## 2 Amplified Spontaneous Emission
### Perovskites Nanocrystals Thin Films  
After their first realization by [PERSON] et al. [28] fully inorganic CsPbX\({}_{3}\) nanocrystals rapidly emerged as extremely interesting active materials for application to photonic and optoelectronic devices, due to their narrow emission, high PLQY in solution and widely tunable emission color by chemical composition engineering (see Figure 2a,b). Only a few months later [PERSON] et al. [5] demonstrated low threshold ASE and lasing at room temperature in CsPbX\({}_{3}\) nanocrystals thin films (see Figure 2c) both under femtosecond and nanosecond pulsed excitation. Moreover, full ASE tuning across the visible was obtained by compositional modulation (see Figure 2d). Almost simultaneously qualitatively similar results were also reported by [PERSON] et al. [29], even if with higher ASE thresholds. The investigation of the temperature dependence of the PL and ASE properties in CsPbBr\({}_{3}\) NC films performed by [PERSON] et al. [30] gave evidence of an ASE threshold reduction of about 20 times with respect to room temperature, down to 147 \(\upmu\)cm\({}^{-2}\) at T = 10 K, under 3 ns pumping at 337 nm. Moreover, the ASE threshold temperature dependence clearly gave evidence of the presence of two critical temperatures (90 K and between 170 K and 190 K) at which the temperature dependence changes, ascribed to the thermally induced formation of nearly ordered orthorhombic subdomains within each nanocrystal. Later several further works from the [PERSON]'s group focused on the optimization of the NCs optical properties, by acting on their chemical composition or on the capping ligands one. In particular, MAPbBr\({}_{3}\) and MAPbI\({}_{3}\) NCs were synthesized by [PERSON] et al. [31], and MAPbBr\({}_{3}\) NCs films showed efficient ASE in the green, with a threshold about 2 times smaller that the CsPbBr\({}_{3}\) ones, but with much lower stability. The chemical stability issue was instead addressed by [PERSON] et al. [32] that reported FAPbBr\({}_{3}\) NCs, with a strongly improved stability during purification processes with respect to CsPbBr\({}_{3}\) and MAPbBr\({}_{3}\) and good ASE properties in the green. In a further experiment [33], FAPbI\({}_{3}\) and FA\({}_{0.1}\)Cs\({}_{0.9}\)PbI\({}_{3}\) NCs were synthesized, characterized by high PLQY and efficient ASE spanning the red and near infrared range. Efficient optical amplification in the nanosecond regime in FAPbI\({}_{3}\) NCs films was also demonstrated by [PERSON] et al. [34] that obtained room temperature ASE with a  
Figure 1: **(a)** Excitation density dependence of the PL spectra of a MAPbI\({}_{3}\) thin film, showing evidence for the appearance of the ASE band for excitation densities above 11 \(\upmu\)cm\({}^{-2}\). **(b)** MAPbI\({}_{3}\) ASE intensity operational stability under continuous pumping at 11 \(\upmu\)cm\({}^{-2}\). **(c)** ASE color tunability as a function of the film chemical composition. Adapted with permission from [4]. Nature Publishing group, 2014.  
minimum threshold of 140 \(\upmu\)Jcm\({}^{-2}\) in films annealed at 90\({}^{\circ}\), under 4 ns pumping at 532 nm, while no ASE was observed in as-deposited films. Further improvements of the NCs stability during purification were obtained by [PERSON] et al. [35] that synthesized CsPbBr\({}_{3}\) NCs capped with zwitterionic long-chain molecules. These NCs demonstrated much higher long term stability and lower tendency to sintering, gave evidence of a PLQY in films comparable to the one in solution and of the retention of about 60% of the initial PLQY after 10 months of storage in ambient conditions. Excellent ASE properties were shown by a very low ASE threshold of only 2 \(\upmu\)Jcm\({}^{-2}\), under 100 fs pumping at 400 nm. The possibility to improve the CsPbBr\({}_{3}\) NCs stability by acting on the ligand modification was also recently demonstrated by [PERSON] et al. [36], who replaced oleic acid (OA) ligands with 2-hexyldecanoic acid (DA).