Nonlinear Diffraction in a Quantum-Dot System with Allowance for the Hubbard Interaction

摘要

The propagation of monochromatic laser radiation in a volume system of quantum dots (QDs) that are tunnel-coupled along one axis is considered. The electron energy spectrum of the QD system is modeled in the tight-binding approximation with allowance for the Coulomb interaction of electrons in the Hubbard model. The electromagnetic field of laser radiation in a QD system is described quasi-classically by Maxwell equations; as applied to this problem, they are reduced to a non-one-dimensional wave equation for the vector potential. As a result of the analysis of the wave equation in the approximation of varying amplitudes and phases, an effective equation describing the electromagnetic field in a QD system is obtained and numerically solved. The influence of the parameters of the system and the amplitude and frequency of the field of incident laser radiation on the character of its propagation is investigated. Nonmonotonic dependences of the factor characterizing the laser beam diffraction spread on the parameters of the electron energy spectrum of the system are obtained.