Two-photon transitions in systems with semiconductor quantum dots

Optical interband and intraband transitions in semiconductor quantum dots (QD's) are analyzed theoretically. It is found that three-dimensional confinement essentially modifies intraband matrix elements of the electron-photon interaction in the QD's as compared to the bulk materials. This effect is quite important for the multiphoton processes. It is shown that two competitive types of two-photon transitions with different selection rules are in the QD's of noncentrosymmetric semiconductor and amplitudes of these transitions differently depend on light polarization, electron and hole effective masses, and QD radius as well. Analytical expressions for the two-photon absorption coefficient are derived for the strong confinement regime, taking into account the size distribution of the nanocrystals.