Four-dimensional relativistic scattering of electromagnetic waves from an arbitrary collection of moving lossy dielectric spheres

Abstract

Four-dimensional (4D) relativistic scattering of electromagnetic waves from an arbitrary collection of uniformly translational moving lossy dielectric spheres is discussed. Two reference frames, four 4D coordinate systems and Lorentz transformation are used to obtain the scattered electromagnetic fields. The direct scattering of the spheres and their interactions are considered with a novel approach. The introduced method is straightforward and the analytical relations for the fields are achieved. To check the validity of the proposed method, different examples for both stationary and moving scatterers are investigated. The effects of key parameters such as the size, material, velocity, number, position of the spheres and also the frequency of the incident wave are discussed. The derived scattered fields are valid for low, medium and high velocities but according to practical applications low and moderate velocities are highlighted in numerical results.