Electromagnetic Scattering From A Gyrotropic Anisotropic Sphere In An Off-axis Obliquely Incident Gaussian Beam

As early as in 1908, Mie gave the analytical solution to the homogeneous isotropic medium sphere of the electromagnetic scattering in the base of Lorenz, which is called the Lorenz-Mie theory. Electromagnetic scattering of a plane wave has been studied in various field by many scholars. However, most of these studies are limited to a plane wave, the research for the Gaussian beam is lacking. It have been successfully established many methods about Gaussian beam through the tireless efforts of many experts and scholars. The internal field of Gaussian beam are expanded by Fourier transform method which will make a large amount of computation.In this paper, an analytical solution to the scattering of an off-axis Gaussian beam obliquely incident by a gyrotropic anisotropic sphere is obtained in the particle-centered system and gives some results of the numerical calculations. At first, the paper solved the problem of the introduction of the Gaussian beam. On this basis, the paper gives the solution about the off-axis Gaussian beam incident by a gyrotropic anisotropic sphere. Based on the local approximation to the off-axis beam shape coefficients and the coordinate rotation theory, the off-axis obliquely incident Gaussian beam is expanded with the spherical vector wave functions in the primary coordinate of the gyrotropic anisotropic sphere. According to the Maxwell’s equations of the anisotropic medium in the passive space, the differential equation of the electromagnetic fields is derived. Solving the differential equation of the electromagnetic fields which is expanded by the spherical vector wave functions, the eigen matrix of the propagation constants k are obtained and the eigenvalue and eigenvector can also be obtained. The internal electromagnetic fields of the gyrotropic anisotropic sphere are proposed in the matrix form of the spherical vector wave functions. In order to cooperate with the form of the internal field, the scattered fields can be transformed with spherical vector wave functions into the form of the plane wave which will make matching the boundary condition easier. Utilizing the continuous tangential boundary conditions, both the scattered fields and the internal field coefficients are derived analytically. The correctness of the theory is verified by comparing our numerical results with that of the plane wave scattering by a gyrotropic anisotropic sphere where the large waist radius of ?? 200?. The influences of the beam waist raduis and the permittivity tensors on the field distributions are analyzed at arbitrary incidence. Numerical results show that with the beam waist radius increasing, the distribution of the RCS is increasing. At the same time, the paper gives some other numerical results about an off-axis Gaussian beam obliquely incident by a gyrotropic anisotropic sphere. The numerical results presented in this paper provide an effective calibration for further research on scattering properties of the layered anisotropic targets and their applications in the stealth technology.