Design and experimental evaluation of TiO\(_2\)/MgF\(_2\) dual-layer anti-reflection coatings for Nd- and Er-doped phosphate glass lasers

Thermal lensing is an inherent phenomenon in high-power laser optical systems, including fiber laser cutting heads, arising from energy absorption–induced thermal and optical variations. This paper presents a numerical study, based on the finite element method, of thermal lensing effects in a 1064 nm fiber laser system operating at 1--6\,kW, using fused silica plano-convex lenses with focal lengths of 125--300 mm. The simulations predict a maximum lens temperature of 952 K at 6 kW, leading to focal shifts up to \(Δ f = -45.4\) mm for a 300 mm focusing lens, and relative refractive index variations of 74.5-114%. While spot diagram asymmetries appear at higher power levels, these are likely numerical artifacts rather than physical optical deformation. The results highlight the significant impact of thermal lensing on focal stability and provide a numerical framework useful for the design and optimization of fiber laser cutting heads operating at kilowatt power levels.