Optical properties of a semispherical quantum dot placed at the center of a cubic quantum box: Optical rectification, second and third-harmonic generations

In the present paper, we first apply finite element method (FEM) and Arnoldi algorithm to obtain energy eigenvalues and eigenfuctions of a semispherical quantum dot located at the center of a cubic box. Then, the compact-density matrix approach and an iterative method are used to find the optical rectification (OR) coefficient, second harmonic generation (SHG) and third harmonic generation (THG). Numerical calculations are performed for the typical $\mathrm{GaAs}/{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ system. It is found that OR coefficient has a red-shift when the semispherical radius R becomes larger. Raising R and potential height V₀, the magnitude of OR coefficient, SHG and THG are increased. Moreover, the position of resonant peaks of OR coefficient, SHG and THG are affected by the semispherical radius and potential height.