Simplified expression for transverse mode instability threshold in high power fiber lasers

In this work, we propose an analytical expression for calculating the transverse mode instability (TMI) threshold power, which clearly shows the role of various fiber parameters and system parameters. The TMI threshold expression is obtained by solving the heat conduction equation and the nonlinear coupling equation using the fundamental mode fitted by Gaussian functions. The calculation results of the proposed TMI threshold expression are consistent with the experimental phenomena and simulation results from the well-recognized theoretical model. The influence of some special parameters on the TMI threshold and the power scaling is also investigated. This work will be helpful for fiber design and TMI mitigation of high-power fiber lasers.