Optimization of band structure and quantum-size-effect tuning for two-photon absorption enhancement in quantum dots

The two-photon absorption, 2PA, cross sections of PbS quantum dots, QDs, are theoretically and experimentally investigated and are shown to be enhanced with increasing quantum confinement. This is in contrast to our previous results for CdSe and CdTe QDs where the reduced density of states dominated and resulted in a decrease in 2PA with a decrease in QD size. Qualitatively this trend can be understood by the highly symmetric distribution of conduction and valence band states in PbS that results in an accumulation of allowed 2PA transitions in certain spectral regions. We also measure the frequency nondegenerate 2PA cross sections that are up to five times larger than for the degenerate case. We use a k·p four-band envelope function formalism to model the increasing trend of the two-photon cross sections due to quantum confinement and also due to resonance enhancement in the nondegenerate case.