Inverse Problems to Determine Constant Permittivity and Coefficient of Nonlinearity in the Problem of TE Wave Propagation in a Layer with Kerr Nonlinearity

摘要

We consider a plane one-layer waveguide structure. The layer is located between two half-spaces with constant permittivities. The permittivity inside the layer is described by Kerr law: ε = ε_2 + α|E|~2, where ε_2 is a constant part of the permittivity, a is a coefficient of nonlinearity and E = (E_x, E_y, E_z)~T is the electric field. We suppose that ε_2 and α are unknown constants. The problem is to find these unknown constants. To solve this problem we can use amplitudes I, R, and T of the incident, reflected, and transmitted waves respectively. Amplitude I is supposed to be prescribed and amplitudes R, T are supposed to be measured.