High-frequency switching and Kerr effect - nonlinear problems solved with nonstationary time domain techniques

A time domain method building on the concept of wave splitting is used to
study direct wave propagation phenomena in weakly nonlinear media. The
starting point is the linear wave equation with time-dependent coefficients.
This means that the studied nonlinear medium in some sense has to be approximated
with a nonstationary medium which changes while the wave passes
through. For the nonstationary equation homogeneous as well as particular
solutions can be obtained. Two different iterative procedures to find the nonlinear
solutions are discussed. They are illustrated by two problems fetched
from different research fields of current interest. In the first case, the nonlinear
term is linearized using the Fr´echet derivative. This leads into a truly
nonstationary, mixed initial boundary value problem with a linear equation
characterized by both time-dependent coefficients and source terms. In this
example a semiconductor device used for switching in high-frequency applications
is considered. It can be described as a coplanar waveguide loaded with
distributed resonant tunnel diodes. In the other example, wave propagation
in Kerr media is considered. Then Taylor expansion transforms the nonlinear
equation into a linear one with nonstationary source terms. In this case the
nonlinearity does not lead to time-depending coefficients in the equation. The
way to obtain the solution is a nonlinear variant of the Born approximation.