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.
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