Effect of the position of a hydrogen-like impurity on the generation of the third harmonic in a cylindrical quantum dot

Abstract

This paper presents a theoretical study of the third-order nonlinear optical susceptibility in a GaAs/Ga_0.6Al_0.4As cylindrical quantum dot (CDQ) with a hydrogen-like impurity inside. The variational method was utilized to calculate the energies and wave functions corresponding to the bound states of the impurity, which include the $1s$-like, $2p_{-}$-like, $2p_{+}$-like, and $2p_z$-like states, with consideration of the impurity’s motion within the cylindrical quantum dot. The findings indicate that the resonant peaks of the optical third harmonic generation (THG) coefficient undergo a red shift as the impurity is displaced from the center of the CDQ towards the potential barrier. This shift can be attributed to a reduction in the average electrostatic interaction between the impurity and the surrounding ion as the impurity approaches the potential barrier. This phenomenon can be attributed to the decreased electrostatic attraction between the impurity and the quantum dot core as the impurity moves away from the center and approaches the region of higher potential confinement. These findings have significant implications for the design and optimization of quantum dot-based optoelectronic devices, as manipulation of the impurity position can provide additional control over the nonlinear optical properties of these systems.