Nonlinear propagation of light in Dirac matter

Pseudorelativistic laser-semiconductor quantum plasma interactions

A model is presented for the nonlinear interaction between a large-amplitude laser and semiconductor plasma in the semirelativistic quantum regime. The collective behavior of the electrons in the conduction band of a narrow-gap semiconductor is modeled by a Klein-Gordon equation, which is nonlinearly coupled with the electromagnetic (EM) wave through the Maxwell equations. The parametric instabilities involving the stimulated Raman scattering and modulational instabilities are analyzed theoretically and the resulting dispersion relation relation is solved numerically to assess the quantum effects on the instability. The study of the quasi-steady-state solution of the system and direct numerical simulations demonstrate the possibility of the formation of localized EM solitary structures trapped in electrons density holes.

Relativistic Klein-Gordon-Maxwell multistream model for quantum plasmas

A multistream model for spinless electrons in a relativistic quantum plasma is introduced by means of a suitable fluidlike version of the Klein-Gordon-Maxwell system. The one- and two-stream cases are treated in detail. A new linear instability condition for two-stream quantum plasmas is obtained, generalizing the previously known nonrelativistic results. In both the one- and two-stream cases, steady-state solutions reduce the model to a set of coupled nonlinear ordinary differential equations, which can be numerically solved, yielding a manifold of nonlinear periodic and soliton structures. The validity conditions for the applicability of the model are addressed.