Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

the local-field factor that accounts for the difference in the field inside andoutside the nanoparticle [45].In this subsection, we briefly discuss the results of the pump-dependentTA studies of CdSe NQDs that focus on the effect of the NQD sizes and thesolvent/matrix material on the strength of excited-state absorption [44].Figure 11a displays absorption spectra of a hexane solution of small CdSeNQDs with R = 1.2 nm recorded at 2 ps after excitation for progressivelyhigher pump intensities (the pump photon energy is 3.1 eV). These spectrado not show any evidence of gain (a< 0), even at the highest pump densityhN 0 i = 6. Instead, the 1S absorption bleaching saturates slightly below a leveljDaja 0 c1 [i.e., right before a crossover to optical gain (Fig. 11b, squares)].Such behavior indicates that the 1S transition is bleached by only one type ofcarrier (electrons), consistent with femtosecond PL data from Section II.C,indicating very fast hole relaxation from the ‘‘absorbing’’ (responsible for the1S absorption) to the lower-energy ‘‘emitting’’ (involved in the PL transition)fine-structure state.However, for this NQD size, optical gain is not detected at the positionof the ‘‘emitting’’ transition either. In the region of this transition, the sampleshows increased absorption (i.e., PA). In contrast to 1S bleaching, whichsaturates at high pump intensities, PA does not show saturation (circles inFig. 11b) and, therefore, cannot be circumvented by simply increasing theexcitation density.Despite the fact that PA is a general feature of hexane solutions of CdSeNQDs, its relative contribution to band-edge TA signals is reduced for largerNQD sizes. This effect is illustrated in Fig. 12a, which displays pumpdependentTA spectra for TOPO-capped NQDs of 3.5-nm radius. Thesespectra clearly show the development of negative absorption (i.e., opticalgain) at the position of the ‘‘emitting’’ transition. As indicated by the TApump dependence in Fig. 12b (open squares), optical gain develops betweenone and two e–h pairs per dot on average and at hNi 0 c 17, it reaches itsmaximum. Gain decreases at higher excitation densities, which is due to theincrease in the relative contribution from excited-state absorption. At veryhigh excitation powers (hNi 0 >100) the band-edge nonlinear optical responseis dominated by PA.Interestingly, the gain magnitude [ g = (a 0 + Da)] at the maximum ofthe pump dependence exceeds the magnitude of the ground-state absorption( g max c 1.1a 0 ) [i.e., greater than the value expected for a complete populationinversion (a 0 )]. This discrepancy indicates a more complex gain mechanism inNQDs than simple state filling in a two-level system, as discussed in Sect.IV.A.Figure 12b compares pump-dependent TA signals recorded at theposition of the emitting transition for NQDs of different radii. These dataclearly illustrate the competition between optical gain and PA as a function ofCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.