Relativistic charged particles in the field of an electromagnetic plane wave in a medium

Solutions of the Klein-Gordon and Dirac equation for a charged particle in the field of an electromagnetic plane wave in a medium with a constant refractive index n are discussed. Generally, for n² < 1, spontaneous pair creation from the vacuum, and for n² > 1, energy bands are observed. The interplay of Compton and Cherenkov scattering is discussed. Some doubts are formulated as to the physical relevance of calculating pair creation in a homogeneous electric field as it is usually done.