# Analysis Seminar

#### Homogenization of Maxwell Equations in Complex Geometries: On the Counter-Intuitive Behavior of Meta Materials

Speaker: Ben Schweitzer, University of Dortmund

Location: Warren Weaver Hall 1302

Date: Thursday, May 10, 2012, 11 a.m.

Synopsis:

Optically active meta-materials can nowadays be constructed as physical objects. They can have astonishing properties or lead to striking effects, the key-words are negative refraction, perfect imaging, and cloaking. I will present the effect of a negative magnetic permeability of the effective material and perfect light transmission through small holes in a metallic structure.

Mathematically, we analyze the time-harmonic Maxwell equations in a heterogeneous medium, the coefficients of the equation can oscillate on a small spatial scale and the oscillations of the values can be very large. The heterogeneity of the optical medium is prescribed by specifying the permittivity, which varies on a small length scale $$\eta$$. The electric and magnetic fields are determined by the time-harmonic Maxwell system. We analyze the weak limits of the electric and magnetic fields as $$\eta$$ tends to zero, obtaining an "effective equation" that characterizes the limits. The coefficients of the effective equation describe the behavior of the metamaterial.

This is joint work with G. Bouchitte and with A. Lamacz.