Abstract
We study the excitonic effects on the second-order nonlinear optical properties of semi-spherical quantum dots considering, on the same footing, the confinement potential of the electron-hole pair and the Coulomb interaction between them. The exciton is confined in a semi-spherical geometry by means of a three-dimensional semi-parabolic potential. We calculate the optical rectification and second harmonic generation coefficients for two different values of the confinement frequency based on the numerically computed energies and wavefunctions of the exciton. We present the results as a function of the incident photon energy for GaAs/AlGaAs quantum dots ranging from few nanometers to tens of nanometers. We find that the second-order nonlinear coefficients exhibit not only a blue-shift of the order of meV but also a change of intensity compared with the results obtained ignoring the Coulomb interaction in the so-called strong-confinement limit.
Highlights
Nonlinear optical properties of semiconductor quantum dots have attracted considerable interest due to their several potential applications [1,2,3,4]
We present the case without excitonic effects, i.e., when only one electron exists in the quantum dot
The optical rectification (OR) and second harmonic generation (SHG) coefficients exhibit different peak intensities depending on the consideration of the Coulomb interaction, as it can be seen in Figures 2 and 3
Summary
Nonlinear optical properties of semiconductor quantum dots have attracted considerable interest due to their several potential applications [1,2,3,4]. Several authors [5,6,8] studied the effects of an exciton on the second-order nonlinear properties in one-dimensional semi-parabolic quantum dots. In this study we find eigenenergies and eigenstates of an exciton in a semi-spherical quantum dot solving the corresponding three-dimensional Schrödinger equation using a finite elements method and taking into account both the confinement and Coulomb potentials of the electron-hole pair. Our results show that energy and intensity of the peaks in the second-order nonlinear optical coefficients change when Coulomb interaction is introduced. In “Results” section, we show the OR and SHG coefficients with and without Coulomb interaction as a function of the incident photon energy for two quantum dot sizes. In one-dimensional case, the confinement potential imposes constraints to spatial coordinates, resulting in a hydrogen-like (asymmetric-harmonic) reduced particle Hamiltonian for weak (strong) limit. Under the double resonance condition, i.e., ħω ≈ E10 ≈ E20/2, the intensity of the peak is given by
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