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Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics$
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G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

Print publication date: 2012

Print ISBN-13: 9780691142173

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691142173.001.0001

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Scattering Problems: A Variety of Topics

Scattering Problems: A Variety of Topics

Chapter:
(p.112) Chapter Six Scattering Problems: A Variety of Topics
Source:
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics
Author(s):

G. F. Roach

I. G. Stratis

A. N. Yannacopoulos

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691142173.003.0006

This chapter continues the study of scattering problems in the case where the considered fields have harmonic time dependence and the involved chiral media are homogeneous. It begins by containing various important concepts of scattering theory. Next, the chapter deals with the establishment of the reciprocity principle, the general scattering theorem, and the optical theorem for the chiral obstacle in an achiral environment problem; moreover, a study of the spectrum of the far-field operator and its relation to that of the T-matrix is included. Hereafter, the chapter deals with the generalisation of the Atkinson–Wilcox expansion theorem to the perfect conductor in a chiral environment problem and presents results on chiral Herglotz wave functions. It also exhibits infinite Fréchet differentiability of the mapping from the boundary of the scatterer onto the far-field patterns. Finally, the chapter discusses topics related to chiral media.

Keywords:   scattering problems, chiral media, scattering theory, reciprocity principle, dyadics, Herglotz wave functions, general scattering theorem, optical theorem, Atkinson–Wilcox expansion theorem, infinite Fréchet differentiability

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