Understanding the influence of the structured cladding on the reflectivity of femtosecond laser written gratings in photonic crystal fibers

Fiber Bragg gratings have been essential elements in fiber optical communication for more than two decades. Although writing gratings using different inscription methods in step-index fibers has become a standard procedure, femtosecond laser based fabrication of such gratings in specialty fibers such as photonic crystal fibers (PCFs) has proven not to be straightforward. This is due to the presence of air holes in the cladding region, which impede sufficient amounts of optical energy to reach the core region. An important consequence of the presence of air holes in the cladding, which is sometimes disregarded, is the non-uniform distribution of the laser intensity in the core region, which results in an equally non-uniform refractive index change in the PCF core cross-section. To study this issue we have built a dedicated model based on coupled mode theory that allows estimating the reflectivity of the grating by modeling the intensity distribution in the PCF core region and the resulting non-linear refractive index change using empirical data. We clearly see that the limited overlap of the fiber mode with the index change reduces the reflectivity of the grating, and that the extent of this effect depends on the angular orientation of the PCF with respect to the direction of the inscription beam and on the laser beam focusing optics.