Theoretical studies on the shape dependence of three-photon absorption in semiconductor nanocrystals

We report a three-photon absorption (3PA) theory which has systematically revealed the characteristics of 3PA in CdSe NCs with four different shapes: sphere, cube, cylinder and cuboid. Due to the splitting of degenerate energy levels caused by the decrease in the degree of symmetry, nanocuboids and nanocubes exhibit greater 3PA cross-sections than nanocylinders and nanospheres with similar sizes, respectively. For a given wavelength, nanocuboids show the strongest size dependence among the four shapes. Also, the size dependence of 3PA cross-section is more sensitive to the lateral size than the longitudinal size in the cases of nanocylinders and nanocuboids. In addition, we estimate the light intensity under which the 3PA process distinguishes itself from the 2PA, and it is found that the light intensity required for the distinguishable observation of 3PA is the lowest in nanosphere, while it is the highest in nanocylinder.