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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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(p.180) Chapter Nine Homogenisation
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

G. F. Roach

I. G. Stratis

A. N. Yannacopoulos

Princeton University Press

This chapter formulates the homogenisation problem for a complex electromagnetic medium. It presents a formal two-scale expansion that motivates this chapter's approach, enabling a prediction of the form of the homogenised system. Next, this chapter provides a rigorous approach to the homogenisation problem for media in the optical response region, which is then generalised for dispersive media. The convergence of the evolution equations for the fields in periodic media to those for a homogenised medium is proved and the coefficients of the homogenised medium are identified in terms of auxiliary elliptic problems. Lastly, this chapter collects some general comments and alternative approaches to the homogenisation problem.

Keywords:   homogenisation, homogenisation problem, two-scale expansion, homogenised system, dispersive media, periodic media, homogenised media, auxiliary elliptic problems

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