Spacially resolved coupled mode analysis for TMI threshold powers in quantum and Rayleigh scattering limits

A 3D spatially resolved coupled mode and perturbation analysis for the transverse mode instability (TMI) threshold powers in Yb-doped fiber amplifiers is presented in this paper. Threshold powers are computed in the quantum and thermal Rayleigh scattering limits and are compared with those calculated by other coupled mode analyses. Quantum-limited threshold powers are found to be more than three times greater than those calculated with coupled-mode analyses that use uniform and/or average gain approximations. The analysis presented here includes pump depletion, gain saturation, and transverse hole burning. Simulations are applied to co-, cnt-, and bidirectionally pump amplifier configurations. The appearance of TMI is attributed to the formation of a dynamic thermal grating, which enables the exchange of optical power between the fundamental mode (FM) and higher-order mode (HOM). The sole approximation made is that the power in the HOM is much less than that in the FM. A distributed thermal Rayleigh scattering model is introduced that includes a ray-optic representation of the fiber mode structure that relates the Rayleigh power captured by the HOM to the waveguide structure. The location and strength of the thermal gratings are identified to assist in the application of mitigation techniques.