System of Nonlinear Boundary-Value Problems and Self-Consistent Analysis of Resonance Scattering and Generation of Oscillations by a Cubically Polarisable Layered Structure

Abstract

The problem of scattering and generation of waves on an isotropic, non-magnetic, linearly polarised (E-polarisation), nonlinear, layered, cubically polarisable, dielectric structure, which is excited by a packet of plane waves, is investigated in the domain of resonance frequencies. The resulting mathematical model can be represented by a system of one-dimensional nonlinear integral equations. The solution of this problem is approximated numerically by the help of quadrature methods and iterative procedures which require the solution of a linear system in each step. Layers with negative and positive values of the coefficient of cubic susceptibility of the nonlinear medium have fundamentally different scattering and generation properties. Here the investigations are restricted to the third harmonic generated by layers with a negative value of the cubic susceptibility of the medium. In such a case, a decanalisation of the electromagnetic field can be detected. Results of calculations of characteristics of the scattered and generated fields of plane waves are presented, taking into account the influence of weak fields at multiple frequencies on the cubically polarisable layer.