Taming Random Lasers through Active Spatial Control of the Pump

Active control of the spatial pump profile is proposed to exercise control over random laser emission. We demonstrate numerically the selection of any desired lasing mode from the emission spectrum. An iterative optimization method is employed, first in the regime of strong scattering where modes are spatially localized and can be easily selected using local pumping. Remarkably, this method works efficiently even in the weakly scattering regime, where strong spatial overlap of the modes precludes spatial selectivity. A complex optimized pump profile is found, which selects the desired lasing mode at the expense of others, thus demonstrating the potential of pump shaping for robust and controllable single mode operation of a random laser.

Figure 1

Principle of active control of a 1D random laser. The black slabs represent the dielectric material which is also the gain medium. Optical pumping (small arrows) is transverse to the structure and amplitude modulated. This spatial modulation may be provided in a real experiment by a spatial light modulator. Lasing (large arrows) occurs along the structure and will depend on the pump profile.

Figure 2

Localized random laser case. (a) Frequency vs threshold of the lasing modes at successive iterations, when the optimization routine is applied to select ${\mathrm{Mode}}_2$. Crosses represent initial positions for uniform pumping. (b) Spatial profile of five localized lasing modes. The mode profile on the left edge corresponds to the leaky mode with the highest threshold at $k=10.4\mu {\mathrm{m}}^{-1}$. (c) Spatial profile of ${\mathrm{Mode}}_2$ after optimization. (d) Resulting optimized spatial pump profile.

Figure 3

(a),(c) Localized case, (b),(d) weakly scattering case. (a),(b) Rejection rate, $R{R}_2$, and threshold $N_2$ for selected mode. (c),(d) Spatial correlations functions, $C_{fi}$, between pump profile and ${\mathrm{Mode}}_i$. Crosses indicate the mode with lowest threshold entering the calculation of $R{R}_2$.

Figure 4

Weakly scattering random laser case. (a) Frequency vs threshold of the lasing modes at successive iterations, when the optimization routine is applied to select ${\mathrm{Mode}}_2$. Crosses represent initial positions for uniform pumping. (b) Spatial profile of ${\mathrm{Mode}}_1$ (envelope) and ${\mathrm{Mode}}_2$ (full). (c) Stationary component of ${\mathrm{Mode}}_2$ before (envelope) and after optimization (full). (d) Resulting optimized spatial pump profile.