First of all, I don't quite understand the following phrase: "The static problem (Ω=0) can be treated in terms of Mie Theory". The Mie theory is for diffraction on a homogeneous sphere, not a cylinder. The complete solution of the problem of diffraction of electromagnetic waves on an infinite homogeneous cylinder was obtained in J. R. Wait, Can. Journ. of Phys. 33, 189 (1955) (or you may find the outline of the Wait's solution for a cylindrical wave in http://arxiv.org/abs/physics/0405091 , Section III). This solution is rather complex, so I suspect your problem can only be solved numerically, as it seems significantly more complex. The Wait's problem is a special case of your problem, so the solution of the latter problem cannot be simpler than the Wait's solution. In particular, it seems advisable to expand your plane wave into cylindrical waves, following Wait. It seems that the material equations for the rotating cylinder can be obtained following http://arxiv.org/abs/1104.0574 (Am. J. Phys. 78, 1181 (2010)). However, the cylinder will not be homogeneous (the material properties will depend on the distance from the axis and may be anisotropic). I suspect the problem can be solved using numerical solution of an ordinary differential equation for the parameters of the cylindrical waves.