Stochastic interference of partially coherent light multiple scattered by a random medium is considered. The relationship between the second- and third-order moments of intensity fluctuations in random interference patterns, the coherence function of probe radiation, and the probability density of path differences for the interfering partial waves in the medium are established. The obtained relationships were verified using the statistical analysis of spectrally selected fluorescence radiation emitted by the laser-pumped dye-doped random medium. Rhodamine 6G water solution was applied as the doping agent for the ensembles of densely packed silica grains which were pumped by the CW radiation (532 nm) from the diode-pumped solid state laser. Experimentally observed abrupt decay of the second- and third-order moments of fluorescence intensity fluctuations for the wavelengths ranging from 620 nm to 680 nm is interpreted in terms of amplification of spontaneous emission at large dye concentrations. This paper discusses the new optical probe of random media defined as "the reference-free path length interferometry with the intensity moments analysis".
Stochastic interference of partially coherent light multiple scattered by a random medium is considered. The relationship between the second- and third-order moments of intensity fluctuations in random interference patterns, the coherence function of probe radiation, and the probability density of path differences for the interfering partial waves in the medium are established. The obtained relationships were verified using the statistical analysis of spectrally selected fluorescence radiation emitted by the laser-pumped dye-doped random medium. Rhodamine 6G water solution was applied as the doping agent for the ensembles of densely packed silica grains which were pumped by the CW radiation (532 nm) from the diode-pumped solid state laser. Experimentally observed abrupt decay of the second- and third-order moments of fluorescence intensity fluctuations for the wavelengths ranging from 620 nm to 680 nm is interpreted in terms of amplification of spontaneous emission at large dye concentrations. This paper discusses the new optical probe of random media defined as "the reference-free path length interferometry with the intensity moments analysis".
We propose a coherence optical method for probing fluorescent randomly inhomogeneous media based on the statistical analysis of spatial fluctuations of spectrally selected fluorescence radiation. We develop a phenomenological model that interrelates the flicker index of the spatial distribution of the fluorescence intensity at a fixed wavelength and the mean path difference of partial components of the fluorescence radiation field in the probed medium. The results of experimental approbation of the developed method using the layers of densely packed silicon dioxide particles saturated with the aqueous rhodamine 6G solution with a high concentration of the dye are presented. The experimentally observed significant decrease in the flicker index under the wavelength tuning from the edges of the fluorescence spectrum towards it central part is presumably a manifestation of spectrally dependent negative absorption in the medium.
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.
We report on the experimental determination of the complete two coordinate spatial coherence function of light emitted by a quasi-random laser, implemented on recently introduced dye-doped transparent wood. The spatial coherence was measured by means of a double grating interferometer, which has some advantages over the standard Young's interferometer. Analysis of the spatial coherence reveals that emission from such a material can be considered as a superposition of several spatial modes produced by individual emitters within semi-ordered scattering medium. The overall degree of coherence, γ¯, for this quasi-random laser was found to be 0.16 ± 0.01, having possible applications in speckle free laser imaging and illumination.
The probability distribution p(n) for the detection of n photons emitted by a single-mode dye laser in a short time at various excitations is measured, together with the distribution of time intervals between pairs of detected photons. The first measurement yields the probability density p(I) and the moments of the light intensity I, and the second one the two-time intensity-correlation function. Measurements are also performed at three different wavelengths. p(I) is found to have a two-component structure, and the relative intensity fluctuations $\frac{〈{(\ensuremath{\Delta}I)}^{2}〉}{{〈I〉}^{2}}$ grow, apparently without limit, as the excitation tends to zero, so that no thermal state is reached. A possible explanation in terms of pumping fluctuations is discussed. The correlation function has the form of a sum of three exponential functions, and the amplitudes and decay constants of the three components are derived. The effective decay-time constant exhibits a thirteenth-power-law dependence on frequency of the laser light.
This is the second of a series of papers devoted to develop a microscopical approach to the dipole emission process and its relation to coherent transport in random media. In this Letter, we deduce a relation between the transverse decay rate of an emitter in a virtual cavity and the complex refraction index of the host medium. We argue on the possibility of a criterion for inhibition/enhancement of spontaneous emission in function of the transition frequency and the correlation length of the host scatterers. In addition, we study the radiative/non-radiative nature of the net power emission through a microscopical analysis of the scattering events involved. This study reveals essential discrepancies with previous interpretations.
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.