the wave vector have been studied for the gradient wave barriers depending on the incoming parameters of the model. It is shown that full enlightenment of the plasma layer for electromagnetic waves is possible for a even very wide wave barriers.
It was found that in a nonuniform layer may contains the narrow sublayers where the wave field may have strong splashes. It is shown that in the considered exactly solvable models the wave vector profiles can automatically satisfy the reflectionless conditions on the boundaries of plasma-vacuum and contain an arbitrary function, which describes the very variable plasma inhomogeneity in the layer.