Numerical modeling and design of mid-infrared FBG with high reflectivity

Based on the coupled-mode equations and transfer matrix theory, the reflective spectrums of a silica FBG centered at 1.9 μm and a fluoride FBG centered at 2.8 μm with different length and refractive index perturbation were calculated, respectively. The results show that the peak reflectivity and the spectrum width increase and decrease with the increasing FBG length, respectively. An increase in refractive index disturbance quantity results in the increase of both reflective peak and spectrum width. Above 99% reflectivity with the spectrum width of ∼0.6 nm can be achieved for the silica FBG at 1.9 μm when the length and refractive index perturbation are chosen in the range of 4.3–6.4 mm and 4.32 × 10−4–5.36 × 10−4, respectively. For the fluoride FBG at 2.8 μm, above 99% of the reflectivity with the spectrum width of ∼0.75 nm can be achieved when the length and disturbance of refractive index are in the range of 6.0–8.0 mm and 4.53 × 10−4–6.0 × 10−4.