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

than 1%. Acceleration of radiative decay in the regime of stimulated emissionas well as selective amplification of propagating waveguide modes make thecontribution of biexcitons dominant over the contribution of excitons in thesample edge emission above the ASE threshold.In order to take into account the existence of two types of emitter(excitons and biexcitons) and the fact that optical gain in NQDs is dominatedby biexcitons and spontaneous emission is primarily due to single excitons,the ASE formula can be rewritten as I = A x l+A bx (e g bxl1)/g bx , where A xand A bx are constants proportional to spontaneous emission power densitiesfor excitons and biexcitons, respectively, and g bx is the biexciton modal gain.Using this formula, one can simultaneously fit both below- and abovethresholdregions of the I-versus-l dependence (solid line in Fig. 25b), whichyields g bx = 155 cm 1 . This estimate represents effective modal gain per unitstripe length measurd for waveguide modes. To estimate the modal gain inthe absence of waveguiding effects (i.e., gain per unit propagation lengthalong the ray), we can scale g bx by a correction factor b = n gl /n c 0.83 (n gl isthe index of a glass substrate), which yields g m = bg bx c130 cm 1 (thisestimate assumes that the ASE is dominated by the mode that corresponds tothe critical angle of the total internal reflection). Because of the transientnature of optical gain in the case of pulsed excitation, the above-derivedquantities represent time-averaged characteristics of the NQD gain medium(i.e., gain average over the gain lifetime).The inset in Fig. 25b displays dynamics of normalized, pump-inducedabsorption changes ( Da/a 0 ) in the same NQD film as the one used in theASE studies discussed earlier, These dynamics indicate that optical gain( Da/a 0 > 1) only exists during time t g c5 ps following photoexcitation. Asdiscussed earlier, the fast gain decay is due to intrinsic, nonradiative Augerrecombination and, possibly, to ultrafast hole trapping [50]. The short gainlifetimes are likely responsible for saturation of the ASE intensity observedin ‘‘variable-stripe-length’’ measurements at l>l s c0.08 cm (Fig. 25b). Thelight propagation time corresponding to the ‘‘saturation’’ length is f6 ps,which is a value close to the gain lifetime (f5 ps). This observation indicatesthat under pulsed-excitation conditions, the transient nature of the NQD gainFigure 25 Room-temperature emission spectra of a CdSe NQD film recordedusing the ‘‘variable-stripe-length’’ configuration (shown schematically in the inset);pump fluence is 1 mJ/cm 2 . (b) Solid circles describe the ASE intensity as a function ofthe stripe length. The dashed line is a fit to I = A(e gl 1)/g ( g = 120 cm 1 ), whereasthe solid line is a fit to I = A x l + A bx (e g bx l1)/g bx ( g bx = 155 cm 1 ); note adifference in gain magnitudes produced by these two fits. Inset: Gain dynamicsmeasured using a TA experiment (t g is a gain lifetime).Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.