Correction of femtosecond laser asymmetric spot size for achieving uniform axial intensity in Bessel beam propagation via GPM

This study introduces a concise phase-engineering technique for producing zero-order Bessel beams with a uniform on-axis intensity profile from femtosecond lasers with asymmetric Gaussian inputs (𝒘𝒙 ≠ 𝒘𝒚). The method involves encoding an axicon phase augmented with Gaussian phase modulation (GPM) by a phase-only spatial light modulator (SLM). Using the stationaryphase method (SPM), we derived closed-form expressions that clarify how input waist asymmetry leads to on-axis intensity decay and elliptical rings. A corrective phase was developed to independently manage axial uniformity, with residual errors minimized through numerical GPM tuning. The results show excellent agreement among theoretical predictions, Hankel-transform beam-propagation method (HT-BPM) simulations, and experimental data from a 1030 nm femtosecond laser. We demonstrate that even with minor asymmetry ( 𝒘𝒚/𝒘𝒙 ≈ 𝟎. 𝟗𝟓 − 𝟏. 𝟎𝟓), we can accurately reconstruct both uniform (with GPM) and non-uniform (without GPM) on-axis intensity profiles, achieving a negligible on-axis error. Thus, a significant improvement over the approximately 15% error was found in the uncorrected asymmetric case. The study concludes by providing practical tolerance limits and an executable protocol for diffractive microfabrication using ultrafast optics.