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

Publiceringsår: 1990
Språk: Engelska
Publikation/Tidskrift/Serie: Technical Report LUTEDX/(TEAT-7006)/1-13/(1990)
Volym: TEAT-7006
Dokumenttyp: Rapport
Förlag: Department of Electromagnetic Theory, Lund Institute of Technology


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.


  • Electrical Engineering, Electronic Engineering, Information Engineering
  • Other Electrical Engineering, Electronic Engineering, Information Engineering


  • Electromagnetic theory-lup-obsolete

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