Abstract
Halide perovskites are a promising optical gain media with high tunability and simple solution synthesis. In this study, two gain regimes, namely amplified spontaneous emission and random lasing, are demonstrated in same MAPbBr3 halide perovskite single crystal. For this, nonlinear photoluminescence is measured at a temperature of 4 K with pulsed femtosecond pumping by UV light with a 80 MHz repetition rate. Random lasing is observed in areas of the sample where a random resonator was formed due to cracks and crystal imperfections. In more homogeneous regions of the sample, the dominant regime is amplified spontaneous emission. These two regimes are reliably distinguished by the line width, the mode structure, the growth of the intensity after the threshold, and the degree of polarization of the radiation.

three groups: random resonators, supporting random lasing (RL) [2] [3] [4] ; optical resonators based on the refractive index contrast between the synthesized perovskite material and air, such as micro-and nano-cubes [5] [6] [7] , rods [8, 9] , wires [10] [11] [12] [13] [14] , platelets [15, 16] , micro pyramids [17] and microspheres [18] ; and external resonators based on distributed Bragg reflectors [19] [20] [21] , gratings for distributed feedback lasers [22] [23] [24] [25] [26] [27] [28] , and nanolithographically fabricated micro disks [29] [30] [31] . The laser generation manifest itself in different ways. In most of the works the main conclusion about the lasing nature of the emission is made based on the narrow line width and threshold behavior of the emission. Rarely the emission polarization was tested [9, 11, 21, [22] [23] [24] [25] [26] [27] 29] , the direct observation of the light field distribution in the resonator was made [8, 11, 12, 14, 15, 16, 17, 24, 29, 31] or the laser emission directionality was observed [18, 21, 24, 26] . To our best knowledge the intensity correlations measurements above the lasing threshold was demonstrated only in [20] , and the spatial coherence of the lasing emission was shown only in [21] . In all of these works either ASE or lasing were demonstrated, and even if both phenomena were reported in the same work, experiments were carried out in different structures.

