Thermal lens focal length statistics for end-pumped solid-state lasers excited with different beam shapes

Recent research has explored the use of non-Gaussian beams, such as ring-shaped pump beams, in end-pumped solid-state lasers to reduce thermal lensing effects. Theoretical studies indicate that the thermal lens is not constant but varies with the radial coordinate r, and can be modeled with two or three components depending on the pumping beam profile, top-hat or ring-shaped. This paper introduces a new, to our knowledge, single-component expression for the thermal lens, derived from the mean value and standard deviation, which is applicable to various pump beam shapes. The results show that the ring-shaped beam produces the lowest average thermal lens dioptric power, with the top-hat beam following closely, exhibiting similar power to the Gaussian beam. These findings align with experimental data reported in the literature. This new approach simplifies the representation of the thermal lensing, offering a more accurate method for correcting its effects.