Mode instability in coiled high power fibre amplifiers: revisiting with a modified theoretical model

Mode instability behaviour in high-power fibre amplifiers with various coiled packages has been investigated numerically by a modified theoretical model, considering the stimulated thermal Rayleigh scattering reseeded by spontaneous thermal Rayleigh noise. The modified model can avoid the physical fake case where the high order mode is reduced to below the spontaneous thermal Rayleigh noise level, which can cause as large as 30% overestimate of the mode instability threshold. The modified model improves the accuracy of the mode instability threshold simulations by >30%, and the discrepancy between experimental results and previous theoretical predictions is explained and eliminated by the modified theoretical model. Mode instability threshold as well as the high order mode evolution in various coiled high power fibre amplifiers is revisited based on this model, which reveals that, from the perspective of mitigating mode instability, fibre amplifiers with the gain fibre coiled in a cylindrical shape are superior to those in a spiral shape, and the mode instability threshold can be increased by nearly two times. It also shows that the current gain fibres do not reach the upper mode instability limits, and have the potential of delivering mode-instability-free 10 kW fibre lasers. This work provides further insight on the physical mechanism of the mode instability, and can guide the design of the high-power fibre lasers to achieve near-diffraction-limited beam quality.