Estudo das propriedades ópticas não lineares de éxcitons em pontos quânticos

Abstract

In this research, we study the effects of exciton confinement on the nonlinear optical susceptibility of one-dimensional quantum dots. We use a direct numerical diagonalization to obtain the eigenenergies and eigenfunctions of the discretized Hamiltonian representing an electron-hole pair confined by a semiparabolic potential and interacting with each other via a Coulomb potential. Density matrix approach and perturbation theory are used to compute the nonlinear optical susceptibilities due to third-harmonic generation, as well as the corresponding nonlinear corrections to the refractive index and absorption coefficient. These quantities are analyzed as a function of ratio between the confinement length L and the exciton Bohr radius a0. The Coulomb potential degrades the uniformity of the level spacings. We show that this effect promotes the emergence of multiple resonance peaks in the third-harmonic generation spectrum. In the weak confinement regime, β = L/a0 > 1, shown that the third-order susceptibility decays as 1/β8 due to the prevalence of the hydrogenoid character of the exciton eigenstates.