Shannon Entropy and Lévy Statistics for Machine Learning-Assisted Spectral Sensing in Random Fiber Lasers With...

We investigate the relationship between Shannon entropy and Lévy statistics in a random fiber laser based on a dye-doped polymer optical fiber with magnetic core-shell ${\text{Fe}}_3{O}_4{@\text{SiO}}_2$ nanoparticles as scatterers. Spectral measurements acquired below and above the lasing threshold, under varying magnetic fields, are statistically analyzed. Shannon entropy analysis reveals that the intensity fluctuations of each random laser mode, which show the emergence of random laser emission peaks, result in low entropy values. We find a positive correlation between Shannon entropy and the stability index $\alpha$ of the Lévy distribution of output intensities for all magnetic fields and pump energies investigated. As an application, we implement a machine learning approach to classify and predict the magnetic field and pump energy from individual spectra when that information is not available. When the network receives only the spectra as input, the prediction accuracy of the model reaches 69%, but when Shannon entropy is also included as an additional feature, the accuracy increases to 98%. These results demonstrate that Shannon entropy provides relevant complementary information for both the physical characterization of random laser dynamics and the development of efficient real-time optical sensing systems.