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Physical Review A

Experimental study of instability in a random laser with immobile scatterers

Guohua Zhu, Lei Gu, Mikhail A. Noginov

Published Apr 2, 2012• 25 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.85.043801

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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.
A numerical study is presented of random lasers as a function of the pumping rate above the threshold for lasing. Depending on the leakiness of the system resonances, which is typically larger in random lasers compared to conventional lasers, we observe that the stationary lasing regime becomes unstable above a second threshold. Coherent instabilities are observed as self pulsation at a single frequency of the output intensity, population inversion, as well as the atomic polarization. We find these Rabi oscillations have the same frequency everywhere in the random laser despite the fact that the field intensity strongly depends on the spatial location.
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.
The spatial and spectral evolution of emission from gain media with homogeneously distributed scatterers is modeled using a Monte Carlo simulation of the random walk of pump and emitted photons. We find a sharp transition to ultrafast, narrow-linewidth emission for a 10-ps incident pump pulse and a rapid approach to steady state for longer pulses. The threshold for this transition is raised significantly when the transverse diffusion of photons out of the excited region is substantial. The quantitative agreement of the results with recent observations of emission from random gain media lends further support to the interpretation of ``random lasers'' in terms of amplified spontaneous emission within a multiply-scattering medium.
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.