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Time-domain approach to the forward scattering sum rule

Publiceringsår: 2010
Språk: Engelska
Sidor: 3579-3592
Publikation/Tidskrift/Serie: Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
Volym: 466
Nummer: 2124
Dokumenttyp: Artikel i tidskrift
Förlag: Royal Society


The forward scattering sum rule relates the extinction cross section integrated over all wavelengths with the polarizability dyadics. It is useful for deriving bounds on the interaction between scatterers and electromagnetic fields, antenna bandwidth and directivity and energy transmission through sub-wavelength apertures. The sum rule is valid for linearly polarized plane waves impinging on linear, passive and time translational invariant scattering objects in free space. Here, a time-domain approach is used to clarify the derivation and the used assumptions. The time-domain forward scattered field defines an impulse response. Energy conservation shows that this impulse response is the kernel of a passive convolution operator, which implies that the Fourier transform of the impulse response is a Herglotz function. The forward scattering sum rule is finally constructed from integral identities for Herglotz functions.


  • Electrical Engineering, Electronic Engineering, Information Engineering


  • Electromagnetic theory-lup-obsolete
  • ISSN: 1364-5021

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