Dispersion relations for linear wave propagation in homogeneous and inhomogeneous media

Richard L Weaver, Yih Hsing Pao

Research output: Contribution to journalArticle

Abstract

For the dispersion of waves in a homogeneous medium there exist the Kramers-Kronig relations for the wave number K (ω) = ω/c(ω). The usual mathematical proof of such relations depends on assumptions for the asymptotic behavior of c(ω) at high frequency, which for electromagnetic waves in dielectrics can be evaluated from the microphysical properties of the medium. In this paper such assumptions are removed and the necessary asymptotic behavior is shown to follow the representation of K (ω) as a Herglotz function. From the linear, causal, and passive properties of the media we thus establish the Kramers-Kronig relations for all linear wave disturbances including acoustic, elastic, and electromagnetic waves in inhomogeneous as well as homogeneous media without any reference to the microphysical structure of the medium.

Original languageEnglish (US)
Pages (from-to)1909-1918
Number of pages10
JournalJournal of Mathematical Physics
Volume22
Issue number9
DOIs
StatePublished - Jan 1 1981
Externally publishedYes

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Inhomogeneous Media
Dispersion Relation
Wave Propagation
wave propagation
Electromagnetic Wave
Asymptotic Behavior
Elastic Waves
Acoustic Waves
electromagnetic radiation
Disturbance
Necessary
elastic waves
disturbances
acoustics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Dispersion relations for linear wave propagation in homogeneous and inhomogeneous media. / Weaver, Richard L; Pao, Yih Hsing.

In: Journal of Mathematical Physics, Vol. 22, No. 9, 01.01.1981, p. 1909-1918.

Research output: Contribution to journalArticle

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