Advanced

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

Åberg, Ingegerd LU (1996) In Technical Report LUTEDX/(TEAT-7052)/1-39/(1996) TEAT-7052.
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7052)/1-39/(1996)
volume
TEAT-7052
pages
39 pages
publisher
[Publisher information missing]
language
English
LU publication?
yes
id
0ae6370c-ea63-405a-b5d9-6d89cfa28936 (old id 530342)
date added to LUP
2007-09-06 11:09:08
date last changed
2016-09-07 16:08:58
@techreport{0ae6370c-ea63-405a-b5d9-6d89cfa28936,
  abstract     = {A time domain method building on the concept of wave splitting is used to<br/><br>
study direct wave propagation phenomena in weakly nonlinear media. The<br/><br>
starting point is the linear wave equation with time-dependent coefficients.<br/><br>
This means that the studied nonlinear medium in some sense has to be approximated<br/><br>
with a nonstationary medium which changes while the wave passes<br/><br>
through. For the nonstationary equation homogeneous as well as particular<br/><br>
solutions can be obtained. Two different iterative procedures to find the nonlinear<br/><br>
solutions are discussed. They are illustrated by two problems fetched<br/><br>
from different research fields of current interest. In the first case, the nonlinear<br/><br>
term is linearized using the Fr´echet derivative. This leads into a truly<br/><br>
nonstationary, mixed initial boundary value problem with a linear equation<br/><br>
characterized by both time-dependent coefficients and source terms. In this<br/><br>
example a semiconductor device used for switching in high-frequency applications<br/><br>
is considered. It can be described as a coplanar waveguide loaded with<br/><br>
distributed resonant tunnel diodes. In the other example, wave propagation<br/><br>
in Kerr media is considered. Then Taylor expansion transforms the nonlinear<br/><br>
equation into a linear one with nonstationary source terms. In this case the<br/><br>
nonlinearity does not lead to time-depending coefficients in the equation. The<br/><br>
way to obtain the solution is a nonlinear variant of the Born approximation.},
  author       = {Åberg, Ingegerd},
  institution  = {[Publisher information missing]},
  language     = {eng},
  pages        = {39},
  series       = {Technical Report LUTEDX/(TEAT-7052)/1-39/(1996)},
  title        = {High-frequency switching and Kerr effect - nonlinear problems solved with nonstationary time domain techniques},
  volume       = {TEAT-7052},
  year         = {1996},
}