We studied experimentally the ensemble-averaged spectral correlation functions and statistical distributions of spectral spacing and intensity of ASE spikes and lasing peaks from weakly scattering systems under local pumping. Their differences revealed distinct physical mechanisms.
We simulate the transition from amplified spontaneous emission (ASE) to lasing in random systems with varying degrees of mode overlap. This is accomplished by solving the stochastic Maxwell-Bloch equations with the finite-difference time-domain method. Below lasing threshold, the continuous emission spectra are narrowed by frequency-dependent amplification. Our simulations reproduce the stochastic emission spikes in the spectra. Well-defined peaks, corresponding to the system resonances, emerge at higher pumping and are narrowed by stimulated emission before lasing takes place. Noise tends to distribute pump energy over many modes, resulting in multimode operation. Well above the lasing threshold, the effects of noise lessen and results become similar to those without noise. By comparing systems of different scattering strength, we find that weaker scattering extends the transition region from ASE to lasing, where the effects of noise are most significant.
We study local and nonlocal correlations of light transmitted through active random media. The conventional approach results in divergence of ensemble-averaged correlation functions due to the existence of lasing realizations. We introduce a conditional average for correlation functions by omitting the divergent realizations. Our numerical simulation reveals that amplification does not affect local spatial correlation. The nonlocal intensity correlations are strongly magnified due to selective enhancement of the contributions from long propagation paths. We also show that by increasing gain, the average mode linewidth can be made comparable to the average mode spacing. This implies that light transport through a diffusive random system with gain may exhibit some similarities with that through a localized passive system.
We study fluctuations of the number of photocounts measured by an ideal photodetector illuminated by light scattered in an amplifying disordered medium, below the threshold for random lasing. We show that the variance of fluctuations and their correlation function carry information about fluctuating properties of the medium. A direct link is established between the fluctuations of the number of photocounts due to the amplified spontaneous emission (ASE) and the dimensionless conductance g of the medium. Our results suggest a possibility of probing amplifying disordered media by analyzing statistics of their ASE, without illuminating them from outside by a probe beam.