Spectral analysis of TE beam scattering from a moving planar dielectric-magnetic half-space

This contribution is concerned with deriving the canonical scattering of a single time harmonic TE beam from a moving planar dielectric-magnetic half-space. The incident wave objects serve as the basis wave propagators of the PhaseSpace Beam Summation Method. By applying the plane wave spectral representation in the laboratory frame, using the Lorentz Transformation and applying Maxwell´s boundary conditions in the co-moving frame, we obtain an exact solution for the reflected and transmitted fields from and into the dielectric magnetic halfspace in both the laboratory and the co-moving frames in the form of spectral integrals.