Emission-energy dependence of ultrafast P-emission decay in ZnO from bulk to nanofilm

Theory of the lifetime of an exciton incoherently created below its resonance frequency by inelastic scattering

“…The excitons are scattered to bare exciton states first, and then they are converted to polaritons in a finite conversion time, which corresponds to the P-emission lifetime observed in the recent experiments using the optical Kerr gating method. 21,23,24 We justify our interpretation by supposing that the scattered excitons should have a finite coherence volume and they are converted to polaritons as the emission process from localized exciton. Since the polariton states require a long enough spatial coherence for their establishment, they cannot be a direct destination of the inelastic scattering because of the small coherence volume of the excitons.…”

“…We do not perform such a calculation in this paper. We instead justified our interpretation from the experimental results 21,23,24 and from the discussion of the spontaneous emission from the bottleneck excitons, in which the coherence volume plays an important role. If the stimulated emission of photons or polaritons occurs and the polaritons do not propagate diffusively, we should observe the escape time τ escape from the sample as the P-emission lifetime.…”

“…This can be the reason why the P-emission lifetime is observed to be inversely proportional to the group velocity v g (ω) in the experiments for bulk materials. 21,23,24 Whereas the escape time τ escape of polaritons after the conversion is also inversely proportional to the group velocity v g (ω), it is estimated to be quite short compared to the conversion time τ conv = 1/Γ (ω). In this way, the P-emission lifetime basically reflects the conversion time τ conv from the scattered excitons to the polaritons in our interpretation.…”

“…22,26,27 Although these lifetimes basically depend on materials of samples, they are generally much shorter than the emission lifetime τ emit of bottleneck excitons at quasi-equilibrium (in the order of nanoseconds). The time-resolved measurements revealed also that the P-emission lifetime is an increasing function of the emission frequency, 20,21,[23][24][25]27 and the lifetime at each emission frequency is almost independent of the pumping power. 24,25 Note that the emissionfrequency-dependence of the P-emission lifetime can be scaled phenomenologically by that of inverse of the group velocity of the photon-like polariton.…”

“…The time-resolved measurements revealed also that the P-emission lifetime is an increasing function of the emission frequency, 20,21,[23][24][25]27 and the lifetime at each emission frequency is almost independent of the pumping power. 24,25 Note that the emissionfrequency-dependence of the P-emission lifetime can be scaled phenomenologically by that of inverse of the group velocity of the photon-like polariton. 21,[23][24][25] The lifetime of the spectrally-integrated P-emission signal was shortened through the lowering of the peak frequency with an increase in pumping power (effective temperature) for InGaN.…”