A theoretical study of third-harmonic generation in semi-parabolic plus semi-inverse squared quantum wells

A theoretical study of third-harmonic generation is performed by using the compact-density-matrix method. An electron is confined in semi-parabolic potential plus semi-inverse squared potential quantum wells. Our calculations show that the absolute value, the imaginary part and the real part of third-harmonic generation coefficients are greatly influenced by the parabolic confinement frequency and the characteristic parameter of the inverse squared potential. The relationship between the absolute value and the imaginary part as well as the relationship between the absolute value and the real part is discussed. It is found that the resonant peaks of the absolute value originate from the imaginary part and are not related to the real part.