  We consider the scattering of time-harmonic electromagnetic waves by a
penetrable thin tubular scattering object in three-dimensional free space. We
establish an asymptotic representation formula for the scattered wave away from
the thin tubular scatterer as the radius of its cross-section tends to zero.
The shape, the relative electric permeability and the relative magnetic
permittivity of the scattering object enter this asymptotic representation
formula by means of the center curve of the thin tubular scatterer and two
electric and magnetic polarization tensors. We give an explicit
characterization of these two three-dimensional polarization tensors in terms
of the center curve and of the two two-dimensional polarization tensor for the
cross-section of the scattering object. As an application we demonstrate how
this formula may be used to evaluate the residual and the shape derivative in
an efficient iterative reconstruction algorithm for an inverse scattering
problem with thin tubular scattering objects. We present numerical results to
illustrate our theoretical findings. Mathematics subject classifications
(MSC2010): 35C20, (65N21, 78A46)
