Exact theory of optical transition radiation in the far and near zones

We present an exact solution for the complex field of transition radiation (TR) emitted by an electron incident on a conductive screen. The solution is valid in all space. In the reactive near zone, it replicates the Coulomb fields of the electron and its image charge and their evolution into radiation fields after termination of the charge's current at the screen. Using a general formulation for radiation diffraction from a current line, we derive diffraction integral expressions in the reactive near zone, the Fresnel near zone, and the Fraunhofer far zone in analogy to diffraction from a planar radiation source. The derived exact complex field expressions can be useful for describing coherent optical TR from a beam of phase-correlated charge particles in the near field and in the imaging plane of the screen.