To best answer your question, I need some more information:

1) Is the cylinder invariant in the z direction?

2) Is the cylinder large compared to wavelength?

Hi Milou,

Thanks for your response. Answering to your questions.

1. Yes cylinder is invariant in the z direction.

2. Yes cylinder is large compared to the wavelength

Since the cylinder is large compared to wavelength (and assuming the radius of curvature is as well), I would recommend you use physical optics (PO) to solve for the backscattering. I wrote a paper a couple of years back where I predicted the PO scattering of a partially coherent wave from a circular cylinder (attached). You could adapt that to a 2D elliptical cylinder.

If the cylinder is not too large compared to wavelength, you could use the Method of Moments (MoM) to exactly solve for the backscatter. There are many references, many of them classic electromagnetic references, that discuss the MoM in regards to 2D scatterers.