Radial-apodization-modulated femtosecond laser PbP inscription for high-quality apodized FBG

This study proposes what we believe to be a novel method for fabricating apodized fiber Bragg grating (AFBG) using radial-apodization-modulated femtosecond laser point-by-point (PbP) inscription. Herein, the fiber radial direction is defined as the axis parallel to the femtosecond laser beam (Z-axis). This approach effectively resolves the issue of laser focus deviation from the fiber core center along the Z-axis-caused by low positioning repeatability of the translation stage/fiber clamp and inconsistent fiber geometric parameters-thereby significantly improving inscription success rates and grating quality. A mathematical model for radially apodized PbP AFBG inscription was developed, which enhances the axial positionin<i>Δ</i>g tolerance (up to several micrometers) by adjusting the Z-axis tilt offset z at the grating's start/end positions. This innovation facilitates stable laser spot focusing within the 9.0±0.5 µm core, with theoretical verification confirming its Gaussian-apodization characteristics. Experimental results using a polyimide-coated single-mode fiber (cladding/core: 125±1 µm/9.0±0.5 µm) demonstrate that AFBGs with a 6 mm effective grating length exhibit a side-lobe suppression ratio (SLSR) exceeding 20 dB and reflectivity above 70%. The fabricated AFBGs exhibit a temperature sensitivity of 10.5 pm/°C (<i>R</i>² = 0.9999), a strain sensitivity of 1.2 pm/µε (<i>R</i>² = 0.9997), and a torsional sensitivity of 11 pm/(rad/m) (<i>R</i>² = 0.9994), providing a robust solution for high-quality PbP AFBG fabrication.