Subject of study . The formation process of high-order bound soliton groups (soliton molecules) in an all-fiber erbium-doped ring laser operating in the mode-locking regime is investigated. Aim of study. The aims of this study are to develop a numerical model that reveals the mechanisms underlying the generation of high-order soliton molecules and to determine the influence of key resonator parameters of a femtosecond fiber laser on the formation of stable multi-pulse states. Method. A numerical approach based on coupled nonlinear Schrödinger equations was employed. The equations were solved using the split-step Fourier method while accounting for refractive index nonlinearity, gain saturation, and polarization effects. The simulations considered the configuration of a fully fiber erbium-doped ring laser with a highly nonlinear fiber incorporated into the resonator. Main results. A stable solution of the Schrödinger equation corresponding to more than ten bound pulses was obtained, confirming the feasibility of generating high-order soliton molecules. The high gain of the active medium was the primary factor responsible for the splitting of the initial pulse into multiple bound solitons, while polarization effects and phase delays provided fine control over the number of pulses and their temporal separation. The obtained results were well aligned with experimental data and the theory of energy quantization in femtosecond fiber lasers. Practical significance. The proposed numerical model can be used to optimize and improve fiber lasers for application in quantum computing and optical communications.
Orekhov et al. (Tue,) studied this question.