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Optimization and Physical Bounds for Passive and Non-passive SystemsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2019 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Växjö, Sweden: Linnaeus University Press, 2019. , p. 217
##### Series

Linnaeus University Dissertations ; 373/2019
##### Keywords [en]

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: urn:nbn:se:lnu:diva-90223ISBN: 978-91-89081-23-9 (print)ISBN: 978-91-89081-24-6 (electronic)OAI: oai:DiVA.org:lnu-90223DiVA, id: diva2:1372058
##### Public defence

2019-12-13, Newton, Hus C, Växjö, 09:15 (English)
##### Opponent

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##### Supervisors

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#####

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##### Funder

Swedish Foundation for Strategic Research , AM13-0011Available from: 2019-11-22 Created: 2019-11-21 Last updated: 2019-11-22Bibliographically approved
##### List of papers

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 L^{p}-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.

1. Passive Approximation and Optimization Using B-Splines$(function(){PrimeFaces.cw("OverlayPanel","overlay1298160",{id:"formSmash:j_idt495:0:j_idt499",widgetVar:"overlay1298160",target:"formSmash:j_idt495:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Passive Approximation with High-Order B-Splines$(function(){PrimeFaces.cw("OverlayPanel","overlay1318323",{id:"formSmash:j_idt495:1:j_idt499",widgetVar:"overlay1318323",target:"formSmash:j_idt495:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Quasi-Herglotz functions and convex optimization$(function(){PrimeFaces.cw("OverlayPanel","overlay1372014",{id:"formSmash:j_idt495:2:j_idt499",widgetVar:"overlay1372014",target:"formSmash:j_idt495:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Non-passive approximation as a tool to study the realizability of amplifying media$(function(){PrimeFaces.cw("OverlayPanel","overlay1372033",{id:"formSmash:j_idt495:3:j_idt499",widgetVar:"overlay1372033",target:"formSmash:j_idt495:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. On the physical limitations for radio frequency absorption in gold nanoparticle suspensions$(function(){PrimeFaces.cw("OverlayPanel","overlay1112798",{id:"formSmash:j_idt495:4:j_idt499",widgetVar:"overlay1112798",target:"formSmash:j_idt495:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. On the plasmonic resonances in a layered waveguide structure$(function(){PrimeFaces.cw("OverlayPanel","overlay1306773",{id:"formSmash:j_idt495:5:j_idt499",widgetVar:"overlay1306773",target:"formSmash:j_idt495:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

7. Optical theorems and physical bounds on absorption in lossy media$(function(){PrimeFaces.cw("OverlayPanel","overlay1368831",{id:"formSmash:j_idt495:6:j_idt499",widgetVar:"overlay1368831",target:"formSmash:j_idt495:6:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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