While conventional lasers use mirrors to confine light in a cavity with gain to achieve spontaneous emission, random lasers take advantage of multiple scattering to trap light in a disordered medium . Such lasers do not require to carefully tune the geometry of the cavity, which greatly simplifies their design. They are potentially cheaper and more robust in the presence of perturbations (temperature, vibration). The resulting emission spectrums and radiation patterns are broad but mainly uncontrolled. In recent studies [2-5] different groups demonstrated numerically and experimentally the modulation of the spatial profile of the pump to control the spectrum [2-4] or the emission pattern .
The researchers in the ESPCI have shown numerically  then experimentally  the use of spatial control of the pump profile of a quasi-one-dimensional random laser to achieve single-mode lasing. The beam of the pump is modulated by a spatial light modulator (SLM). Using an iterative feedback algorithm, the wavefront of the pump is changed to minimize the ratio of the threshold of one particular mode at a given frequency to the thresholds of the other modes. A schematic of the experiment as suggested in  is shown in Fig. 1.
Figure 1. The principle of the experiment suggested in . Image from [N. Bachelard et al., Phys. Rev. Lett., 109, (2012)].
Two cases are studies, the cases of strongly and weakly scattering media. We see in Fig. 2 that in both cases the threshold of the target mode is decreased compared to the other ones, allowing to use the random laser as a single-mode laser at the frequency of the selected mode.
Figure 2. Evolution of the thresholds of the lasing modes during the optimization process in the strongly (a) and weakly (b) scattering regime. Image from [N. Bachelard et al., Phys. Rev. Lett., 109, (2012)].
When the amount of scattering is high enough, the spatial profiles of the lasing modes are approximately the same as the ones of the quasi-modes of the passive system. These modes are narrow band, spatially localized and with a low overlap between them. We see in Vid 1. that in the strongly scattering regime, the simulated pump profile converges to the profile of the target mode, which is not modified. This confirms the experiments of selective excitation of lasing modes by local pumping in the strongly scattering regime [6-7].
Video 1. Evolution of the pump profile (blue line) during the optimization process in the strongly scattering regime. The red line represents the spatial profile of the target mode. Video from [N. Bachelard et al., Phys. Rev. Lett., 109, (2012)].
In the weakly scattering regime, lasing modes are spatially extended and they overlap. The variations of the spatial profile of the pump induce changes in the lasing modes due to the small index contrast of the scattering medium. The shape of the target mode changes during the optimization as we see in Vid. 2. Nevertheless, the system reaches a state in which the target mode has a lower threshold than the other ones [see Fig.2(b)].
Video 2. Evolution of the pump profile (blue line) during the optimization process in the weakly regime. Video from [N. Bachelard et al., Phys. Rev. Lett., 109, (2012)].
The same team demonstrated experimentally the selection of one particular emission frequency using wavefront shaping of the pump . The random laser consists of a quasi-one-dimensional microfluidic system with a dye [see Fig 3.(a)]. The experiment takes place in the weakly scattering regime. The wavefront of the pump is iteratively optimized to increase the ratio of the intensity of the emission at one particular frequency to the intensity of the brightest other frequency. The results presented in Fig 3.(b) show that they successfully selected one frequency of the emission spectrum.
Figure 3. (a) Schematic and picture of the random laser. (b) laser emission spectrums before (black line) and after (blue line) optimization. Image from [N. Bachelard et al., arXiv, 1303.1398, (2013)].
In , a research team of the CSIC in Madrid optimized the 2D spatial profile of the pump to select one frequency in the emission spectrum of a 3D random laser. The random laser consists of a layer of TiO2 nanoparticles embedded in a laser dye solution [see Fig. 4(a)]. The laser beam used as the pump is modulated by an amplitude SLM. The shape of the illumination is a combination of a disk and a directive pie shape. By changing the angle and the size of the spatial profile of the illumination using an iterative scheme, the authors are able to select one particular frequency of the emission as shown in Fig. 5.
Figure 4. (a) sketch of the setup used and (b) shape of the illumination area. Image from [M. Leonetti et al., Appl. Phys. Lett., 102, (2013)].
Figure 5. The emission spectrum of the random laser before (a) and after (b) optimization of the spatial profile of the pump. Image from [M. Leonetti et al., Appl. Phys. Lett., 102, (2013)].
In , T. Hisch from the Vienna University of Technology and his colleagues studied in simulation the effect of the spatial shaping of the pump profile in a 2D random laser to optimize the directivity of the emission. The laser consists of a collection of dielectric particles in a gain medium [see Fig. 6]. For each spatial profile of the pump, the authors calculate the near and far-field profile of the laser emission (calculating the threshold constant flux states ). The goal is to achieve a lasing emission pattern with a given directivity. For each illumination, the overlap between the calculated far-field emission pattern and the target pattern is calculated. Using a sequential algorithm, the pump profile is optimized to maximize this overlap.
Figure 6. Schematic of the experiment simulated in [T. Hisch et al., Phys. Rev. Lett., 111, (2013)].
Similarly to , the cases of strong and weak scattering are studied. In the strongly scattering, the optimal illumination pattern consists of exciting a localized mode close to the edge of the random medium, in the same direction as the target far-field emission [see Fig.7].
Figure 7. Strongly scattering regime. (a) profile of the first lasing mode. (b) optimized pump profile. (c) directivity of the optimized laser emission (blue line) and the target (red line). Image from [T. Hisch et al., Phys. Rev. Lett., 111, (2013)].
In the weakly scattering regime, since the shape of modes is modified by the illumination profile, the directivity pattern can be finely tuned to fit with a very good agreement with the target pattern. An example of an optimized directive emission is shown in Fig 8. The authors show in  that more complicated patterns can be obtained.
Figure 8. Weakly scattering regime. (a) profile of the first lasing mode. (b) optimized pump profile. (c) directivity of the optimized laser emission (blue line) and the target (red line). Image from [T. Hisch et al., Phys. Rev. Lett., 111, (2013)].
The results of these different studies shed new light on the use of random lasers. Instead of designing a laser that has the desired properties, which can be very long and complicated, one can use any random laser and learn the pump profile that optimizes the emission.