Harmonic generations in a lens-shaped GaAs quantum dot: Dresselhaus and Rashba spin-orbit couplings under electric and magnetic fields

In this work, effects of external electric and magnetic fields in the presence of both Rashba and Dresselhaus spin-orbit couplings on the second and third harmonic generations (SHG and THG) of a lens-shaped GaAs quantum dot are studied. Energy eigenvalues and eigenvectors are calculated numerically and optical properties are obtained using the compact density matrix approach. Our results reveal that, an increase in the magnetic field, leads to both red and blue shifts in resonant peaks of both SHG and THG. On the other hand, augmentation of electric field leads to blue shift in all resonant peaks except the first peak related to lowest transition. Also the dipole moment matrix elements increase by enhancing both electric and magnetic fields. Finally the effect of dot size is studied and results illustrate that increment in size reduces the transition energies except the lowest one and thus leads to red shift in resonant peaks while the first peak remains constant.