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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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Towards a Scattering Theory

Towards a Scattering Theory

Chapter:
(p.212) Chapter Ten Towards a Scattering Theory
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/9780691142173.003.0010

This chapter indicates how scattering theories can be developed when wave motions in chiral media are studied. To begin, this chapter remarks that a scattering process describes the effects of a perturbation on a system about which everything is known in the absence of the perturbation. It then presents a general formulation of the class of problems thus described in terms of evolution operators, and outlines an approach to scattering theory in the time domain. The chapter also shows how the use of spectral theory allows the explicit construction of solutions to abstract initial boundary value problems in terms of generalised integral transforms, and how these generalised integral transforms can be used for the construction of the wave operators and the scattering operator. Furthermore, this chapter explores the extension of these ideas to the study of electromagnetics of complex media.

Keywords:   scattering theories, wave motions, chiral media, scattering process, wave operators, evolution operators, time domain, spectral theory, generalised integral transforms

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