Femtosecond laser writing of fiber Bragg gratings using the phase mask technique: a geometrical optics analysis based on the Bravais refractive index.

Material modification is produced inside silica-based optical fibers of different diameters using tightly focused near-infrared (central wavelength at 800 nm) femtosecond laser pulses and the phase mask technique which is often employed for laser inscription of fiber Bragg gratings. 1-, 2-, and 3-order phase masks designed for the operation at 800 nm are used in the experiments. The inscription is performed at different distances from the fiber's front surface by translating the focusing cylindrical lens along the laser beam propagation direction. The results show that the material modification produced by means of the 2- and 3-order phase mask can be positioned at any predetermined distance from the fiber's front surface. In contrast, when the 1-order mask is used for laser writing, the maximum distance from the fiber's front surface at which material modification can be produced is limited and determined by three main parameters: the diffraction angle of the phase mask, the refractive index of the fiber and the diameter of the fiber.