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Optics Communications

Gaussian-to-Lévy statistical crossover in a random amplifying medium: Monte Carlo simulation

Divya Sharma, Hema Ramachandran, Narendra Kumar

Published Jan 2, 2007• 6 citations
Publisher
DOI
10.1016/j.optcom.2006.12.009

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We estimate the parameters of intensity fluctuations in amplifying nanophotonic random media, based on analytical and numerical methods. The statistics of such media belong to the Levy domain due to underlying power-law distributions. The power-law exponent is determined by the gain length and the mean first-passage length of the photon in the system. We employ a Monte-Carlo simulation to accurately estimate the excitation region of the medium, which yields the gain length and the geometric features of this region. The aspect ratio of this pumped region allows to further analytically calculate the mean first-passage length of a photon diffusing out of the amplifying region. Our calculations are in excellent agreement with experimental trends regarding the Gaussian to Levy transition.
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.