Dispersion Relations in Scattering and Antenna Problems
(2008) In Series of licentiate and doctoral theses; ISSN 1654790X 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 lowfrequency and highfrequency 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 lowfrequency and highfrequency 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.
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<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 lowfrequency considerations.
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The dissertation consists of 11 scientific papers of which several have been published in peerreviewed 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 KramersKronig relations, the mathematical foundations of Herglotz functions, the extinction paradox for scattering of waves and particles, and nonforward dispersion relations with application to the prediction of bistatic radar cross sections. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1221227
 author
 Sohl, Christian ^{LU}
 supervisor

 Gerhard Kristensson ^{LU}
 opponent

 Professor Bohren, Craig F., Pennsylvania State University, United States
 organization
 publishing date
 2008
 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 1654790X
 volume
 6
 pages
 233 pages
 publisher
 Department of Electrical and Information Technology, Lund University
 defense location
 Lecture hall E:1406, Ebuilding, Ole Römers väg 3, Faculty of Engineering, Lund University
 defense date
 20080923 10:15
 ISBN
 9789162875145
 language
 English
 LU publication?
 yes
 id
 cecd83a49da047b685bceb77562d6a36 (old id 1221227)
 date added to LUP
 20080827 16:04:12
 date last changed
 20160919 08:45:07
@phdthesis{cecd83a49da047b685bceb77562d6a36, 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 lowfrequency and highfrequency 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> <br><br/><br> <br><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 lowfrequency considerations.<br/><br> <br><br/><br> <br><br/><br> The dissertation consists of 11 scientific papers of which several have been published in peerreviewed 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 KramersKronig relations, the mathematical foundations of Herglotz functions, the extinction paradox for scattering of waves and particles, and nonforward dispersion relations with application to the prediction of bistatic radar cross sections.}, author = {Sohl, Christian}, isbn = {9789162875145}, keyword = {acoustic and electromagnetic waves,sum rules,scattering and absorption,causality,Herglotz functions}, language = {eng}, pages = {233}, publisher = {Department of Electrical and Information Technology, Lund University}, school = {Lund University}, series = {Series of licentiate and doctoral theses; ISSN 1654790X}, title = {Dispersion Relations in Scattering and Antenna Problems}, volume = {6}, year = {2008}, }