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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Light diffusion with gain and random lasers

Diederik Sybolt Wiersma, Ad Lagendijk

Published Oct 1, 1996• 457 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.54.4256

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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.
Random lasing is a phenomenon in which light amplification is favoured by a disordered environment[1]. A vast body of research exists that endorses the exciting physics seen in such media[2-4]. Hitherto, however, these systems have always been studied in the self-amplification mode where the spontaneous fluorescence of the medium is amplified. In this paper, we experimentally demonstrate the amplification of an external coherent signal by a random amplifying system. This is the first such demonstration, which has potential applications in optical amplifiers, frequency control of random lasers[5,6] etc.
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.
Atoms can scatter light and they can also amplify it by stimulated emission. From this simple starting point, we examine the possibility of realizing a random laser in a cloud of laser-cooled atoms. The answer is not obvious as both processes (elastic scattering and stimulated emission) seem to exclude one another: pumping atoms to make them behave as amplifier reduces drastically their scattering cross-section. However, we show that even the simplest atom model allows the efficient combination of gain and scattering. Moreover, supplementary degrees of freedom that atoms offer allow the use of several gain mechanisms, depending on the pumping scheme. We thus first study these different gain mechanisms and show experimentally that they can induce (standard) lasing. We then present how the constraint of combining scattering and gain can be quantified, which leads to an evaluation of the random laser threshold. The results are promising and we draw some prospects for a practical realization of a random laser with cold atoms.
Introduction Previous discussions (see Section 10.4) suggested that stimulated emission can be used to generate optical gain, that is, to amplify radiation. The reader certainly has experience in the amplification of electronic signal. For example, radio receivers capture faint radio waves and turn them into a signal that is powerful enough to drive large speakers. This electronic amplification increases the amplitude of the signal while faithfully preserving its acoustic frequencies and modulation characteristics. Similarly, optical amplification is expected to increase the amplitude of an optical signal while preserving its frequency, its modulation characteristics, and its coherence. The latter requirement is of particular significance for optical radiation, where the coherence of naturally occurring radiation rarely exceeds one micrometer. Lasers are the primary source for coherent radiation. They depend on stimulated emission for amplification and for the generation of coherent radiation (the word laser is the acronym of Light Amplification by Stimulated Emission of Radiation). For amplification, an atomic system that is part of the laser medium must be prepared with a sufficiently large number of particles in the excited state. (The term atomic system is used here to describe all microscopic systems including molecules and free electrons.) Radiation passing through that excited medium encounters multiple events of stimulated emission, each event contributing one photon that is added coherently to the propagating beam. When the number of events of stimulated emission exceed all losses by absorption or scattering, the incident radiation is amplified.
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.