We report the studies of emission from a novel random amplifying medium that we term a ``Levy Laser'' due to the non-Gaussian statistical nature of its emission over the ensemble of random realizations. It is observed that the amplification is dominated by certain improbable events that are ``larger than rare'', which give the intensity statistics a Levy like ``fat tail''. This, to the best of our knowledge, provides the first experimental realization of Levy flight in optics in a random amplifying medium.
We report the observation of Lévy-like statistical configuration-to-configuration fluctuations in the intensity of emission from a novel system, the fiber-random amplifying medium, where active fiber segments are embedded randomly in a bulk of pointlike passive scatterers. Some rare configurations of fibers provide long, guided amplifying paths for the photons, leading to high jumps in the intensity, and thus to Lévy statistics. This system provides an optical realization of the Arrhenius cascade.
The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to constrain light propagation by L\'evy walks, i.e., with a ``heavy-tailed'' distribution of steps, has opened the opportunity to investigate the behavior of a superdiffusive optical gain medium that can lead to a ``superdiffusive random laser.'' Here, we present a theoretical investigation, based on Monte Carlo simulations, on such a kind of medium, focusing on the widespread presence of fluctuation regimes, that, in contrast to a diffusive random laser, appears very hard to switch off by changing the gain and scattering strength. Hence, the superdiffusion appears as a condition that increases the value of the threshold energy and promotes the presence of fluctuations in the emission spectrum.
We consider interacting many-particle systems with quenched disorder having strong Griffiths singularities, which are characterized by the dynamical exponent,
z, such as random quantum systems and exclusion processes. In several
d=1 and
d=2 dimensional problems we have calculated the inverse time scales, ${\ensuremath{\tau}}^{\ensuremath{-}1}$, in finite samples of linear size,
L, either exactly or numerically. In all cases, having a discrete symmetry, the distribution function, $P({\ensuremath{\tau}}^{\ensuremath{-}1},L)$, is found to depend on the variable, $u={\ensuremath{\tau}}^{\ensuremath{-}1}{L}^{z}$, and to be universal given by the limit distribution of extremes of independent and identically distributed random numbers. This finding is explained in the framework of a strong disorder renormalization group approach when, after fast degrees of freedom are decimated out, the system is transformed into a set of noninteracting localized excitations. The Fr\'echet distribution of $P({\ensuremath{\tau}}^{\ensuremath{-}1},L)$ is expected to hold for all random systems having a strong disorder fixed point, in which the Griffiths singularities are dominated by disorder fluctuations.