Information Entropy and Its Periodic Features in Hermite–Gaussian Correlated Schell-Model Beams in a Gradient-Index Fiber

This paper investigates the evolution of information entropy (IE) in Hermite–Gaussian correlated Schell-model (HGcSM) beams propagating through a gradient-index (GRIN) fiber using Shannon information theory. Our results reveal that the IE of such beams evolves periodically, with the beam order significantly influencing its initial distribution. Compared with traditional Gaussian Schell-model beams, HGcSM beams exhibit more complex IE dynamics, characterized by periodically emerging low-entropy regions whose IE decreases with increasing beam order. Furthermore, the fiber’s central refractive index and core radius strongly affect the evolution period and fluctuation amplitude of IE. These findings provide a theoretical basis for optimizing partially coherent beams in optical fiber applications.