Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Observation of Lévy statistics in one-dimensional erbium-based random fiber laser

Bismarck Costa Lima, Anderson S. L. Gomes, Pablo I. R. Pincheira, André L. Moura, Mathieu Gagné, Ernesto P. Raposo, Cid Bartolomeu de Araujo, Raman Kashyap

Published Jan 6, 2017• 70 citations
Publisher

Abstract

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.

DOI
10.1364/josab.34.000293

Related papers

Lévy spectral intensity statistics in a Raman random fiber laser

Jiaqi Li, Han Shui Wu, Zinan Wang +5 more

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.

Optics Letters•May 24, 2019•44 citations

Experimental study of instability in a random laser with immobile scatterers

Guohua Zhu, Lei Gu, Mikhail A. Noginov

Pulse-to-pulse instability in the emission from a random laser based on Nd:Sc${}_{3}$(BO${}_{3}$)${}_{4}$ ceramic with immobile scatterers was studied below, at, and above the stimulated emission threshold ${P}_{\mathrm{th}}$. The correlation between pumping and emission intensities was found to be surprisingly low, especially in the vicinity of the lasing threshold. When the sample was excited by reasonably stable (\ifmmode\pm\else\textpm\fi{}5$%$) pumping pulses, a strong fluctuation of output intensities was observed in the range of pumping energies ${P}_{\mathrm{th}}$/2 $P$ 2${P}_{\mathrm{th}}$---the range in which the L\'evy statistics of emission fluctuations has been predicted in random lasers. We thus report on experimental evidence of the L\'evy statistics in a random laser with firmly fixed scatterers.

Physical Review A•Apr 2, 2012•25 citations

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

Divya Sharma, Hema Ramachandran, Narendra Kumar

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.

Optics Letters•May 25, 2006•39 citations

Intensity noise of erbium-doped fiber laser based on full quantum theory

Wenjun Yue, YunXiang Wang, Cai-Dong Xiong +2 more

Traditionally, by means of full quantum theory, we present the intensity noise transfer function of an Er-doped fiber laser, on the basis of which we analyze the spectrum of the intensity noise. Our theoretical results are in agreement with the existing experiment results. This model explains not only how the noise is produced, but also how the spontaneous emission and dipole fluctuations have an effect on the output noise, which cannot be explained via rate equation theory. We analyze the physical sources of various contributions to the noise spectrum as well. The simulation results show that the noise of the Er-doped fiber laser mainly consists of the vacuum noise resulting from the output coupling, dipole fluctuation noise, the pump source intensity noise, and the spontaneous emission from the upper level to the ground level, which provides the theoretical basis for noise suppression. Compared to the solid laser, the Er-doped fiber laser shows lower resonant relaxation oscillation frequency.

Journal of the Optical Society of America B•Jan 7, 2013•28 citations

Experimental investigation of photon statistics in Raman random fiber laser

Yifei Qi, Runhao Li, Taichao Wang +4 more

In this work, a comprehensive experimental investigation of the photon statistics in random fiber laser (RFL) is conducted using the classical temporal second-order correlation function, and its unique evolutionary behavior is unveiled for the first time.

•Jan 1, 2026•0 citations

Thermalization of one-dimensional photon gas and thermal lasers in erbium-doped fibers

Rafi Weill, Alexander Bekker, Boris Levit +2 more

We demonstrate thermalization and Bose-Einstein (BE) distribution of photons in standard erbium-doped fibers (edf) in a broad spectral range up to ~200nm at the 1550nm wavelength regime. Our measurements were done at a room temperature ~300K and 77K. It is a special demonstration of thermalization of photons in fiber cavities and even in open fibers. They are one-dimensional (1D), meters-long, with low finesse, high loss and small capture fraction of the spontaneous emission. Moreover, we find in the edf cavities coexistence of thermal-equilibrium (TE) and thermal lasing without an overall inversion (T-LWI). The experimental results are supported by a theoretical analysis based on the rate equations.

arXiv:1607.01681•Optics Express•Jul 27, 2017•12 citations
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.
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.
Pulse-to-pulse instability in the emission from a random laser based on Nd:Sc3{}_{3}3​(BO3{}_{3}3​)4{}_{4}4​ ceramic with immobile scatterers was studied below, at, and above the stimulated emission threshold Pth{P}_{\mathrm{th}}Pth​. The correlation between pumping and emission intensities was found to be surprisingly low, especially in the vicinity of the lasing threshold. When the sample was excited by reasonably stable (\ifmmode\pm\else\textpm\fi{}5%) pumping pulses, a strong fluctuation of output intensities was observed in the range of pumping energies Pth{P}_{\mathrm{th}}Pth​/2 PPP 2Pth{P}_{\mathrm{th}}Pth​---the range in which the L\'evy statistics of emission fluctuations has been predicted in random lasers. We thus report on experimental evidence of the L\'evy statistics in a random laser with firmly fixed scatterers.
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.
Traditionally, by means of full quantum theory, we present the intensity noise transfer function of an Er-doped fiber laser, on the basis of which we analyze the spectrum of the intensity noise. Our theoretical results are in agreement with the existing experiment results. This model explains not only how the noise is produced, but also how the spontaneous emission and dipole fluctuations have an effect on the output noise, which cannot be explained via rate equation theory. We analyze the physical sources of various contributions to the noise spectrum as well. The simulation results show that the noise of the Er-doped fiber laser mainly consists of the vacuum noise resulting from the output coupling, dipole fluctuation noise, the pump source intensity noise, and the spontaneous emission from the upper level to the ground level, which provides the theoretical basis for noise suppression. Compared to the solid laser, the Er-doped fiber laser shows lower resonant relaxation oscillation frequency.
We demonstrate thermalization and Bose-Einstein (BE) distribution of photons in standard erbium-doped fibers (edf) in a broad spectral range up to ~200nm at the 1550nm wavelength regime. Our measurements were done at a room temperature ~300K and 77K. It is a special demonstration of thermalization of photons in fiber cavities and even in open fibers. They are one-dimensional (1D), meters-long, with low finesse, high loss and small capture fraction of the spontaneous emission. Moreover, we find in the edf cavities coexistence of thermal-equilibrium (TE) and thermal lasing without an overall inversion (T-LWI). The experimental results are supported by a theoretical analysis based on the rate equations.