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

The second harmonic generation (SHG) and the sum frequency generation (SFG) processes are investigated in the conduction band states of the singly charged ZnO quantum dot (QD) embedded in the HfO2, and the AlN matrices. With two optical fields of frequency ωp and ωq incident on the dot, we study the variation with frequency of the second order nonlinear polarization resulting in SHG and SFG, through the electric dipole and the electric quadrupole interactions of the pump fields with the electron in the dot. We obtain enhanced value of the second order nonlinear susceptibility in the dot compared to the bulk. The effective mass approximation with the finite confining barrier is used for obtaining the energy and wavefunctions of the quantized confined states of the electron in the conduction band of the dot. Our results show that both the SHG and SFG processes depend on the dot size, the surrounding matrix and the polarization states of the pump beams.