The influence of the mode intensity profile on the population kinetics of terbium ion levels and the excitation of luminescence in a few-mode chalcogenide fiber

Based on the concepts of the wave theory of optical fibers, the excitation of luminescence in a few-mode fiber made of chalcogenide glass doped with terbium ions is considered. According to the wave theory, radiation propagating in a fiber is a set of modes, each having its own intensity profile in the cross section of the fiber. A simplified theoretical model is developed, which differs from the generally accepted phenomenological model in that the radiation intensity in the cross section of the fiber is assumed not to be constant, but to depend on the radial coordinate in accordance with the intensity profile of the given mode. By solving the model problem of population kinetics of terbium ion energy levels in the Ga₅Ge₂₀Sb₁₀Se₆₅ glass upon absorption of pump radiation with a given intensity profile, it was established that the rate of population change and the time of formation of population inversion depend on the radial coordinate. It is shown that, due to the radial dependence of the levels populations, the intensity profiles of modes propagating in the fiber at the pump and luminescence wavelengths are distorted. The radiation losses arising from the rearrangement of mode profiles and the applicability of the generally accepted phenomenological model are discussed.