Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-04-12
Phys. Rev. B 71, 054203 (2005)
Physics
Condensed Matter
Disordered Systems and Neural Networks
16 pages, 2 figures
Scientific paper
10.1103/PhysRevB.71.054203
We consider the random lasing from a weakly scattering medium and demonstrate that the distribution of the threshold gain over the ensemble of statistically independent finite-size samples is universal. Universality stems from the facts that: (i) lasing threshold in a given sample is determined by the highest-quality mode of all the random resonators present in the sample, and (ii) the areal {\em density} of the random resonators decays sharply with the quality factor of the mode that they trap. We find analytically the shape of the universal distribution function of the lasing threshold. The shape of this function is governed by a single dimensionless parameter, $\beta$. This parameter increases as a power law with $\ln S$, where $S$ is the sample area (length, volume), and decreases as a power law with disorder strength. The powers depend on the microscopic mechanism of the light trapping. As a result, the distribution of the thresholds narrows with $S$ and broadens with the disorder strength.
Apalkov Vadim M.
Raikh Mikhail E.
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