Random laser tailored by directional stimulated emission

The spectrum of a random laser (RL) may appear either as a set of sharp resonances or as a smooth line superimposed on the fluorescence. Recently, Leonetti, Conti, and Lopez [Nat. Photonics 5, 615 (2011)] accounted for this duality with the onset of a mode-locked regime that is triggered by the increase of both the number of activated modes and of the intermode interaction and is accompanied by a pulse shortening. Here we report an extensive review of the experimental approach used by Leonetti et al., including the sample preparation and the particulars of the setup. Here we describe also the way in which our approach allows us either to set the degree of interaction between modes or to have a certain degree of control over the effective set of resonances brought to lasing. Moreover we report an investigation on the spatial properties of the RL which brings further confirmation of the synchronization picture, whose physical origin is deepened.

Figure 1

Sample preparation: (a) A drop of the solution containing scattering particles and dye is placed on a glass substrate with two plastic spacers. (b) A second substrate is placed on the top of the sample, squeezing the drop.

Figure 2

Sample (a) before and (b) after the isolation protocol.

Figure 3

Passive speckle pattern from a single cluster obtained (a) before and (b) after 150 pump shots (Image size 16 × 12 mm). The correlation between the two images is 0.85.

Figure 4

A sketch of the experimental setup. The vertically polarized laser beam is first reflected by a high-power dichroic polarizing mirror (P1) to clean residual unpolarized light and then passes through a 5$\times$ beam expander (BE) before impinging on the spatial light modulator (SLM). A demagnifying telescope (DT) images the spatial light modulator on the sample after a polarizing dichroic mirror (P2), which selects horizontal polarization, while residual vertically polarized light is absorbed by a beam dump (BD). Emitted light is collected by a microscope objective (numerical aperture of 0.40, working distance of 6 mm) to be imaged by an enlarging telescope (10$\times$) on a 50-$\mu$m-core fiber after being filtered by an edge filter (F) cutting residual green laser light. RL light is divided by a beam splitter to feed a spectrograph and a CCD imaging camera, both of which are triggered by the pumping laser. The right inset shows an explicative perspective view of the SLM, while the left inset represents the sample under pumping.

Figure 5

FWHM (red squares) and peak intensity (black circles) as a function of the length of the illuminated stripe. The measurement has been performed with a pump power of 0.1 nJ/$\mu$m${}^2$ pulse.

Figure 6

(a) Spectrum (solid line) obtained with configuration 1 (see text) together with the spectrum obtained with the same orientation but with a 32-$\mu$m-thick stripe (configuration 2, dashed red line arbitrarily translated along the ordinate). (b) Spectrum obtained by pumping with configuration 3 obtained by tilting the stripe by 15${}^{\circ }$ with respect to configuration 1. The spectrum obtained from configuration 1 is reported as a dashed red line and arbitrarily translated along the ordinate for comparison. The spatial distribution of intensity for configurations (c) 1, (d) 2, and (e) 3. The inset represents the pumping shape of configurations 1 and 3. Al measurements are obtained with a 0.1 nJ/$\mu$m${}^2$ pump fluence

Figure 7

Spectrum obtained for two different values of the pump power with a circular pump spot (left inset) on the cluster in Fig. 6. An image of the intensity distribution of the cluster is shown in the right inset.

Figure 8

(a) An image of the sample shined with the pie-shaped pumping. (b) and (c) A perspective scheme of the pumped sample for two different values of $\theta$.

Figure 9

(a) Number of modes $N$ and (b) spikiness as a function of $\Theta$. Squares and triangles correspond to different pump energies for cluster C1. Circles (error bars) corresponds to the average (standard deviation) of five measurements from different clusters. (c) Three-dimensional graph showing normalized spectra (average over 100 shots with a fluence of 0.2 nJ/$\mu$m${}^2$) for different $\Theta$. Spectra are arbitrarily shifted in frequency to superimpose intensity maxima. $\Delta \lambda$ is the wavelength shift from the most intense peak.

Figure 10

Normalized average spectra from cluster C1 for (a) $\Theta ={18}^{\circ }$ and (b) $\Theta ={360}^{\circ }$. Asterisks indicate the positions of the modes analyzed in (c) and (d). (c) Intensity values of the modes at wavelengths ${\lambda }_1=597.2$ nm and ${\lambda }_2=596.7$ nm obtained for 100 single-shot realizations in the pumping configuration with $\Theta ={18}^{\circ }$. (d) As in (c) for wavelengths ${\lambda }_3=598.4$ nm and ${\lambda }_4=598.7$ nm and $\Theta ={360}^{\circ }$.

Figure 11

Average correlation C as a function of $\Theta$ obtained for five different clusters. In the graph for C1, $\Sigma$ is also plotted as a function of $\Theta$ (open squares).

Figure 12

$C$ (circles) and $S$ (squares) as a function of $\Theta$ in the fixed volume configuration. Pumping is 0.1 nJ/$\mu$m${}^2$

Figure 13

(a) Surface plot of the intensity pattern for the same cluster for three different values of $\Theta$. (b) $\Omega$ plotted as a function of the parameter $\Theta$.

Figure 14

Intensity as a function of time for cluster C1 pumped with wedges of different aperture. Measurements are performed at a pump fluence of 0.1 nJ/$\mu$m${}^2$.

Figure 15

Results from numerical simulations. Temporal evolution of phases for different degrees of intermode coupling. $N_c$ is (a) 3, (b) 6, and (c) 10.