Analysis of Long Period Gratings Inscribed by CO₂ Laser Irradiation and Estimation of the Refractive Index Modulation

Long period gratings (LPGs) inscribed in single mode fibers (SMFs) using CO₂ laser irradiation were modelled numerically using the coupled mode method. The model considers the specifications of the inscription technique, such as the shape of the refractive index modulation that mimics the circularly symmetric point-to-point laser irradiation profile. A simple expression for predicting the resonant wavelength was obtained assuming a two-mode coupling model. However, to explain the spectra of the experimental LPGs, it was necessary to assume a reasonably high refractive index change and a multimode coupling model. Furthermore, using the developed model and a genetic algorithm to fit experimental resonances to simulated ones, we were able to estimate the maximum refractive index change, obtaining a value of 2.2 × 10^-3, confirming the high refractive index change. The proposed model also predicts a second order resonance for this high value of refractive index change that was confirmed experimentally. Hence, with this model, we found some significant differences in the LPGs behavior when compared with conventional ones, namely, the emergence of coupling between different cladding modes and the competition of first and second order resonances which change the LPG transmission spectrum.