lnu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Quasi-Herglotz functions and convex optimization
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.ORCID iD: 0000-0002-3928-6064
Stockholm University, Sweden.
Lund University, Sweden.
KTH Royal institute of technology, Sweden.
Show others and affiliations
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modeling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions, and we show that several of the important properties and modeling perspectives of Herglotz functions are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modeling of a non-passive gain media formulated as a convex optimization problem,where the generating measure is modeled by using a finite expansion of B-splines and point masses.

Keywords [en]
Quasi-Herglotz functions, non-passive systems, approximation, convex optimization, sum rules
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering Other Mathematics
Research subject
Physics, Waves and Signals; Physics, Electrotechnology
Identifiers
URN: urn:nbn:se:lnu:diva-90218OAI: oai:DiVA.org:lnu-90218DiVA, id: diva2:1372014
Funder
Swedish Foundation for Strategic Research , AM13-0011Available from: 2019-11-21 Created: 2019-11-21 Last updated: 2019-12-18Bibliographically approved
In thesis
1. Optimization and Physical Bounds for Passive and Non-passive Systems
Open this publication in new window or tab >>Optimization and Physical Bounds for Passive and Non-passive Systems
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Physical bounds in electromagnetic field theory have been of interest for more than a decade. Considering electromagnetic structures from the system theory perspective, as systems satisfying linearity, time-invariance, causality and passivity, it is possible to characterize their transfer functions via Herglotz functions. Herglotz functions are useful in modeling of passive systems with applications in mathematical physics, engineering, and modeling of wave phenomena in materials and scattering. Physical bounds on passive systems can be derived in the form of sum rules, which are based on low- and high-frequency asymptotics of the corresponding Herglotz functions. These bounds provide an insight into factors limiting the performance of a given system, as well as the knowledge about possibilities to improve a desired system from a design point of view. However, the asymptotics of the Herglotz functions do not always exist for a given system, and thus a new method for determination of physical bounds is required. In Papers I–II of this thesis, a rigorous mathematical framework for a convex optimization approach based on general weighted Lp-norms, 1≤p≤∞, is introduced. The developed framework is used to approximate a desired system response, and to determine an optimal performance in realization of a system satisfying the target requirement. The approximation is carried out using Herglotz functions, B-splines, and convex optimization. 

Papers III–IV of this thesis concern modeling and determination of optimal performance bounds for causal, but not passive systems. To model them, a new class of functions, the quasi-Herglotz functions, is introduced. The new functions are defined as differences of two Herglotz functions and preserve the majority of the properties of Herglotz functions useful for the mathematical framework based on convex optimization. We consider modeling of gain media with desired properties as a causal system, which can be active over certain frequencies or  frequency intervals.  Here, sum rules can also be used under certain assumptions.

In Papers V–VII of this thesis, the optical theorem for scatterers immersed in lossy media is revisited. Two versions of the optical theorem are derived: one based on internal equivalent currents and the other based on external fields in terms of a T-matrix formalism, respectively. The theorems are exploited to derive fundamental bounds on absorption by using elementary optimization techniques. The theory has a potential impact in applications where the surrounding losses cannot be neglected, e.g., in medicine, plasmonic photothermal therapy, radio frequency absorption of gold nanoparticle suspensions, etc.  In addition to this, a new method for detection of electrophoretic resonances in a material with Drude-type of dispersion, which is placed in a straight waveguide, is proposed.

Place, publisher, year, edition, pages
Växjö, Sweden: Linnaeus University Press, 2019. p. 217
Series
Linnaeus University Dissertations ; 373/2019
Keywords
Convex optimization, physical bounds, Herglotz functions, quasi-Herglotz functions, passive systems, non-passive systems, approximation, absorption in lossy media
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Physics, Waves and Signals
Identifiers
urn:nbn:se:lnu:diva-90223 (URN)978-91-89081-23-9 (ISBN)978-91-89081-24-6 (ISBN)
Public defence
2019-12-13, Newton, Hus C, Växjö, 09:15 (English)
Opponent
Supervisors
Funder
Swedish Foundation for Strategic Research , AM13-0011
Available from: 2019-11-22 Created: 2019-11-21 Last updated: 2019-11-22Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Fulltext

Authority records BETA

Ivanenko, YevhenNordebo, Sven

Search in DiVA

By author/editor
Ivanenko, YevhenNordebo, Sven
By organisation
Department of Physics and Electrical Engineering
Other Electrical Engineering, Electronic Engineering, Information EngineeringOther Mathematics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 35 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf