Transverse Mode Instability in High-Power Yb-Doped Double-Clad Fiber Amplifiers: A Three-Layer Optical–Thermal Analysis Based on Stimulated Thermal Rayleigh Scattering

Transverse mode instability (TMI) in high-power ytterbium-doped double-clad fiber lasers is widely interpreted as being a consequence of a thermo-optic nonlinear phenomenon driven by stimulated thermal Rayleigh scattering. This work presents a coupled optical-thermal model for a continuous-wave forward-pumped (λp=976nm) fiber amplifier emitting at λs=1064nm over an optimal length of 12 m. The formulation explicitly resolves the three radial regions of a double-clad fiber, avoiding single-clad approximations. Modal fields are computed using the weakly guiding approximation (WGA) in the core combined with the semi-WGA at the cladding interfaces, enabling accurate calculation of higher-order modes of penetration into the inner cladding and of the transverse eigenvalues U01 and Umn relevant to TMI. Within this framework, the nonlinear stimulated thermal Rayleigh scattering coupling coefficient is evaluated, including gain saturation and the thermal eigenmodes of the multi-layer geometry. The results show that the inner cladding modifies both the optical and thermal mode structures, altering the optical-thermal overlap between LP01 and higher-order modes and changing the effective strength of STRS, directly influencing the predicted TMI threshold. The proposed formulation provides a quantitative and physically consistent tool for analyzing thermo-optic dynamics in Yb-double-clad fiber amplifiers and supports the design of next-generation high-power fiber lasers with improved modal stability.