Numerical results are given for the backscattering cross section of a dielectric elliptical cylinder. Computations are carried out using the exact solutions in terms of Mathieu functions. Both polarizations of the incident wave are considered: one with the incident electric vector in the axial direction and the other with the incident magnetic vector in the axial direction. The parameters considered are: K02q2=0.004, 0.4, 4.0, 8.0, 12.0, 16.0, 20.0; 0≤qK0 cosξ0 <6.5;<1/ε0=2.0; 0≤θ≤90°. K0 is the free-space wavenumber, q is the semifocal length, q cosξ0 is the length of the semimajor axis, θ is the angle of incidence with respect to the major axis, and ∊1/∊0 is the relative dielectric constant of the cylinder.
C. YEH, "Backscattering Cross Section of a Dielectric Elliptical Cylinder," J. Opt. Soc. Am. 55, 309-312 (1965)