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

IV.MULTIPARTICLE EFFECTS AND OPTICAL GAIN INNQDsA. Band-Edge Transient Absorption and Optical Gainin NQDsIn terms of the TA spectroscopy, optical gain (i.e., negative absorption)corresponds to pump-induced absorption bleaching with a magnitude that isgreater than sample absorption in the ground state. In strongly confinedcolloidal NQDs, pump-induced absorption changes are primarily due to statefilling and Coulomb multiparticle interactions (the carrier-induced Starkeffect) [32,33]. State filling arises from Pauli exclusion and leads to thebleaching of the interband optical transitions that involve populated quantizedstates. The Stark effect is associated with local fields generated byphotoexcited carriers and leads to a shift of optical transitions and changes intransition oscillator strengths as a result of modifications in the selectionrules. In contrast to state filling, which selectively affects only transitionsinvolving populated states, the carrier-induced Stark effect does not have thisselectivity and modifies NQD transitions that involve both occupied andunoccupied electronic states [47]. However, in the case of transitions thatcouple populated NQD states, the relative contribution of the Stark effect toTA signals is significantly smaller than that of state filling [33]. The statefillingeffect, for example, is almost entirely responsible for the pump-dependentbleaching of the strong 1S absorption resonance [33]. On the otherhand, involvement of Coulomb multiparticle interactions is essential for theexplanation of optical-gain signals detected in the region of the lowest‘‘emitting’’ transition (discussed later).The absorption changes resulting from the state-filling effect are proportionalto the sum of the electron and hole occupation numbers. If wepresent the linear absorption spectrum of NQDs as a superposition ofseparate absorption bands corresponding to different quantized opticaltransitions, the state-filling-induced absorption changes (Da) can be calculatedusingDað txÞ ¼X ia i G i ð tx tx i Þðn e i þ n h i Þ ð2Þin which G i ( tx tx i ) is the unit-area absorption profile of the tx i transition,a i is its area, and n e i and n h i are occupation numbers of the electron andhole states involved in the transition. Under thermal quasiequilibrium (afterthe intraband relaxation is finished), the occupation numbers can be foundusing the Fermi distribution function. Within this model, a normalized ab-Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.