# Homogenization of Maxwell Equations—Macroscopic and Microscopic Approaches

• Franko Küppers
Chapter
Part of the Springer Series in Optical Sciences book series (SSOS, volume 211)

## Abstract

We consider as a starting point a system of microscopic MEs in the following form: \left\{ \begin{aligned} & \text{rot}\, \vec {e} \;= \frac{{i\omega}}{c}\vec {h} \\ & \text{div} \vec {h} \;= 0 \\ & \text{div} \,\vec {e} \;= 4\pi \rho \\ & \text{rot} \,\vec {h} \;= - \frac{{i\omega}}{c}\vec {e} + \frac{{4\pi}}{c}\vec {j} \\ \end{aligned} \right.\quad \quad \left\{ \begin{aligned} &\rho \quad\;= \sum\limits_{i} {q_{i}\delta\left( {\vec {r} - \vec {r}_{i} } \right)} \\ & \vec {j} \quad\;= \sum\limits_{i} {\vec {v}_{i} q_{i}\delta\left( {\vec {r} - \vec {r}_{i} } \right)} \\ & \frac{{\text{d}\vec {p}_{i} }}{\text{d}t} = q_{i} \vec {e} + \frac{{q_{i} }}{c}\left[ {\vec {{v_{i} }} *\vec {h} } \right]. \\ \end{aligned} \right.

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