An analytic continuation method for the analysis and design of dispersive materials

Rodolfo Diaz, Nicolaos G. Alexopoulos

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

All materials, by nature, possess a frequency-dependent permittivity. This dispersion can be expressed in the form of the Kramers-Krönig relations by invoking the analytic consequences of causality in the upper half of the complex frequency plane. However, the Hubert transform pair character of these relations makes them useful only when half of the answer is already known. In order to derive a more general form useful for both synthesis and analysis of arbitrary materials, it is necessary to analytically continue the permittivity function into the lower half plane. Requiring that the dielectric polarization be expressible in terms of equations of motion, in addition to obeying causality, conservation of energy and the second law of thermodynamics is sufficient to obtain the desired expression as a sum of special complex functions. In the appropriate limits, this sum reduces to the Debye relaxation and Lorentz resonance models of dielectrics, but it also contains phenomena not expressible in terms of those classical models. In particular, the classic problem of the existence of optical transparency in water is resolved.

Original languageEnglish (US)
Pages (from-to)1602-1610
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Volume45
Issue number11
DOIs
StatePublished - Dec 1 1997
Externally publishedYes

Fingerprint

Permittivity
permittivity
dielectric polarization
half planes
Transparency
Equations of motion
conservation
Conservation
equations of motion
Thermodynamics
Polarization
thermodynamics
synthesis
water
Water
energy

Keywords

  • Dispersive media

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electrical and Electronic Engineering

Cite this

An analytic continuation method for the analysis and design of dispersive materials. / Diaz, Rodolfo; Alexopoulos, Nicolaos G.

In: IEEE Transactions on Antennas and Propagation, Vol. 45, No. 11, 01.12.1997, p. 1602-1610.

Research output: Contribution to journalArticle

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