Electromagnetic Scattering by Magnetic Biaxial Cylinders

In this work a volume integral equation method is proposed for the evaluation of the electromagnetic scattering by multilayered magnetic biaxial circular cylinders with infinite length. The key point of the proposed method is the expansion of the magnetic field and magnetic flux density in Dini-type cylindrical vector wave functions, which consitute an orthogonal vectorial basis in the transversal circular cross section of the cylinder. These expansions reduce the two-dimensional volumetric-type integrals to sets of algebraic equations. The cylinder is illuminated by a normally impinging, on cylinder's axis, plane wave. Both types of $H$ -and $E$ -wave polarization of the incident plane wave are considered. The formalism used in this method allows for an easy and direct incorporation of the multilayered magnetic biaxial permeability profiles through the constitutive relations. The method is validated by comparison of the normalized scattering cross section with the exact solution for the case of uniaxial anisotropy. Moreover, we employ HFSS commercial software to verify our results for homogeneous and inhomogeneous magnetic biaxial profiles.