Time-domain constraints for passive materials: The Brendel-Bormann model revisited

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dc.contributor.authorNordebo, Svencs
dc.contributor.authorÅ tumpf, Martincs
dc.coverage.issue2cs
dc.coverage.volume110cs
dc.date.issued2024-07-09cs
dc.description.abstractThis paper presents a systematic approach to derive physical bounds for passive systems, or equivalently for positive real (PR) functions, directly in the time-domain (TD). As a generic, canonical example we explore the TD dielectric response of a passive material. We will furthermore revisit the theoretical foundation regarding the Brendel-Bormann (BB) oscillator model which is reportedly very suitable for the modeling of thin metallic films in high-speed optoelectronic devices. To this end, an important result here is to re-establish the physical realizability of the BB model by showing that it represents a passive and causal system. The theory is based on Cauer's representation of an arbitrary PR function together with associated sum rules (moments of the measure) and exploits the unilateral Laplace transform to derive rigorous bounds on the TD response of a passive system. Similar bounds have recently been reported for more general casual systems with other a priori assumptions. To this end, it is important to note here that the existence of useful sum rules and related physical bounds rely heavily on an assumption about the PR functions having a low- or high-frequency asymptotic expansion at least of odd order 1. As a particular numerical example, we consider here the electric susceptibility of gold (Au) which is commonly modeled by well established Drude or BB models. Explicit physical bounds are given as well as an efficient fast-Fourier transform-based numerical procedure to compute the TD impulse response associated with the nonrational BB model.en
dc.formattextcs
dc.format.extent024307-1-024307-15cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationPHYSICAL REVIEW B. 2024, vol. 110, issue 2, p. 024307-1-024307-15.en
dc.identifier.doi10.1103/PhysRevB.110.024307cs
dc.identifier.issn2469-9969cs
dc.identifier.orcid0000-0002-7477-7694cs
dc.identifier.other189098cs
dc.identifier.scopus25631441900cs
dc.identifier.urihttp://hdl.handle.net/11012/249385
dc.language.isoencs
dc.publisherAmerican Physical Societycs
dc.relation.ispartofPHYSICAL REVIEW Bcs
dc.relation.urihttps://journals.aps.org/prb/abstract/10.1103/PhysRevB.110.024307cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/2469-9969/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectPassive materialsen
dc.subjectPassive systemsen
dc.subjectPositive real functionsen
dc.subjectSum ruleen
dc.subjectTime domainen
dc.subjectTime domain constraintsen
dc.subjectLaplace transformen
dc.subjectBrendel-Bormann oscillator modelen
dc.titleTime-domain constraints for passive materials: The Brendel-Bormann model revisiteden
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-189098en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:41:53en
sync.item.modts2025.01.17 16:34:15en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav radioelektronikycs
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