Photon induced relativistic band structure in dielectrics

New exact solutions of the Dirac equation of a charged particle interacting with an electromagnetic plane wave in a medium

“…with a real index of refraction n m < 1 or n m > 1), or the strong laser field is modelled by a time-periodic electric field, then the by now studied solutions of the relativistic wave equations can be expressed by the solutions of the corresponding Mathieu or Hill equations (see Narozhny and Nikishov 1974, Becker 1977, Cronström and Noga 1977. Such an analysis have for example been applied in the mathematical study of pair creation in strong fields (Nikishov andRitus 1967, Nikishov1970).…”

On beam models and their paraxial approximation

“…On the one hand, this allows testing of the locally-constant field approximation [35] used throughout numerical codes, and on the other hand opens up the possibility of studying new phenomena due to focussing [36][37][38][39], medium effects [40][41][42][43][44][45] and non-planewave longitudinal structure [46]. A focused pulsed laser background can be included in QED calculations perturbatively if it is weak enough, where it enters calculations as the Fourier transform of the vector potential.…”

Effective photon mass and exact translating quantum relativistic structures

“…Numerous works [31][32][33][34][35][36][37][38][39][40] on the KGE assume a (right-handed) circularly polarized electromagnetic (CPEM) wave. For a monochromatic field with four-wave-vector k l ¼ ðx=c; 0; 0; kÞ, it amounts to…”

“…Although the relation between x and k could be left completely undefined, the transverse plasma dispersion relation is assumed to keep resemblance with the previous analysis in the literature. [31][32][33][34][35][36][37][38][39][40][41][42] Substitution of the Ansatz (6) into the KGE, taking into account the mass-shell condition and the dispersion relation (7), gives…”

“…Examples are provided by the analysis of the Zitterbewegung (trembling motion) of Klein-Gordon particles in extremely small spatial scales, and its simulation by classical systems, 16 the KGE as a model for the Weibel instability in relativistic quantum plasmas, 17 the description of standing EM solitons in degenerate relativistic plasmas, 18 the KGE as the starting point for the wave kinetics of relativistic quantum plasmas, 19 the KGE in the presence of a strong rotating electric field and the QED cascade, 20 the Klein-Gordon-Maxwell multistream model for quantum plasmas, 21 the negative energy waves and quantum relativistic Buneman instabilities, 22 the separation of variables of the KGE in a curved space-time in open cosmological universes, 23 the resolution of the KGE equation in the presence of Kratzer 24 and Coulombtype 25 potentials, the KGE with a short-range separable potential and interacting with an intense plane-wave EM field, 26 electrostatic one-dimensional propagating nonlinear structures and pseudo-relativistic effects on solitons in quantum semiconductor plasma, 27 the square-root KGE, 28 hot nonlinear quantum mechanics, 29 a quantum-mechanical free-electron laser model based on the single electron KGE, 30 and the inverse bremsstrahlung in relativistic quantum plasmas. Very often, the treatment of charged particle dynamics described by the Klein-Gordon or Dirac equations assumes a circularly polarized electromagnetic (CPEM) wave, [31][32][33][34][35][36][37][38][39][40] mainly due to the analytical simplicity. However, the CPEM wave is not the ideal candidate for particle confinement.…”