Size-dependent enhancement of nonlinear optical susceptibilities due to confined excitons in CuBr nanocrystals

We have investigated the third-order nonlinearity on resonance with the confined exciton level in CuBr nanocrystals with radii in the range $2.7--42$ nm embedded in glass by means of degenerate four-wave mixing, time-resolved luminescence, and resonant luminescence measurements. The third-order optical susceptibility χ⁽³⁾ exhibits resonant behaviors at Z₁₂ and Z₃ excitons, which are weakly confined in nanocrystals. The figure of merit |χ⁽³⁾|/α increases with increasing radius R in the whole range studied here. We have measured homogeneous widths and lifetimes of Z₁₂ excitons and obtained size dependences of those relaxation parameters. Assuming a two-level atomic model for the confined exciton, we have deduced the size dependence of the oscillator strength of Z₁₂ excitons from the measured lifetimes, homogeneous widths, and χ⁽³⁾. The oscillator strength exhibits the R2.0 dependence in the whole range studied here, which reveals the giant oscillator strength effect on the confined exciton that is coherently generated in the nanocrystal. The oscillator strength per nanocrystal is enhanced by a factor 1.7×10³ for $R=42$ nm compared to that of bulk excitons. We also discuss the derivation of χ⁽³⁾ in the stationary regime from the χ⁽³⁾ in the transient regime where the nonlinear time response shows a multiexponential decay.