Analysis and modeling of CLBG using the transfer matrix

Gratings in optical fibers have been increasingly used in a variety of applications such as sensors and Telecomm. Depending on perturbation separation, they are classified as: fiber Bragg gratings (FBG), and long period gratings (LPG), whose each spectral output offer advantages for certain applications. Nowadays there is a great interest in the study of arrays formed by the combination of long period gratings and Bragg gratings in cascade (CLBG), where the propagation modes of the core and the cladding propagate in the Bragg grating after they propagate in the LPG. In this work, analysis and modeling of Cascaded Long Bragg Gratings using the Transfer Matrix method was performed for the case of two gratings in series along one fiber. We analyzed the variation of the FWHM of the reflectance and transmittance spectra for different values of the difference of the refractive indexes of the core and the perturbation of the grating, using the typical core refractive index of an SMF-28 as reference value. For smaller index difference a narrow intensity peak was observed. After the number of perturbations was varied, when there is a greater number of perturbations in the grating, there is greater intensity in reflectance. However, as our results show, this dependence is not a linear function. The results were obtained under the maximum-reflectivity condition (tuned) for each single grating. The development of the mathematical model, the results of the simulation and the analysis of results are part of the development of the present work.