In this study we present the observation of ASE and RL in the same MAPbBr3 halide perovskite single crystal. A reliable separation of the two emission regimes was achieved by comparing the emission line width, mode structure, the growth of the emission intensity after the threshold, and its polarization degree.
Results and Discussion
MAPbBr3 halide perovskite single crystals were synthesized using the solution method. Figure S1 (a, b) shows the XRD pattern of the single crystal as obtained after the synthesis (a) and of the grounded crystal (b). In the pattern of the single crystal only four reflexes can be observed, which belong to the (001) facet and multiples of that facet. Thus the crystal has a clear orientation without other facets being present. The XRD pattern of the powder is containing only reflexes that can be addressed to methylammonium lead tribromide, assuring the perovskite structure and the phase purity of the material. The orientation of the single crystal can be seen as well in the SEM images ( Figure S2 ). The crystal has a rough surface, and small cracks can be noticed (Figure 1 (b) , marked by arrow). With backside illumination the cracks are visible also in the optical microscope (Figure 1 (a) ).
Results and Discussion
For the optical emission measurements the MAPbBr3 single crystal was cooled down to a temperature of 4 K. Figure 1 (c) shows PL (green curve) and normal reflectivity (orange curve) spectra. A clear free excitonic transition could be observed in the pamelagray@example.net eV. The PL spectra has a narrow peak with a Stokes-shift of around 5 meV, and a defect-related broad PL at energies below this peak [33] . For the PL pumping femtosecond UV laser pulses with a 80 MHz repetition rate were used.
Results and Discussion
With the increase of the pump intensity at the low-energy tail of the PL spectra a new nonlinear PL signal appears at pump densities per pulse Ipump > 1 μJ cm -2 . Depending on the region of the sample, two different types of the nonlinear PL signal can be distinguished. In most regions, a broad PL line with the quality factor Q ~ 10 2 was observed (Figure 2 ASE process is the spontaneous emission which was optically amplified by the stimulated emission in the perovskite gain medium after the pump pulse. The presence of a threshold is inherent in this process, and a more rapid increase in the PL intensity is expected after the threshold. In Figure 2 A direct comparison of the slopes after the threshold is not entirely correct, since the result will also depend on the directional diagram of the emission. However, in the ASE regime, it is expected that the emission is non-directional. Therefore, the 38-times larger slope in the RL regime indicates a greater gain due to multiple light passages of the resonator.
Results and Discussion
The emission polarization allows to distinguish ASE and RL regimes. The inset in the Figure   2 (Figure 2 (d) ) shows that this emission is polarized. The polarization degree could be estimated as:
Results and Discussion
where Imax and Imin are the maximum and minimum nonlinear PL intensities at different polarizations. For ASE this parameter is P ~ 0.06 indicating the non-polarized emission, for RL it is P ~ 0.96 indicating polarized lasing. The red dashed curves in Figure 2 (b,d) insets
Results and Discussion
show fittings of the polarization diagrams by the equation:
Results and Discussion
where is the analyzer rotation angle, representing the combination of the non-polarized background and the polarized emission determined by the Malus's law. Table S4 summarizes nonlinear PL emission parameters for different sample points with the ASE and RL regimes. It can be seen that the described ASE and RL properties are sufficiently universal and could be used to clearly distinguish these two regimes.
Conclusions
In this study we have shown that the nonlinear PL signals from the MAPbBr3 single crystal at 4 K and pulsed UV pumping could be separated into two distinct groups: ASE and RL, depending on the emission intensity growth after the threshold, quality factor and emission polarization degree. The formation of resonators for RL is a random process, however with their help it becomes possible to study the nature of laser generation in the highest quality single-crystalline material. Low-temperature study of RL in single crystals will help to precisely establish the amplification mechanism in the halide perovskite gain medium, and to find a way for its optimization for further applications.
Experimental Section
Chemicals: Methylammonium bromide (98 %, Sigma Aldrich), lead bromide (≥ 98 %, Sigma Aldrich) and dimethylformamide (DMF) were used as received without further purification.
Experimental Section
Synthesis: 1M solutions of methylammonium bromide and lead bromide were prepared by dissolving both compounds in 3 ml DMF. After stirring for some minutes the solution was filtrated using a 0.2 µm PTFE filter. The solution was transferred into a vial, which was closed with a glass cap and sealed with Parafilm. Afterwards the vial was placed in a beaker and heated in a water/ethanol bath to 60°C and the temperature was kept constant overnight.
Experimental Section
On the next day the temperature was increased to 80°C and after two hours of further heating the crystals were obtained (< 15 crystals). The crystals have been dried and used without further treatment for the measurements. The XRD measurements were performed with a Bruker D8 Advance diffractometer with the Cu Kα radiation. Scanning electron microscopy images were obtained using a Zeiss Crossbeam 1540XB workstation. lens. The same lens was used to collect the PL. PL spectra were measured using the spectrometer with a grating 1200 mm -1 equipped with the linear CCD-detector. An achromatic λ/2 plate and a Glan-Taylor prism were mounted in front of the spectrometer slit in order to measure the PL polarization.
Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.
Supporting Information
Received: ((will be filled in by the editorial staff)) Revised:
Supporting Information
((will be filled in by the editorial staff)) Published online: ((will be filled in by the editorial staff)) . Typical nonlinear PL spectra for different pump densities per pulse Ipump for ASE (a) and RL (c). The inset in (c) shows the magnified PL spectrum for Ipump = 8.4 μJ cm -2 (red curve) and its Lorentzian fit (black dashed curve) (ΔEdetuning from the peak central energy). Dependence of the PL intensity on Ipump for ASE (b) and RL (d) for peaks denoted by (*). Dotsexperimental data, solid lineslinear fits below and above the threshold. Spectra are normalized by the PL intensity growth below the threshold. Insets in (b) and (d) show PL polarization diagrams above the threshold for peaks denoted by (*). Blue curvesexperimental data, red curvesfits by (2) .
TOC entry:
Amplified spontaneous emission and random lasing regimes are differentiated in the nonlinear photoluminescence from MAPbBr3 single crystals at 4 K and pulsed UV pumping. This two regimes are differentiated by the line width, mode structure and polarization of the emission, and its growth after the threshold. Figure S3 . More examples of nonlinear PL spectra with the ASE (left column) and RL (right column) regimes from different sample points. For each panel the blue (red) curve corresponds to the spectrum below (above) the threshold. Spectra are normalized to the highest energy emission peak intensity. Insets show PL polarization diagrams above the threshold for peaks denoted by (*). Blue curvesexperimental data, red curvesfits by (2) from the main text. Table S4 . Nonlinear PL parameters for peaks denoted by (*) in Figure S3 .
Keyword


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