## 3 Optically Pumped Lasers
### Random Lasers  
Random lasers are the simplest systems in which it is possible to observe narrow and coherent emission from a material showing optical gain. The lasing feedback is provided by constructive interference of the light partially scattered during its propagation in the active material. As light scattering can be obtained simply from morphological irregularities of the active film, random lasing is often observed also in experiments aiming to characterize the ASE and gain properties of thin films, whose surface morphology often present defects acting as scattering centers. The first experiment on perovskites random lasers [39] was published only a few months after the demonstration of ASE from MAPbX\({}_{3}\) thin films [4] and basically exploited the tendency of perovskites materials to form films with morphological defects. In particular, the authors deposited a MAPbI\({}_{3}\) film, by spin coating a 20% in weight dimethylformamide (DMF) precursor solution containing CH\({}_{3}\)NH\({}_{3}\)I and PbI\({}_{2}\) mixed in a 1:1 molar ratio. They observed the spontaneous formation of a network of planar elongated microcrystals, with a typical length of about 50 um and a typical thickness in the range 300-500 nm (see Figure 4e). The emission spectra of the sample, under pumping with a 0.8 ns pulsed UV laser at 335 nm, showed only the broad unstructured band-edge photoluminescence typical of the MAPbI\({}_{3}\) at low pump fluence, with a peak wavelength at 765 nm. When the excitation density increased above 200 uJcm\({}^{-2}\) sharp peaks appeared in the spectra (see Figure 4a) and become progressively more evident as the excitation density was further increased. The appearance of the narrow peaks also leaded to a variation in the slope of the PL intensity increase with the excitation density (see Figure 4b), which is the typical signature of lasing threshold. The local emission properties of the sample were investigated by micro-PL measurements showing evidence of (see Figure 4c,d) the appearance of bright spots in the PL maps at excitation densities above the random lasing threshold, in positions corresponding to the junctions within the different microcrystals. This result suggested that light mainly propagated along the individual crystals, and it was then scattered at the crystals junctions thus forming random closed loops determining the lasing wavelengths. A couple of years later a further experiment was performed on MAPbI\({}_{3}\) films deposited by a two step spin coating of a PbI\({}_{2}\) solution in DMF, followed by a methylammonium iodide (MAI, CH\({}_{3}\)NH\({}_{3}\)I) in 2-propanol (IPA) [40]. This deposition procedure allowed to obtain a film with a thickness of about 450 nm, with a full surface coverage and a grainy structure, with an average grain size of about 200 nm (see Figure 5a). The excitation density dependence of the PL spectra, under 1 ns UV pumping at 335 nm, showed the appearance of random lasing peaks, with a threshold reduced to 102 uJcm\({}^{-2}\) (see Figure 5b), whose number and intensity increased with the excitation density. This result wasascribed to random lasing considering that the formation of standard resonant cavities within the individual grains can be excluded both due to the irregular grains shape and size and to the irregular evolution of the number and the wavelength of the lasing modes as the excitation density increased. The proposed lasing mechanism is schematically depicted in Figure 5c, considering the randomly arranged MAPbI\({}_{3}\) grains both as the gain media and the multiple scattering sources. The emitted light undergoes multiple scattering at the grain boundaries eventually returning to a path from which they were scattered before, thus forming closed-loop cavities and providing lasing oscillation at the resonant frequency of the corresponding feedback loop when the optical gain exceeds the losses.