Finite Element Steady Periodic Beam Propagation Analysis of Mode Instability in High Power Fiber Amplifiers

A finite element steady periodic scalar beam propagation method suited to treating mode instability in amplifiers incorporating fibers with complicated design features is presented and demonstrated on test cases. These incorporate large pitch photonic crystal fibers with confined and down-doped cores in co-pumped and counter-pumped configurations. Seed power fluctuations and slight launch misalignment is proposed and implemented as a noise source to seed the instability. Down doping the confined core by -7.0E-5 was found to increase the instability threshold by 25% in the co-pumped case and 9% in the counter-pumped case. The increase in threshold is correlated with the suppression of higher frequency components of intensity gratings associated with the instability.