Fig. 1. The concept of the stimulated polariton emission in low-dimensional perovskite photon cavities. (a) Illustration of studied perovskite structures: thin film (2D), nanowire (1D) and nanocube (0D). (b) Scheme of the linear PL regime, estimated photon cavity modes (grey dashed lines) strongly coupled with exciton resonance (red dashed lines) resulting in exciton-polariton formation (green lines) for each of the structures. Green dashed lines show unobserved, but theoretically predicted polariton state. Dashed blue lines in the lower plot show the existing phonon energies, counted from the second Mie-polariton state. Uncoupled Mie-polariton states are beyond the given energy range. Waveguide mode in 2D perovskite film results in a guided polariton; Quantized Fabry-Perot (F-P) states originating from waveguide mode in 1D nanowires resulting in F-P polariton resonances; Mie resonances supported in 0D nanocubes results in Mie-polaritons. Red circles represent excitons in the systems, and green circles correspond to exciton-polaritons. (c) Scheme of the stimulated polariton relaxation appeared in the different systems with increasing the pump fluence F₂ > F₁ which leads to the onset of ASE in 2D thin films, multimode lasing in 1D nanowire structure, and few-mode lasing in 0D nanocubes. (d) Scheme of the polariton interaction at higher pump fluences F₃>F₂. Polaritons in 2D and 1D relax at lower energy, and in 0D they accumulate at the ground level, which blueshifts with increase of pump fluence. (e) Measured normalized emission spectra at pump fluences F₁, F₂, F₃ from each of the perovskite structures. The colors of the spectra correspond to the fluences of F₁, F₂, F₃ respectively in (b–d).

Fig. 2. Measurements of the stimulated emission of perovskite thin film, nanowire, and nanocuboid. (a) SEM image of the studied perovskite thin film. (b–d) Angle-resolved emission spectra of the thin film, obtained under a non-resonant fs pump at 6 K for pump fluences of 1, 60, and 500 μJ/cm², which correspond to the linear PL, polariton ASE, and red-broadened polariton ASE, respectively. (e) Angle-resolved reflection spectra of the guided guided mode, measured at room temperature below the light cone. The dashed orange line shows the estimated uncoupled photon mode, the dashed red line shows the estimated exciton level and the solid green line shows the fitted polariton mode. (f) SEM image of the studied perovskite nanowhisker with a length of around 5 μm. (g–j) Angle-resolved emission measurements of the nanowire for pump fluences of 1, 40, and 850 μJ/cm², respectively. The data shows the dynamics of polariton multimode lasing emission. (j) The group refractive index of the studied nanowire as a function of the energy, estimated from the FSR of lasing peaks (See SI for the details). (k) SEM image of the studied perovskite nanocuboid. (l–n) Angle-resolved emission measurements of the nanocuboid for pump fluences of 1, 27, and 250 μJ/cm², respectively. (o) The estimated spectral position of the mode as a function of the inverted volume.

Fig. 3. Lasing emission measurements of perovskite nanocuboids with different sizes. (a–c) SEM images of studied perovskite nanocuboids with different geometry. The physical volume of the cuboids is 0.37, 0.02, and 0.007 μm³ respectively. (d–f) Emission spectra as a function of the pump fluence obtained at 6 K for respective samples are shown below in (a–c). Intensive peaks in the spectra correspond to the lasing emission. Dashed blue lines in (f) correspond to phonon energies shifted from the spectral center of the lasing mode. (g–j) The intensity of the lasing peaks, shown in (d–f) as a function of the pump fluence. Dashed lines in (h) correspond to the results of the theoretical model of the polariton lasing and phonon relaxation in perovskite nanocuboid based on Eq. (1).

Fig. 4. Analysis of the Mie-mode observed in the smallest perovskite nanocuboid. (a–c) Identification of the laser mode in cuboid with the smallest physical volume V = 0.007 μm³ (0.04 ${\lambda }_0^3$, where ${\lambda }_0$ = 0.53 μm) (SEM image in Fig. 3(c)), providing the single mode lasing as shown in Fig. 3(f, j). (a) Electric field distribution of the identified electric quadrupole (EQ) mode in three cross-sections. (b) Angle-resolved spectrum obtained at fluence around 10 μJ/cm². The presented laser line at 2.33 eV occurs at EQ resonance with Q ~ 68 (shown by the orange circle) with field localization shown in (a). The dashed red line corresponds to the exciton energy level, while empty black circles denote two more low-Q modes, presenting in this cuboid, but insufficient for lasing. (c) Angle-resolved spectrum in (b), plotted in polar coordinates (orange dots), and numerical simulated directivity (dashed orange curve), obtained in the far-field of EQ eigenmode (a). (d) The highest quality factor, Q, presenting in cuboid on metal-dielectric (yellow dots) and glass (blue dots) substrates versus normalized cuboid volume, $\text{V}/{\lambda }_0^3$. Here, the gradual transition defines the threshold level required for laser generation, obtained from a semiempirical approach, whereas modes under threshold are denoted by empty circles for clarity. The black star corresponds to the smallest laser achieved in this work, having a physical volume V = 0.007 μm³ (0.047 ${\lambda }_0^3$, where ${\lambda }_0$ = 0.53 μm) (see SEM image in Fig. 3(c)).

Fig. 5. Comparison of the smallest perovskite polariton nanolaser with previous reports. (a) Reported perovskite laser designs (nanowire, microsphere, and cuboids) having small normalized volumes, V/λ³, with lasing wavelength over the whole VIS range at room (filled marker) and cryogenic (empty marker) temperatures. (b) Normalized volume versus year showing the status of green light emitting perovskite nanolasers miniaturization. Data were adapted from the following references: I⁷⁰; II⁷¹; III⁷²; IV⁷³; V⁷⁴; VI⁷⁵; VII⁷⁶; VIII⁷⁷. The red arrow indicates progress achieved in this work.