Cross-axis Bragg gratings in few-mode fibers inscribed with a femtosecond laser point-by-point technique

Point-by-point (PbP) cross-axis Bragg gratings in a step-index two-mode fiber are fabricated by tightly focused femtosecond laser pulses. The grating is formed by inscribing a line of periodic damage points crossing the fiber axis at a certain tilting angle. We experimentally show that the cross-axis structure can introduce multiple mainband resonances associated with the higher-order modes, with wavelength spacing proportional to the tilting angle. We also develop a numerical model for the PbP-inscribed gratings based on pulse-wave approximation and the standard coupled-mode theory, the resulting simulation exhibits a good agreement with the experimental findings. This work suggests the higher-order fiber modes, synergizing with the PbP technique, has the potential to add a new dimension to designing gratings with desired spectral spacing; such an inverse problem of PbP gratings can be assisted by the numerical modal we developed.