Homogenization of Maxwell Equations—Macroscopic and Microscopic Approaches

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


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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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Microwave Engineering and PhotonicsTechnical University of DarmstadtDarmstadtGermany
  2. 2.Department of Electrical Engineering and Information TechnologiesTechnical University of DarmstadtDarmstadtGermany

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