Amplified Extended Modes in Random Lasers

We report on a new random laser phenomenon that gives rise to narrow emission modes without requiring optical cavities. Sharp emission peaks are observed experimentally over a broad range of scattering strengths and analyzed in numerical calculations. We find that the introduction of exponential gain in a multiple light scattering process strongly increases the importance of very long light paths. Such long paths are rare and often neglected in passive disordered materials but we show that they can dominate the emission spectrum from an amplifying disordered system.

Figure 1

Experimentally observed emission spectrum from suspensions of ZnO in Rh6G. Narrow emission modes are seen from modest and even relatively weakly scattering samples, with mean free path $\ell =87.8\mu \mathrm{m}$ (upper panel) and $\ell =538\mu \mathrm{m}$ (lower panel). The sample dimensions are $1\times 1\times 1\mathrm{c}\mathrm{m}$.

Figure 2

Calculated emission spectra for the same sample parameters and excitation energies as in the experiments reported in Fig. 1. Sharp emission modes are seen from samples with $\ell =87.8\mu \mathrm{m}$ (upper panel) and $\ell =538\mu \mathrm{m}$ (lower panel). Each sharp peak can be identified in the Monte Carlo simulation as originating from a rare long light path that was amplified exponentially.

Figure 3

(a) Calculated path length distribution of the spon­taneously emitted photons. Sample dimensions: $10\mathrm{m}\mathrm{m}\times 10\mathrm{m}\mathrm{m}\times 100\mu \mathrm{m}$ (slab geometry), $\ell =10\mu \mathrm{m}$. (b)–(d) Inten­sity contribution to the emission spectrum as a function of number of scattering events for different values of the excitation energy $E$: (b) 0.1 mJ, (c) 0.3 mJ, and (d) 0.4 mJ. The noise in the path length distribution is amplified to such an extent that it contributes in a dominating way to the total emission.