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Crossover from strong to weak exciton confinement and third-harmonic generation on one-dimensional quantum dots

2012; Elsevier BV; Volume: 11; Issue: 1 Linguagem: Inglês

10.1016/j.photonics.2012.06.010

1569-4429

Jessica E. Q. Bautista, M. L. Lyra, R. P. A. Lima,

Molecular Junctions and Nanostructures

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 eigenstates 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 perturbation theory is used to compute the nonlinear optical susceptibilities due to third-harmonic generation and 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 separation. 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, the third-order susceptibility is shown to decay as 1/β8 due to the prevalence of the hydrogenoid character of the exciton eigenstates.