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Journal of Experimental and Theoretical Physics Letters

On the Minimum Length of Fluorescence Enhancement upon Laser Pumping of Randomly Inhomogeneous Media

Dmitry A. Zimnyakov, S. S. Volchkov, L. A. Kochkurov, Alexander Dorogov

Published Jul 1, 2022• 2 citations
Publisher

Abstract

The saturation of the spectral quality of the fluorescence response of randomly inhomogeneous media to external laser pump with intensities above the random lasing threshold in a medium has been studied. It has been found that the saturation of the fluorescence spectral quality is due to a decrease in the fluorescence enhancement length in the medium to the minimum value determined by the average size of local fluorescence emitters associated with laser speckles and by radiative exchange between emitters.

DOI
10.1134/s0021364022601038

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The saturation of the spectral quality of the fluorescence response of randomly inhomogeneous media to external laser pump with intensities above the random lasing threshold in a medium has been studied. It has been found that the saturation of the fluorescence spectral quality is due to a decrease in the fluorescence enhancement length in the medium to the minimum value determined by the average size of local fluorescence emitters associated with laser speckles and by radiative exchange between emitters.
Abstract Based on the analysis of experimental data on the effect of the pulsed laser pump intensity on the spectral properties and the size of the fluorescent response zone in randomly inhomogeneous fluorescent layers, we found that the amplification of spontaneous and stimulated emission significantly affects the statistical properties of the propagation lengths of the fluorescent field partial components in the layers. The experiments are performed with layers of SiO2 and TiO2 nanoparticles saturated with rhodamine 6G, pumped by 532-nm laser radiation in the intensity range corresponding to the transient regime from excitation of spontaneous fluorescence to random lasing in the layer. The experimental data are compared with the results of statistical modelling of fluorescence transfer. It is shown that, even at a pump intensity below the random lasing threshold, the spontaneous emission amplification in a layer leads to a significant increase in the contributions to the fluorescence response from partial components with propagation lengths much larger than the layer thickness. This can be interpreted as a manifestation of the quasi-waveguide effect, in which the probability of propagation of diffuse fluorescence components along the layer over distances many times greater than its thickness and the size of the pumped region increases significantly with a decrease in the characteristic radiation amplification length in the layer.
The features of fluorescence emission in a dye-doped dense multiple scattered medium under pulsed laser pumping are considered in terms of confined excitation in small zones associated with laser speckles occurring in a pumped medium. The results of numerical modeling of the fluorescence emission kinetics are compared to the experimental data obtained using the rhodamine 6G-doped layers of the densely packed TiO2 (anatase) particles pumped at 532 nm by 10 ns laser pulses. The intensity of pump radiation during the action of laser pulses was varied from 1·105 W/cm2 to 5·107 W/cm2. In the recovery of the ratios of stimulated to a spontaneous emission, the spectra of the stimulated component were fitted using the spectral function derived by R. Dicke. In the framework of the considered concept, saturation of the ratio of the stimulated to a spontaneous emission and linear growth of an integrated fluorescence output with a practically unchangeable half-width of the emission spectra at high pump intensities are interpreted.
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.
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".
The characteristics of a random laser based on a nanocomposite medium consisting of a transparent dielectric and scattering doped nanocrystals are calculated. It is proposed to use ytterbium laser media with a high concentration of active ions as nanocrystals and to use gases, liquids, or solid dielectrics with a refractive index lower than that of nanocrystals as dielectric matrices for nanocrystals. Based on the concept of nonresonant distributed feedback due to the Rayleigh scattering, an expression is obtained for the minimum length of a nanocomposite laser medium at which the random lasing threshold is overcome. Expressions are found for the critical (maximum) and the optimal size of nanocrystals, as well as for the optimal relative refractive index of nanocomposites that corresponds not only to the maximum gain but also to the minimum of the medium threshold length at the optimal size of nanocrystals. It is shown that the optimal relative refractive index of a nanocomposite increases with increasing pump level, but is independent of the other nanocomposite parameters.
Based on the time dependent theory of random lasers, which was built via combining Maxwell equations with the rate equations of a four-level atomic system, the output intensity of a lasing mode varying with the pumping rate is simulated for a two-dimensional random active medium by use of the finite difference time domain method. Results show that the pumping rate dependence of the output intensity presents not only a threshold property, but also a saturation property, just like that of lasing modes in conventional lasers. Charactering the mode's localization extent via the mode's area indicates that the stronger the mode's localization extent is, the lower the mode's threshold is. However, such a relation is not a one-to-one correspondence, meaning that the mode's localization extent is an important fact to determine the mode's threshold, but is not alone.