## 3 Optically Pumped Lasers
### Whispering Gallery Mode (WGM) Lasers  
The name whispering gallery was originally introduced for architectonic buildings (typically domes) in which weak sounds emitted close to the walls can be easily heard even at large distances. This process is basically related to sound reflections and refocusing from the curved walls, which allows efficient sound propagation. The optical analogous of these systems are dielectric cavities with regular shape, like spheres, disks and rings containing a luminescent material. Under optical excitation the PL emitted by the active material propagates within the structure, experiencing total internal reflections at the cavity edges. For proper wavelengths the emitted waves make an integer number of oscillation in any closed loop, thus forming standing waves at discrete wavelengths. If the active material is pumped above the optical gain threshold this system emits multimode laser light. The technological reasons of interests of WGM lasers are related to the typical cavity size required to obtain a few modes in the visible range, that is of the order of tens of microns, which can be easily realized by standard photolithography. Moreover, many active materials, including perovskites, spontaneously form micrometric crystals or domains in the films with regular shape, thus allowing the realization of self assembled micrometric lasers. In this section we review the main results recently published on perovskites WGM lasers, starting from the self assembled ones and concluding with the lithographically realized cavities. The simplest perovskites systems showing lasing in WGM resonators were obtained in MaPbI3\({}_{-a}\)X\({}_{a}\) (X = I, Br, Cl) nanoplatelets, spontaneously formed during vapor transport chemical vapor deposition (CVD) on a mica substrate [48]. The nanoplatelets show a regular geometry, with triangular or hexagonal shape with an edge length in the range 5-50 \(\upmu\)m, a thickness in the range 20-300 nm and an extremely low surface roughness of about 5 nm (see Figure 7a). Clear diffraction patterns of the pump laser were observed in single platelets (see Figure 7a), indicating good optical confinement in the nanoplatelet WGM cavities. The excitation density dependence of the PL spectra of individual nanoplatelet, under 50 fs pumping at 400 nm, showed only spontaneous emission at low excitation density, and the appearance of several sharp peaks centered around 780 nm, with a linewidth of about 1.2 nm and a constant distance between consecutive peaks of about 2.5 nm (see Figure 7b). The presence of equally spaced modes is the typical signature of multimodes resonant cavities. Further evidence of lasing were obtained by investigating the excitation density dependence of the emission intensity, showing a clear slope variation at the lasing threshold of about 37 \(\upmu\)Jcm\({}^{-2}\) (see Figure 7b left inset), and of the emission lifetime, showing a long average spontaneous emission lifetime of about 2.6 ns below the threshold and a much lower resolution-limited lifetime of about 80 ps above the threshold, due to the fast excited state depletion induced by lasing (see Figure 7b right inset). A couple of years later, the same group realized, with the same technique, fully inorganic CsPbX\({}_{3}\) (X = I, Br, Cl) nanoplatelets [49], showing a well-defined square and rectangular shapes (see Figure 7c), ascribed to the intrinsic cubic crystalline phase of the perovskite. The optical images of the nanoplatelets showed rich colors, due to interference effect between the light reflected from the top and from the bottom surfaces, and to different nanoplatelets thickness in the 50-300 nm range. Also In this case, as the excitation density increased the emission spectra revealed the appearance of multiple, equidistant, narrow peaks, with much lower linewidth (down to 0.15 nm), with a threshold decreased to 2.2 \(\upmu\)cm\({}^{-2}\), under 50 fs pumping at 400 nm.