Research On Theoretical Model Of Few-mode Erbium-doped Fiber Amplifiers

The few-mode erbium-doped fiber amplifiers(FM-EDFAs)are the key device for building up mode division multiplexing system.The optimal design of FM-EDFAs is inseparable from the corresponding theoretical model.This paper studies the analytical solution to the intensity model,the beat model,and the mode coupling characteristics of FM-EDFAs.The main research contents and innovations of this article are as follows:1.Based on the intensity model of FM-EDFAs,an analytical analysis method for FM-EDFAs is proposed by introducing the uniformity coefficient of metastable state population inversion.For five different pump combinations,the uniformity coefficient is optimized and compared with the numerical calculation method,and the adaptability of the uniformity coefficient to different pump optical power combinations is verified.This analytical method may to some extent change the situation that the design of FM-EDFAs can only depend on the numerical calculation.2.Regarding the gain as a perturbation,we deduce the beat propagation model for signal and pump light in multi-mode optical fibers according to the coupled-mode theory of guided-wave light.The influence of the beat effect between the few-mode pump light on the population inversion is analyzed.Using the beat model of FM-EDFAs with linearly polarized(LP)mode pumps,the dependences of the gain and differential mode gain(DMG)of FM-EDFAs on the erbium-doped fiber length are calculated by simulation,and are compared with the results from the intensity model.Our simulation shows that,by using the pump beat effect,the DMG of FM-EDFAs can be further reduced by 1.59 dB compared with the intensity model.Thus,the optimal control of the pump beat effect provides another method for further improving the gain performance of FM-EDFAs.3.The beat model of FM-EDFAs is extended to the case with non-gain perturbation such as a refractive index change in erbium-doped fibers,and the analytical solution to the modified coupled mode equations is given and verified by the numerical simulation.Based on the previous analysis,the dependences of the mode extinction ratio(ER)on the propagation constant difference,the coupling coefficient,and the fiber length are analyzed.Our calculation shows that,when the difference in propagation constant is greater than 10 times the coupling coefficient,the mode extinction ratio is greater than 20 dB.In addition,the DMG also affects the mode extinction ratio.