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Optics Letters

Lévy statistics of emission from a novel random amplifying medium: an optical realization of the Arrhenius cascade

Divya Sharma, Hema Ramachandran, Narendra Kumar

Published May 25, 2006• 39 citations
Publisher

Abstract

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.

DOI
10.1364/ol.31.001806

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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.
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.
The statistical behavior of spectral intensity fluctuations in a Raman gain random fiber laser is investigated for the first time, to the best of our knowledge. Through a fiber Fabry–Perot tunable filter, the intensity of the filtered single wavelength from random laser (RL) spectra is measured at different pump powers. The probability density function (PDF) of spectral intensity values is analyzed. Well below the lasing threshold, the intensity of a single wavelength is stable in the time domain, and the PDF exhibits a typical Gaussian behavior. However, around the threshold, strong fluctuations in intensity emerge. In this case, the statistical distribution is characterized by a power-law-tailed function consistent with a Lévy α-stable distribution. We identify the statistical evolution as the injected pump power increases, from a Gaussian to a Lévy and then back to a Gaussian distribution, which is similar to the case of RLs with a strong disorder due to the presence of photon scatterers and gain related to electronic transitions in the active medium, indicating the universal existence of such statistical properties in random lasing systems.
We report on measurements of the statistical fluctuations of the output intensity in a continuous-wave-pumped erbium-doped one-dimensional random fiber laser (RFL), with specially designed Bragg grating scatterers. Transitions from Gaussian to Lévy-like and back to the Gaussian regime, similar to those observed in three-dimensional random lasers, are described as the input excitation power increases from below to above the RFL threshold. Our results are consistent with theoretical predictions for the sequence of statistical regimes of output intensity in random laser systems. We also discuss experimental and theoretical connections with the photonic spin-glass behavior of the erbium-doped RFL, which displays a replica-symmetry-breaking phase above the threshold.
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.
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.