Coherent instabilities in random lasers

A numerical study is presented of random lasers as a function of the pumping rate above the threshold for lasing. Depending on the leakiness of the system resonances, which is typically larger in random lasers compared to conventional lasers, we observe that the stationary lasing regime becomes unstable above a second threshold. Coherent instabilities are observed as self pulsation at a single frequency of the output intensity, population inversion, as well as the atomic polarization. We find these Rabi oscillations have the same frequency everywhere in the random laser despite the fact that the field intensity strongly depends on the spatial location.

Figure 1

Emission spectra ${\left|E\left(\lambda \right)\right|}^2$ for a 2D random system. The values of the pumping rate $P_r$ are written in each panel in units ns${}^{-1}$. The gain curve (dotted line) is overlaid.

Figure 2

Emission spectra ${\left|E\left(\lambda \right)\right|}^2$ for a 1D random system. The values of the pumping rate $P_r$ are written in each panel in units ns${}^{-1}$. The gain curve (dotted line) is overlaid.

Figure 3

(a) Population inversion (solid line) and intensity ${\left|E\left(t\right)\right|}^2$ (dotted line) for a 1D random system with $P_r=0.48$ ns${}^{-1}$. (b) Temporal standard deviation $\sigma$ of the population inversion vs. pumping rate $P_r$.

Figure 4

Emission spectra ${\left|E\left(\omega \right)\right|}^2$ (a,b) and population inversion $\Delta N\left(\omega \right)$ (c,d) with $P_r=4.00$ ns${}^{-1}$ (a,c) and $P_r=8.00$ ns${}^{-1}$ (b,d) for a 1D random system. ${\omega }_N$ is the smallest (nonzero) frequency peak in $\Delta N\left(\omega \right)$ and corresponds to the frequency spacing in the emission spectrum.

Figure 5

Atomic polarization spectra at different spatial locations for (a) 1D random system with $P_r=6.00$ ns${}^{-1}$ and (b) 2D random system with $P_r=13.0$ ns${}^{-1}$. (Insets) Time-averaged spatial intensity distributions marking (a) 3 sampling locations and (b) 11 sampling locations. All locations yield the same low oscillation frequency in both cases.

Figure 6

Estimated Rabi frequency $\Omega$ (squares) and the population inversion frequency ${\omega }_N$ (triangles) for 1D (open symbols) and 2D (solid symbols) random systems vs. the internal field $I_a^{1/2}$.

Figure 7

Emission spectra ${\left|E\left(\lambda \right)\right|}^2$ for a large ($L^2=5.0\times 5.0\mu$m${}^2$) 2D random system. The values of the pumping rate $P_r$ are written in each panel in units ns${}^{-1}$. The gain curve (dotted line) is overlaid. The two side peaks in (b) with smaller amplitudes (by 9 orders of magnitude) are due to four-wave mixing.