We report efficient non-resonant ground state excitation at 1064 nm of trivalent neodymium (Nd 3+ ) ions in stoichiometric neodymium aluminum borate NdAl 3 (BO 3 ) 4 nanoparticles, which are crystalline and, besides the large content of Nd 3+ ions, present excellent photoluminescence properties. Up-conversions (UCs) were observed and the energy pathways identified, as starting by multi-phonon assisted ground state absorption ( 4 I 9/2 → 4 F 3/2 ) and excited state absorption ( 4 I 11/2 → 4 F 3/2 ) with the population of the 4 I 11/2 level by thermal coupling with the ground state. The excited state 4 I 11/2 is also populated by relaxations of the Nd 3+ increasing the population of the 4 F 3/2 level. Cross-relaxation among two Nd 3+ ions ( 4 F 3/2 , 4 I 9/2 )→( 4 I 15/2 , 4 I 15/2 ) with subsequent phonon emission leads to two ions at the 4 I 11/2 level every iteration triggering a photon avalanche mechanism which greatly enhances the efficiency of the UCs. Ladder thermal excitation 4 F 3/2 →[ 4 F 5/2 , 2 H 9/2 ]→[ 4 F 7/2 , 4 S 3/2 ]→ 4 F 9/2 was achieved, and the ground state relaxation from these levels provided emission at 880 nm, 810 nm, 750 nm, and 690 nm, respectively. Energy transfer UCs (Auger) between Nd 3+ ions at the 4 F 3/2 level allowed population of the [ 2 G 3/2 , 4 G 7/2 ] from which relaxations to the 4 I 9/2 , 4 I 11/2 , and 4 I 13/2 states provided emissions around 536 nm, 600 nm, and 660 nm, respectively. Associated to the nonradiative relaxations, we observed the heating of the nanoparticles (22 °C to 240 °C) with subsequent thermal enhancement of the frequency UCs due to the redistribution of population among coupled energy levels of the Nd 3+ ions. The present results have potential applications in super-resolution imaging and nanothermometry.

Lévy flights for light have been demonstrated in disordered systems with and without optical gain, and remained unobserved in ordered ones. In the present letter, we investigate, numerically and experimentally, Lévy flights for light in ordered systems due to an ordered (conventional) laser. The statistical analysis was performed on the intensity fluctuations of the output spectra upon repeated identical experimental realizations. We found out that the optical gain and the mirrors reflectivity are critical parameters governing the fluctuation statistics. We identified Lévy regimes for gain around the laser threshold, and Gaussian-Lévy-Gaussian crossovers were unveiling when increasing the gain from below to above the threshold. The experimental results were corroborated by Monte Carlo simulations, and the fluctuations were associated to a Langevin noise source that takes into account the randomness of the spontaneous emission, which seeds the laser emission and can cause large fluctuations of the output spectra from shot-to-shot under identical experimental realizations.

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Random lasers (RLs) rely on obtaining laser emission in disordered systems with gain. The characterization of the RLs are performed by the observations of bandwidth narrowing, increasing in the slope efficiency, time shortening of the upper level of the RL transition, intensity and spectral fluctuations, and even photon statistics transitions when increasing the optical gain. However, the gain clamping, which is a known phenomenon in conventional lasers, i.e. lasers with well-defined cavity, was never investigated in RLs. Here we realize an experimental-theoretical investigation of the gain clamping in RLs, and demonstrate that it can be used as an alternative tool to characterize the transition from spontaneous emission to the RL regime.