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A fundamental limitation of the spectral response of laser-pumped fluorescent nanostructured media was considered in terms of a probabilistic model establishing the relationship between the enhancement factor of a spectral quality and characteristic propagation and amplification scales of pump light and fluorescence in the medium. It was shown that the minimum spectral width of fluorescent response of the pumped medium is limited by competition between the stimulated emission and radiation losses in microscopic fluorescence emitters associated with the speckles randomly modulating the pumping light field. Theoretical results were compared to the experimental data on the spectral properties of the fluorescent response of laser-pumped nanostructured “anatase nanoparticles—dye solutions” systems with various structural and optical properties. Rhodamine 6G and 4-(dicyanomethylene)-2-methyl-6-(p-dimethylaminostyryl)-4H-pyran (DCM) were applied as fluorescent components in the examined systems with various scatter volume fractions, which were pumped by pulse-periodic laser radiation with various intensities at 532 nm. Comparison showed a fair agreement between the theoretical and experimental results.

A method of reference-free speckle spectroscopy based on the statistical analysis of intensity spatial fluctuations of the spectrally-selected multiple-scattered fluorescence radiation is examined in the case of the finite-band spectral selection of fluorescence light emitted by the laser-pumped random medium, and detection conditions far from the ideal case. Intensity fluctuations are recorded during point-to-point scanning of the surface of a random multiple-scattering medium, which is characterized by the dependences of the second- and third-order statistical moments of intensity on the wavelength of detected spectrally selected light. In turn, the statistical moments of intensity fluctuations are determined by the average propagation path of fluorescent radiation in the medium. This makes it possible to analyze the features of the light-medium interactions at a scale of the order of the transport mean free path of radiation propagation in the medium. Depending on the spectral selection conditions, the method is applicable for characterizing micro- or nano-structured fluorescent layers with thicknesses from tens of micrometers to several millimeters. In the examined case, the finite-band spectral selection results in the values of coherence length of the detected fluorescence radiation compared with the ensemble-averaged absolute value of the path-length difference between the stochastically interfering and spectrally selected partial contributions to the fluorescence field. In addition, non-ideal detection conditions (usage of a multimode optical fiber in the light-collecting unit) cause additional strong damping of the detected speckle intensity fluctuations. These factors lead to a remarkable suppression of spatial fluctuations of the fluorescence intensity in the course of spatially- and spectrally-resolved surface scanning of the laser-pumped probed random medium. Nevertheless, with appropriate procedures of the intrinsic noise reduction and data correction, the obtained spectral dependencies of the normalized third-order statistical moment of the band-limited fluorescence intensity clearly indicate the fluorescence propagation features in the probed multiple-scattering random media (such as a strong influence of the scattering strength and multiple self-absorption−re-emission events on the average propagation path of light in the medium).The possibilities of noise reduction and data correction in the case of applying the band-limited reference-free spectroscopic instrumentation with low spectral and spatial resolution are illustrated by the experimental results obtained using the Rhodamine-6G-doped and continuous wave (CW)-laser-pumped layers of the densely packed titania and silica particles.