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Non-passive approximation as a tool to study the realizability of amplifying media
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.ORCID iD: 0000-0002-3928-6064
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.ORCID iD: 0000-0002-7018-6248
2019 (English)Conference paper, Published paper (Refereed)
Abstract [en]

Non-passive approximation is presented as a tool to study the realizability of amplifying media. As an interesting physical example, we derive first a suitable approximation of the plasmonic singularity of a dielectric sphere with respect to a hypothetical amplifying background medium. A non-passive approximation based on convex optimization is then employed to investigate the necessary bandwidth requirements to achieve the approximate pole singularity.

Place, publisher, year, edition, pages
2019.
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering Other Mathematics
Research subject
Physics, Waves and Signals
Identifiers
URN: urn:nbn:se:lnu:diva-90222OAI: oai:DiVA.org:lnu-90222DiVA, id: diva2:1372033
Conference
URSI EM Theory Symposium, EMTS 2019, San Diego, CA, 27–31 May 2019
Funder
Swedish Foundation for Strategic Research , AM13-0011Available from: 2019-11-21 Created: 2019-11-21 Last updated: 2019-11-21
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

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