Dynamics of phase-locking random lasers

Laser modes may coalesce into a mode-locked state that enables femtosecond pulse compression. The nature of the interaction and the interaction time play fundamental roles in the onset of this collective state, but the investigation of the transition dynamics is technically challenging because phases are not always experimentally accessible. This is even more difficult for random lasers, a kind of disordered laser in which energies in play are much smaller than in the ordered macroscopic case. Here we investigate experimentally and numerically the dynamics of the phase-locking transition in a random laser. We developed an experimental setup able to pump individual modes with different pulse durations and found that the mode-locked regime builds only for quasicontinuous pumping, resulting in an emission linewidth dependent on the pump duration. Numerical simulation confirms experimental data.

Figure 1

Experimental setup. The pulsed lasers (532 nm, repetition rate 10 Hz, and fluence 0.1 $\mathrm{nJ}/\mu {\mathrm{m}}^2$ for the nano and 0.03 $\mathrm{nJ}/\mu {\mathrm{m}}^2$ for the pico) are collected on the same beamline shaped by a SLM in amplitude configuration (exploiting polarizer P1). The two beams converge on a single titanium dioxide cluster (diameter between 5 and 12 $\mu$m). Insets: Images of the cluster collected in the pico configuration (a, c) and in the nanoconfiguration (b, d).

Figure 2

Cluster and pumped area (evidenced in white) for small theta (a) and for large theta (b).

Figure 3

(a) Spectra for a nano pumping (150 shots average) with $\Theta =8^{\circ }$ and pump fluence 0.1 nJ/$\mu$m${}^2$. The pico pumping is as in panel (a), and 0.03 nJ/$\mu$m${}^2$ is reported in panel (b). (c, d) The number of peaks, respectively, in the spectrum and the intermode correlation as a function of $\Theta$.

Figure 4

(a, b): the spectrum obtained, respectively, for the nano and for the pico configurations. (c) The FWHM of the spectra for different clusters both in the nano (squares) and the pico (circles) pumping.

Figure 5

Results of the numerical simulations. (a–c) The spectra obtained for various pumping durations. (d) The spectral waist retrieved by Gaussian fitting (red line in the first three panels) as a function of the pumping duration $D$. (e, f) The phases and the total intensity, respectively, as a function of time. The pump pulse shape ($D=2.5$ ps) is represented as a thick line.