## 3 Experimental Technique
### BLRFS Bench-Top Instrumentation and Probing Technique
As \(\beta\) is inversely proportional to the number of excited modes \(N_{m}\) the value of \(N_{m}\) for the step index patch-cord can be roughly estimated as \(\approx 4\pi^{2}a^{2}\big{(}N\Delta_{p}^{2}\big{)}/2\lambda^{2}\), where \(a\) is the core radius, in particular, \(N_{m}\approx 1550\) at \(\lambda=700\) nm. Actually, the real effective number of the excited modes occurs smaller than this upper estimation due to non-uniform excitation. The output tip of the fiber-optic patch-cord was connected to the input optical connector of the Ocean Optics HR4000 CG-UV-NIR spectrometer, and the fluorescence spectra of the examined samples were recorded in the spectral ranges corresponding to their fluorescence emission bands (between 600 and 700 nm) with the spectral resolution \(\Delta\lambda\) approximately equal to 1 nm. These spectral selection parameters correspond to the coherence length \(l_{c}\approx\overline{\lambda}^{2}/n_{ef}\Delta\lambda\) of the detected radiation in the examined samples, which varies from \(\approx\)250 um to \(\approx\)330 um (here, \(\overline{\lambda}\) is the central wavelength of the radiation selected by the used spectral window \(\Delta\lambda\), and \(n_{ef}\) is the effective refractive index of the examined medium). Fluorescence radiation was collected from the various areas of the sample surface using a step-by-step scanning with the scan step \(\Delta x\) equal to 10 micrometers. In the course of the scanning, the examined sample was sequentially displaced in the lateral direction with respect to the axis of the light-collection system. For each position of the sample, the fluorescence spectrum from the given light-collection zone was recorded; the data acquisition time was equal to 10 s, and the acquisition procedure began with a 5 s delay after setting the sample to the fixed position (to minimize the influence of mechanical oscillations in the system on the acquired data). A sufficiently larger value of \(\Delta x\) in comparison with \(d_{z}\) provided confidence in statistical independence of the spectral data obtained from the various light-collection zones on the sample surface. In the course of the spectral data acquisition, the examined samples were irradiated by a diverging continuous-wave laser beam using the oblique incidence illumination geometry (Figure 1); the used concave lens expanding the pumping beam had a focal length equal to \(-\)200 mm. The angle of incidence was equal to \(86^{\circ}\) and the laser light spot totally covered the sample surface. The incidence angle of the given value, which corresponds to an almost sliding fall of the pumping beam onto the sample surface, was chosen to exclude vignetting of the irradiated surface by the objective body. The wavelength of laser radiation was equal to 532 nm (a Nd/YAG DPSS laser with the frequency doubling, 50 mW output), and a roughly estimated value of the energy flux density of the pumping light, which penetrates through the sample surfaces was roughly estimated as \(\approx\)1-3 W/cm\({}^{2}\). The samples were scanned along an arbitrarily chosen trace, the number of scan points for each trace was chosen equal to 100. The scan runs were repeated 5 times with an arbitrarily chosen initial point. Thus, the statistical moments of intensity fluctuations \(\langle I\rangle\), \(\langle I^{2}\rangle\), \(\langle I^{3}\rangle\) were averaged for the chosen wavelength over the sampling sets containing 500 values. The noise-accounting technique included the following procedures: recording of the fluorescence spectra from the dye solution and the dye-impregnated samples without scanning (at a fixed position of the light-collecting unit, the \"static\" measurements). In the course of spectral data acquisition for noise accounting, the acquisition parameters (in particular, the integration time of the spectrometer) were chosen the same as for the scanning experiments.