## 2 Amplified Spontaneous Emission
### Perovskites Bulk Polycrystalline Thin Films  
The first evidence of optical gain in lead halide perovskites were reported back in 2004 by [PERSON] et al. [8; 9] in microcrystalline films of CsPbCl\({}_{3}\), obtained by recrystallization from the amorphous phase, showing evidence for the presence of ASE at low temperature (up to about 180 K). The same group also later demonstrated room temperature ASE in CsPbCl\({}_{3}\)[10] and in CsPbBr\({}_{3}\)[11]. These initial results however remained basically isolated, probably due to the complex realization procedure of the active materials, and the interest in lead halide perovskites for lasing application strongly increased only after the first demonstration of room temperature optical gain and ASE in organic-inorganic solution processed methylammonium (CH\({}_{3}\)NH\({}_{3}\), MA) lead halides MAPbX\({}_{3}\) (where X = Cl, Br, I) films by [PERSON] et al. [4]. The authors investigated the excitation density dependence of the PL spectra of MAPbI\({}_{3}\) films under 150 fs pulses pumping at 600 nm, observing the typical MAPbI\({}_{3}\) spontaneous emission spectra at low excitation density, and the progressive appearance of a narrow band at 788 nm as the excitation density increased (see Figure 1a). The lineshape variation also resulted in a superlinear intensity increase and in a clear spectral narrowing, allowing to ascribe these results to the appearance of ASE, above a threshold of 12 \(\upmu\)cm\({}^{-2}\). A remarkable ASE operational stability was also reported, with almost stable ASE intensity during continuous laser pumping at 18 \(\upmu\)cm\({}^{-2}\) in vacuum up to 9 \(\times\) 10\({}^{7}\) laser shots (see Figure 1b). Finally, complete coverage of the visible range was obtained by changing the chemical composition through halide substitution. In particular, by using either mixtures of bromides and iodides or chlorides and iodides, a bandgap (and ASE peak wavelength) tuning from 390 nm to 790 nm was demonstrated (see Figure 1c). The combination of easy deposition from solution, low ASE threshold and high stability strongly stimulated further research in order to optimize the ASE properties. The initial works focused on a physical approach, based on the optimization of the waveguide structure, in order to improve the light amplification efficiency of the active layer. A first example of this approach was reported by [PERSON] et al. [12] that obtained ASE under 5 nanoseconds pumping at 532 nm in MAPbI\({}_{3}\) thin films sandwiched between two 50 nm-thick polymethlymethacrylate (PMMA) layers and two cholesteric liquid crystals (CLC) reflectors, with a minimum threshold of only 7.6 \(\upmu\)cm\({}^{-2}\). This result was ascribed to the increase of the optical path length in the medium due to reflection and redirection toward the active layer by the CLC layers of the emission that propagates along the out-of-plane and oblique paths. Another approach is the realization of perovskite-PMMA bilayers, as reported by [PERSON] et al. [13] with MAPbBr\({}_{3}\) active films. The perovskite layer was realized by a two step sequential deposition process, and was then coated with a top PMMA layer deposited by spin coating. The authors observed that the PMMA coated film showed higher PL intensity, slower PL relaxation dynamics, and ASE threshold about 2.2 times lower. These results were ascribed in part to the passivation of defects in the perovskite top surface, accounting for the higher PL intensity, the slower PL relaxation and for about 20% of the ASE threshold decrease. The remaining ASE threshold decrease wasinstead ascribed to improved waveguiding, allowed by the realization of an almost symmetric glass-perovskite-PMMA waveguide that results in higher mode confinement in the perovskite layer with respect to the asymmetric glass-perovskite one, as also demonstrated some years before in organic polymers amplifying waveguides [14].