Let us consider the following [Gedankenexperiment](http://en.wikipedia.org/wiki/Thought_experiment):

A cylinder **rotates** symmetric around the $z$ axis with [angular velocity](http://en.wikipedia.org/wiki/Angular_velocity) $\Omega$ and a plane wave with $\mathbf{E}\text{, }\mathbf{B} \propto e^{\mathrm{i}\left(kx - \omega t \right)} $ gets scattered by it.

We assume to know the *isotropic* [permittivity](http://en.wikipedia.org/wiki/Permittivity) $\epsilon(\omega)$ and [permeability](http://en.wikipedia.org/wiki/Permeability_%28electromagnetism%29) $\mu(\omega)$ of the cylinder's material *at rest*. Furthermore, the cylinder is infinitely long in $z$-direction.

The static problem ($\Omega = 0$) can be treated in terms of [Mie Theory](http://en.wikipedia.org/wiki/Mie_theory) - here, however, one will need a **covariant** description of the system for very fast rotations (which are assumed to be possible) causing nontrivial transformations of $\epsilon$ and $\mu$.

Hence my question:

> 
> ### What is the scattering response to a plane wave on a fastly rotating cylinder?
> 
> 
> 

[RotatingDisc http://www.personal.uni-jena.de/~p3firo/PhysicsSE/RotatingDisc.png](http://www.personal.uni-jena.de/~p3firo/PhysicsSE/RotatingDisc.png)

Thank you in advance