Modeling and analysis of wave scattering and generation on cubically polarisable layered structures

We investigate the problem of scattering and generation of waves on an isotropic, non-magnetic, linearly polarised (E-polarisation), non-linear, layered, cubically polarisable, dielectric structure, which is excited by a packet of plane waves, in the domain of resonance frequencies. The resulting mathematical model can be represented equivalently by a system of non-linear boundary-value problems of Sturm - Liouville type with respect to the components of the scattered and generated fields or by a system of one-dimensional non-linear Fredholm integral equations. For each of these problems we obtain sufficient conditions for existence and uniqueness of the solution. The solutions of these problems are approximated numerically by the help of quadrature methods. The numerical algorithms of the solution of the non-linear problems are based on iterative procedures which require the solution of a linear system in each step. In this way the approximate solution of the non-linear problems is described by means of solutions of linear problems with an induced nonlinear dielectric permeability.