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arXiv:1906.12306 · Physical Review A

Superdiffusive random laser

Federico Tommasi, Lorenzo Fini, Fabrizio Martelli, Stefano Cavalieri

Published Jun 28, 2019• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.99.063836

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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.
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.
In this paper we present calculations on light diffusion with amplification that can explain previous experiments on the spontaneous emission from such a medium. Also we discuss the experimental considerations on realizing a medium that both multiply scatters and amplifies light. In an amplifying random medium different processes can occur. We argue that one can distinguish three regimes depending on the amount of scattering, and discuss these regimes in the context of random laser action. \textcopyright{} 1996 The American Physical Society.
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 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.
Randomness is essential ingredient for applications in cryptography, stochastic simulation, and fundamental science experiments [American Scientist 89, 4 (2001); PRL 115, 25 (2015)]. Common practice is to generate random numbers from mathematical algorithm using Pseudo-random number generators. We are interested in tackling this problem with quantum technology. Phase diffusion in spontaneous emission events is a quantum phenomena with inherent randomness [Opt. Express 19, 21 (2011)]. Implementations of this scheme using pulsed lasers can yield high-speed quantum random number generation (QRNG) [Opt. Express 22, 2 (2014)]. The general interest in the laser phase diffusion QRNG setup has been mainly focused on and motivated by the speed of the random number generations. Little has been stated about the performance of quantum phase noise as a randomness source in QRNG, from the perspective of the physics involved. We reanalyze the process of phase diffusion based QRNG and give an intuitive explaining picture of the underlying physics. Our findings show that a pulsed process is beneficial over the continuous-wave approach and give a upper bound of maximum random bit rate for a given experimental setting. In detail, the output of a semiconductor laser contains fluctuations in intensity and phase. This was originally studied first by Charles Henry in 1982 [J. Lightwave Techn. 4, 3 (1986)]. Based on that one can identify two phenomena contributing to the phase noise, which takes the form of a random walk. First, there will be phase changes due to the carrier-induced change in refractive index in the semiconductor laser. Second, spontaneous emission events take place in the active medium [Opt. Express 19, 21 (2011)]. Naturally, taking spontaneous emission events into account necessitates the application of stochastic laser rate equations for theoretical description. We solve these equations numerically be a Monte-Carlo simulation and investigate several random walk scenarios. One of our essential findings is that the phase fluctuation becomes much larger in the pulsed laser regime than in the continuous-wave mode. Additionally, there is a natural limit on the maximum pulse repetition rate for a given pulse width, since the phase jumps become smaller for shorter pulse distances. Since phase measurement is not a feasible procedure for optical signals, the phase fluctuation needs to be converted to an observable macroscopic parameter such as the optical intensity. This can be done by using an interferometer setup. The whole experimental setting is shown in Fig. 2 (left). An DFB laser diode is modulated using gain-switching technique to generate uniform amplitude signals with random phases. Each signal interferes with neighboring pulses through an unbalanced Mach-Zehnder interferometer. The delay in one arm was set to equal to the pulse repetition rate. With this setup we investigate the influence of several parameters on the shape of the probability distribution determining the quality of QRNG. The theoretical as well as experimental findings can help to find physical standards for QRNG verification rather than the ones based on classical statistical information theory.
We derive the photon number probability distribution of light emitted from a random multiple-light-scattering medium with gain, using a generalized master equation. Our model treats the random laser medium as a collection of low quality-factor cavities, coupled by random photon diffusion. We demonstrate that, with stronger scattering, the pumping threshold for the transition from chaotic to isotropic coherent light emission decreases and the local second order coherence, above threshold, increases.