Imaging of a rotationally symmetric dielectric cylinder by a quadratic approach

A quadratic approximation of the electromagnetic scattering equation is used to solve the inverse problem of the reconstruction of the dielectric permittivity function of a rotationally symmetric cylindrical object embedded in a homogeneous medium and illuminated by an incident plane wave at fixed frequency. The problem is formulated as the minimization of a properly defined functional. Because the operator involved in the inversion is quadratic, it is possible to discuss and avoid the presence of local minima (a well-known problem in nonlinear inversion). Theoretical considerations and numerical examples show the advantages of using a quadratic model in comparison with a linear one.