The dynamics of stimulated emission in random lasers is studied using the system of rate equations for population inversion and density of emitted photons. In order to model the behavior of random lasers with nonresonant feedback, no coherence effects are intentionally taken into account. It has been shown that the feedback in the system is necessary for the realization of the regime of relaxation oscillations and spatial confinement of the stimulated emission to the interior regions of the pumped volume. The model also predicts the possibility of localization of stimulated emission in several spatially separated subvolumes of the random laser medium. Finally, it has been demonstrated that two adjacent random laser volumes can strongly enhance the stimulated emission in each other (the ``critical mass'' effect in random lasers).
The dynamics of stimulated emission in random lasers is studied using the system of rate equations for population inversion and density of emitted photons. In order to model the behavior of random lasers with nonresonant feedback, no coherence effects are intentionally taken into account. It has been shown that the feedback in the system is necessary for the realization of the regime of relaxation oscillations and spatial confinement of the stimulated emission to the interior regions of the pumped volume. The model also predicts the possibility of localization of stimulated emission in several spatially separated subvolumes of the random laser medium. Finally, it has been demonstrated that two adjacent random laser volumes can strongly enhance the stimulated emission in each other (the ``critical mass'' effect in random lasers).
In two recent works, the authors have investigated the spectro-temporal properties of the random laser emission from solid state dye-doped powders in picosecond pumping regime. Each emission pulse consists, both above and below threshold, in a collection of narrow peaks of a spectro-temporal width at the theoretical limit (ΔωΔt≅1). The distribution of path lengths traveled inside the diffusive active medium by photons that can be amplified by stimulated emission explains this behavior, as demonstrated by a simple theoretical model developed by the authors. The aim of the present work is, first, to develop an implemented model that does not depend on fitting parameters, and which is compatible with the energetic and spectro-temporal properties of the material; and second, to get knowledge about the spatial properties of the emission. The transverse coherence size of each emitted photon packet has been measured; and in addition, we have shown the existence of spatial fluctuations of the emission of these materials, as our model predicts.
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 the last decade Anderson Localization of Light and Random Lasing has attracted a variety of interest in the community of condensed matter theory. The fact that a system so inartificial as a thin layer consisting of dust particles, which have amplifying properties, can produce coherent laser emission, is of a simple elegance, which promises new insights in fundamental physics. There is no need of an external feedback mechanism, like in the system of a conventional laser. Whereas several attempts try to enter the subject numerically by considering cavity approximations, this thesis is concerned with building a microscopically self-consistent theory of random lasing. Designing this method, we had to study light localization effects in random media including absorption and gain. Incorporating interference effects by means of Cooperon contributions we derived Anderson localized states for passive media. Mapping this on a system which consists of laser active Mie-scatterers in a passive medium, we found that by incorporation of the Cooperon, we loose the Anderson localization, but the system is weakly localized, which is sufficient for population inversion and stimulated emission.
In any quantum or wave system dissipation leads to decoherence. Therefore, it was surprising in first instance when experiments on strongly lossy random lasers showed unambiguously by measurements of the photon statistics and of the lasing mode volume that coherent feedback is possible in such systems3-5,8. In coherent-feedback lasers the photons form a far-from-equilibrium condensate in the sense that a single quantum state is occupied by a macroscopic number of photons15. We demonstrate that the lossy dynamics of random lasers alone imply a three dimensional finite lasing mode extent, thus resolving the puzzle about coherent feedback without resonator. Our theory of random lasing including nonlinear gain and gain saturation predicts a characteristic dependence of this lasing mode volume on the pump intensity, which can be tested experimentally.
A photon, unlike an electron, can stimulate an excited atom to emit a second photon into the same electromagnetic mode. This stimulated emission process is the foundation for light amplification and oscillation (i.e., self-generation). Initially, the term LASER referred to Light Amplification by Stimulated Emission of Radiation. Nowadays laser often means Light Oscillation by Stimulated Emission, which should literally be called "LOSER" instead of "LASER." To distinguish the above two devices, the former is called a laser amplifier, the latter a laser oscillator (Siegman 1986). Laser oscillation occurs when the photon generation rate exceeds the photon loss rate in a system. If gain saturation were absent, the photon number in a laser oscillator would diverge in time. In other words, the rate equation for the photon number would acquire an unstable solution above the oscillation threshold. In reality, gain saturation reduces the photon generation rate to the photon loss rate so that the number of photons in the oscillator remains at a finite value.
We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.