Physical limitations on the scattering of electromagnetic vector spherical waves

Anders Bernland, Mats Gustafsson, Sven Nordebo

Research output: Book/ReportReportResearch

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Understanding the interaction between electromagnetic waves and matter is vital in applications ranging from classical optics to antenna theory.
This paper derives physical limitations on the scattering of electromagnetic vector spherical waves.
The assumptions made are that the heterogeneous scatterer is passive, and has constitutive relations which are on convolution form in the time domain and anisotropic in the static limit.
The resulting bounds
limit the reflection coefficient of the modes over a frequency interval,
and can thus be interpreted as limitations on the absorption of power from a single mode.
They can be used within a wide range of applications, and are particularly useful for electrically small scatterers.
The derivation follows a general approach to derive sum rules and physical limitations on passive systems on convolution form.
The time domain versions of the vector spherical waves are used to describe the passivity of the scatterer, and
a set of integral identities for Herglotz functions are applied to derive sum rules from which the physical limitations follow.
Original languageEnglish
Publisher[Publisher information missing]
Number of pages24
Publication statusPublished - 2010

Publication series

NameTechnical Report LUTEDX/(TEAT-7194)/1-24/(2010)

Bibliographical note

Published version: Journal of Physics A: Mathematical and Theoretical, Vol. 44, No. 14, pp. 145401, 2011.

Subject classification (UKÄ)

  • Electrical Engineering, Electronic Engineering, Information Engineering


  • physical limitations
  • sum rules
  • vector spherical waves
  • scattering
  • Herglotz functions


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