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Dispersion Relations in Scattering and Antenna Problems

Sohl, Christian LU (2008) In Series of licentiate and doctoral theses; ISSN 1654-790X 6.
Abstract
This dissertation deals with physical bounds on scattering and absorption of acoustic and electromagnetic waves. A general dispersion relation or sum rule for the extinction cross section of such waves is derived from the holomorphic properties of the scattering amplitude in the forward direction. The derivation is based on the forward scattering theorem via certain Herglotz functions and their asymptotic expansions in the low-frequency and high-frequency regimes. The result states that, for a given interacting target, there is only a limited amount of scattering and absorption available in the entire frequency range. The forward dispersion relation is shown to be valuable for a broad range of frequency domain problems involving acoustic... (More)
This dissertation deals with physical bounds on scattering and absorption of acoustic and electromagnetic waves. A general dispersion relation or sum rule for the extinction cross section of such waves is derived from the holomorphic properties of the scattering amplitude in the forward direction. The derivation is based on the forward scattering theorem via certain Herglotz functions and their asymptotic expansions in the low-frequency and high-frequency regimes. The result states that, for a given interacting target, there is only a limited amount of scattering and absorption available in the entire frequency range. The forward dispersion relation is shown to be valuable for a broad range of frequency domain problems involving acoustic and electromagnetic interaction with matter on a macroscopic scale. In the modeling of a metamaterial, i.e., an engineered composite material that gains its properties by its structure rather than its composition, it is demonstrated that for a narrow frequency band, such a material may possess extraordinary characteristics, but that tradeoffs are necessary to increase its usefulness over a larger bandwidth.

<br>

<br>

The dispersion relation for electromagnetic waves is also

applied to a large class of causal and reciprocal antennas to establish a priori estimates on the input impedance, partial realized gain, and bandwidth of electrically small and wideband antennas. The results are compared to the classical antenna bounds based on eigenfunction expansions, and it is demonstrated that the estimates presented in this dissertation offer sharper inequalities, and, more importantly, a new understanding of antenna dynamics in terms of low-frequency considerations.

<br>

<br>

The dissertation consists of 11 scientific papers of which several have been published in peer-reviewed international journals. Both experimental results and numerical illustrations are included. The General Introduction addresses closely related subjects in theoretical physics and classical dispersion theory, e.g., the origin of the Kramers-Kronig relations, the mathematical foundations of Herglotz functions, the extinction paradox for scattering of waves and particles, and non-forward dispersion relations with application to the prediction of bistatic radar cross sections. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Professor Bohren, Craig F., Pennsylvania State University, United States
organization
publishing date
type
Thesis
publication status
published
subject
keywords
acoustic and electromagnetic waves, sum rules, scattering and absorption, causality, Herglotz functions
in
Series of licentiate and doctoral theses; ISSN 1654-790X
volume
6
pages
233 pages
publisher
Department of Electrical and Information Technology, Lund University
defense location
Lecture hall E:1406, E-building, Ole Römers väg 3, Faculty of Engineering, Lund University
defense date
2008-09-23 10:15
ISBN
978-91-628-7514-5
language
English
LU publication?
yes
id
cecd83a4-9da0-47b6-85bc-eb77562d6a36 (old id 1221227)
date added to LUP
2008-08-27 16:04:12
date last changed
2016-09-19 08:45:07
@misc{cecd83a4-9da0-47b6-85bc-eb77562d6a36,
  abstract     = {This dissertation deals with physical bounds on scattering and absorption of acoustic and electromagnetic waves. A general dispersion relation or sum rule for the extinction cross section of such waves is derived from the holomorphic properties of the scattering amplitude in the forward direction. The derivation is based on the forward scattering theorem via certain Herglotz functions and their asymptotic expansions in the low-frequency and high-frequency regimes. The result states that, for a given interacting target, there is only a limited amount of scattering and absorption available in the entire frequency range. The forward dispersion relation is shown to be valuable for a broad range of frequency domain problems involving acoustic and electromagnetic interaction with matter on a macroscopic scale. In the modeling of a metamaterial, i.e., an engineered composite material that gains its properties by its structure rather than its composition, it is demonstrated that for a narrow frequency band, such a material may possess extraordinary characteristics, but that tradeoffs are necessary to increase its usefulness over a larger bandwidth.<br/><br>
&lt;br&gt;<br/><br>
&lt;br&gt;<br/><br>
The dispersion relation for electromagnetic waves is also<br/><br>
applied to a large class of causal and reciprocal antennas to establish a priori estimates on the input impedance, partial realized gain, and bandwidth of electrically small and wideband antennas. The results are compared to the classical antenna bounds based on eigenfunction expansions, and it is demonstrated that the estimates presented in this dissertation offer sharper inequalities, and, more importantly, a new understanding of antenna dynamics in terms of low-frequency considerations.<br/><br>
&lt;br&gt;<br/><br>
&lt;br&gt;<br/><br>
The dissertation consists of 11 scientific papers of which several have been published in peer-reviewed international journals. Both experimental results and numerical illustrations are included. The General Introduction addresses closely related subjects in theoretical physics and classical dispersion theory, e.g., the origin of the Kramers-Kronig relations, the mathematical foundations of Herglotz functions, the extinction paradox for scattering of waves and particles, and non-forward dispersion relations with application to the prediction of bistatic radar cross sections.},
  author       = {Sohl, Christian},
  isbn         = {978-91-628-7514-5},
  keyword      = {acoustic and electromagnetic waves,sum rules,scattering and absorption,causality,Herglotz functions},
  language     = {eng},
  pages        = {233},
  publisher    = {ARRAY(0x91c0c20)},
  series       = {Series of licentiate and doctoral theses; ISSN 1654-790X},
  title        = {Dispersion Relations in Scattering and Antenna Problems},
  volume       = {6},
  year         = {2008},
}