Transverse-Mode Instability in High-Gain Few-Mode Yb3+-Doped Fiber Amplifiers With a 10-μm Core Diameter With or Without Backward Reflection

Spatio-temporal transverse instability of the fundamental mode in high-gain fiber amplifiers based on a highly Yb
³⁺
-doped few-mode polarization maintaining fiber with a core diameter of 10 μm was studied. Both experimental and theoretical analyses revealed the nonlinear power transformation of the LP
₀₁
fundamental mode into high-order modes. Numerical simulation showed a self-consistent growth of the higher order mode and traveling refractive index grating accompanying the population grating induced by the mode interference field (due to different polarizability of the excited and unexcited Yb
³⁺
ions). The threshold power for the transverse-mode instability was observed to change from a fraction of a Watt to tens of Watts depending on the fiber core diameter, numerical aperture, dopant concentration, power of the input signal, and the signal bandwidth. The threshold was registered to decrease dramatically in the presence of a backward reflection of the signal from the output fiber end. Numerical simulation revealed that the presence of the backward-propagating wave resulted in four-wave mixing on the common long-period index grating induced by the interference field of mode pairs. The dynamic of the instability threshold variation and a specific case of larger core fiber characterized by competition of the electronic and temperature index gratings is discussed.