Excitonic effects on the second-order nonlinear optical properties of semi-spherical quantum dots

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.

Quadrupole second harmonic generation and sum-frequency generation in ZnO quantum dots

“…4,20 The nonlinear optical properties are reported for different forms of ZnO such as single crystals, thin films, nanowires and nano-ribbons. 14 The enhancement of the nonlinear optical properties as compared to bulk counterpart is observed for thin films. 30 ZnO owing to its non-centrosymmetric uniaxial crystal structure possesses second order nonlinear coefficient of the order of 10 −12 m/V.…”

“…Since the first observation of the SHG 9 several studies are reported on the materials with large second order nonlinearity. 8,[10][11][12][13][14][15][16][17][18][19] The second order nonlinear optical properties in semiconductor nanostructures associated with the interband transitions (between the levels of different bands) and the intraband transitions (between levels of the same band) have been studied by several authors. 8,20,21 The second order nonlinearity has potential applications such as in harmonic generation, biological imaging, and nonlinear optical microscopy.…”

“…Most of the studies on the second order nonlinear processes are reported using quantum wells 16,[22][23][24] and only fewer reports have used quantum wires 25 and quantum dots (QDs). 8,[13][14][15][26][27][28] The first demonstration of the nonlinearity associated with the intersublevel (ISL) transitions in quantum well was reported by Fejer et al 29 Later on Sauvage et al 8 observed the SHG from the ISL transitions of the conduction band states in QDs. The reasons for the growing interest in the second order nonlinear process associated with QDs are three fold; first the similarities between atoms and QD structures with size-tunable atomic like properties which offer an opportunity to manipulate the nonlinear optical responses by tailoring the energy states and the strength of transitions.…”

Exciton related nonlinear optical properties of a spherical quantum dot

“…Some of the previous works make an approximation about the shape of the dot. Some take it as onedimensional [7,13,17], two-dimensional [8,16], disk-like [10,11,15], or semi-spherical [9]. This may simplify the calculation of the electronic structure of the QD.…”

“…There have been a number of investigations of the problem of exciton-related nonlinear optical properties of a QD [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The majority of these works are either numerical or considering only the strong confinement limit.…”