Polaron effects on the optical rectification and the second harmonic generation in cylindrical quantum dots with magnetic field

Polaron effects on the optical rectification (OR) and the second harmonic generation (SHG) in cylindrical quantum dots (CQDs) with the radial parabolic potential and the z  -direction linear potential in the presence of the magnetic field are theoretically investigated. The expressions for both the OR and the SHG are obtained within the framework of the compact-density-matrix approach and the iterative method. After considering the electron-LO-phonon interaction (ELOPI) as perturbation, the energy levels and the wave functions of an electron confined in CQD are obtained by perturbation theory. Numerical calculations are presented for GaAs/AlGaAsGaAs/AlGaAs. It is found that when we consider the ELOPI, the resonant peak of the OR χ0(2) is enhanced, whereas the magnitude of the SHG χ2ω(2) is greatly enhanced. It is also found that when we ignore the ELOPI, with the increase of the radial confinement frequency ωρωρ and the magnetic field B  , respectively, the resonant peak of the OR χ0(2) remains constant, whereas the magnitude of the SHG χ2ω(2) becomes small. However, when we consider the ELOPI, with the increase of ωρ,Bωρ,B and V   respectively, both the resonant peak of the OR χ0(2) and the magnitude of the SHG χ2ω(2) become small. Our results also find that whether the ELOPI is considered or not, with the increase of ωρ,B and V  , respectively, both χ0(2) and χ2ω(2) exhibit a blue shift.

► The radial potential is paprabic potential.
► The z-direction potential is linear potential.
► Optical rectification with polaron effects are enhanced.
► Second harmonic generation with polaron effects are enhanced.