Nonlinear scattering by a polyconductor slab

A solution of the nonlinear electrothermal problem of the scattering of plane electromagnetic waves normally incident on a polyconductor slab with a metal substrate is presented. Since the electrical conductivity of the slab is a nonlinear function of the temperature profile, and hence the power absorbed at every point in the slab, the formulation for the electric field and temperature distribution in the slab leads to a pair of coupled nonlinear second order partial differential equations which are solved by the W.K.B. and finite difference methods. The variations of the reflection and transmission coefficients, the surface impedance and surface temperature (above initial temperature) with frequency and incident electric field, as well as the resulting profiles of the electric field, conductivity and temperature inside the slab are presented in graphical form. These results suggest certain practical applications which are also described.