High-frequency switching and Kerr effect - nonlinear problems solved with nonstationary time domain techniques
(1996) In Technical Report LUTEDX/(TEAT-7052)/1-39/(1996)- 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:
https://lup.lub.lu.se/record/530342
- author
- Åberg, Ingegerd LU
- organization
- publishing date
- 1996
- type
- Book/Report
- publication status
- published
- subject
- in
- Technical Report LUTEDX/(TEAT-7052)/1-39/(1996)
- pages
- 39 pages
- publisher
- [Publisher information missing]
- report number
- TEAT-7052
- language
- English
- LU publication?
- yes
- additional info
- Published version: Waves PIER 17, Ed. J.A. Kong, pp 185-235, EMW Publishing, Cambridge, Massachusetts, USA, 1997.
- id
- 0ae6370c-ea63-405a-b5d9-6d89cfa28936 (old id 530342)
- date added to LUP
- 2016-04-04 13:08:48
- date last changed
- 2018-11-21 21:12:26
@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}},
number = {{TEAT-7052}},
series = {{Technical Report LUTEDX/(TEAT-7052)/1-39/(1996)}},
title = {{High-frequency switching and Kerr effect - nonlinear problems solved with nonstationary time domain techniques}},
url = {{https://lup.lub.lu.se/search/files/6060394/624880.pdf}},
year = {{1996}},
}