In this work we develop a theoretical model to analyze the response of a two coupled-cavities fiber laser. This
setup operates as an additive pulse mode-locking (APM) laser and its design is based on the combined action
of an active cavity and a passive cavity. The first one is generated with an erbium-doped fiber and two fiber
Bragg gratings (FBGs) as reflective components, while the passive cavity is built with a fiber pigtail being the
corresponding mirrors one of the FBGs and the Fresnel reflection at the fiber end. It is proposed a numerical
model that solves the Non-Linear Schr¨odinger Equation (NLSE) by using the Split-Step Method (SSM) together
with the T-Matrix Method (TMM) to calculate the coupling factor on each reflective component. The main
parameters are: the group velocity dispersion (GVD), the self-phase modulation (SPM), the gain and/or loss
factors of the fibers including self-saturation effect and the reflectivity and dispersion characteristics of each
FBG. The dependence of both, temporal and frequency behaviour of the generated emission with the several
involved setup parameters are analyzed. The numerical results produced by applying the theoretical model are
compared with previously obtained experimental results, and a good agreement between them is observed.
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