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Direct and inverse scattering problems in dispersive media-Green's functions and invariant imbedding techniques

Kristensson, Gerhard LU (1990) In Technical Report LUTEDX/(TEAT-7006)/1-13/(1990) TEAT-7006.
Abstract
Transient electromagnetic wave propagation in a dispersive medium is reviewed.

The medium is assumed to be 1) linear, 2) invariant to time translations,

3) causal, 4) continuous, and 5) isotropic. The constitutive relations

are then uniquelyrepresen ted bya Riemann-Stieltjes integral in the time variable.

The kernel in this convolution is the susceptibilityk ernel. Two explicit

examples of mathematical models of the susceptibilityk ernel are given. The

medium treated in this paper is assumed to varyonlywith depth. In the direct

problem the reflection and transmission data are computed. The inverse scattering

problem is to find the susceptibilityk ernel from known... (More)
Transient electromagnetic wave propagation in a dispersive medium is reviewed.

The medium is assumed to be 1) linear, 2) invariant to time translations,

3) causal, 4) continuous, and 5) isotropic. The constitutive relations

are then uniquelyrepresen ted bya Riemann-Stieltjes integral in the time variable.

The kernel in this convolution is the susceptibilityk ernel. Two explicit

examples of mathematical models of the susceptibilityk ernel are given. The

medium treated in this paper is assumed to varyonlywith depth. In the direct

problem the reflection and transmission data are computed. The inverse scattering

problem is to find the susceptibilityk ernel from known reflexion data.

It is, thus, a problem of finding a function depending on the time variable. In

the spatiallyhomogeneous case the inverse scattering problem is solved from

reflexion data bysolving a Volterra integral equation of the second kind. This

inverse problem is therefore well-posed and easyto solve. (Less)
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Book/Report
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published
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in
Technical Report LUTEDX/(TEAT-7006)/1-13/(1990)
volume
TEAT-7006
pages
13 pages
publisher
[Publisher information missing]
language
English
LU publication?
yes
id
390e4817-d476-4aad-9ed0-72d37997de4b (old id 530188)
date added to LUP
2007-09-07 10:56:46
date last changed
2016-08-30 10:22:04
@misc{390e4817-d476-4aad-9ed0-72d37997de4b,
  abstract     = {Transient electromagnetic wave propagation in a dispersive medium is reviewed.<br/><br>
The medium is assumed to be 1) linear, 2) invariant to time translations,<br/><br>
3) causal, 4) continuous, and 5) isotropic. The constitutive relations<br/><br>
are then uniquelyrepresen ted bya Riemann-Stieltjes integral in the time variable.<br/><br>
The kernel in this convolution is the susceptibilityk ernel. Two explicit<br/><br>
examples of mathematical models of the susceptibilityk ernel are given. The<br/><br>
medium treated in this paper is assumed to varyonlywith depth. In the direct<br/><br>
problem the reflection and transmission data are computed. The inverse scattering<br/><br>
problem is to find the susceptibilityk ernel from known reflexion data.<br/><br>
It is, thus, a problem of finding a function depending on the time variable. In<br/><br>
the spatiallyhomogeneous case the inverse scattering problem is solved from<br/><br>
reflexion data bysolving a Volterra integral equation of the second kind. This<br/><br>
inverse problem is therefore well-posed and easyto solve.},
  author       = {Kristensson, Gerhard},
  language     = {eng},
  pages        = {13},
  publisher    = {ARRAY(0x9649c48)},
  series       = {Technical Report LUTEDX/(TEAT-7006)/1-13/(1990)},
  title        = {Direct and inverse scattering problems in dispersive media-Green's functions and invariant imbedding techniques},
  volume       = {TEAT-7006},
  year         = {1990},
}