Relativistic Scattering of Electromagnetic Waves by Moving Obstacles

The excitation for an obstacle moving with constant velocity in free space (Σ) is transformed to the scatterer's rest system (Σ′), and the corresponding far-field scattering U′∼Ua′(g) is transformed to Σ to obtain U ∼ Ua(G). A simple expression is derived for the scattering amplitude G in terms of the conventional g, and known functional forms U[G] give the scattered field in Σ as a complex integral and its inverse-distance expansion. In dyadic form, G̃ = p̃r·g̃·p̃, where p̃ corresponds to transforming the excitation from Σ to Σ′, and p̃r (a planar reciprocal) to transforming the scattering from Σ′ to Σ. Then we transform the Green's function surface and volume integral representations, and the multipole series for U′, and apply the results to spherically symmetric scatterers, arbitrary small scatterers, large tenuous scatterers, and to cylinders and slabs.