Haus, Gross and Pitaevskii, the fellowship of random lasers. Our proposed equation for describing the linewidth of random lasers is based on the work of these three scientists. In arXiv:1005.2082 (Josa B 27, 1446 (2010)), the derivation of our model (originally introduced here, Phys. Rev. Lett. 101, 143901 (2008)) is detailed and it is shown how a single equation quantitatively predicts the observed random laser linewidth.
The model is not based on the diffusive approximation for light; conversely it starts from the general Haus model for passively mode-locked lasers and arrives to an equation that is formally identical to that describing one-dimensional zero-temperature Bose-Einstein condensation in an external potential (the Gross-Pitaevskii equation).
The basic idea follows that of a stochastic resonator, originally introduced by Lethokov in 1968, i.e., an open system sustaining a large number of electromagnetic resonances with overlapping linewidths, as sketched in the following figure
By extending the ideas of Haus for multi-mode lasers to such a kind of resonator we derive the following equation:
The Fourier transform of the solution gives the spectrum of the Random Laser.
The equation contains only one parameter: the "nonlinear eigenvalue" E, which depends on the gain bandwidth and the coefficients that measure the spread of the mode decay-time distribution. When the nonlinear eigenvalue E is greater than 1, a bell-shaped linewidth is attained.
This allows to define rigorously a threshold for random lasers, and is in quantitative agreement with our experiments.
This also shows how random lasing can be understood as a classical condensation process of electromagnetic resonances in open disordered resonators.
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