Optical fiber Bragg gratings. Part I. Modeling of infinitely long gratings

We present an accurate numerical method based on the Floquet-Bloch formalism to analyze the propagation properties and the radiation loss in infinitely long uniform fiber Bragg gratings. The model allows us to find all the propagation characteristics including the propagation constants, the space harmonics and the total field distribution, the guided and radiated power, and the modal loss induced by the periodic structure. The influence of the geometrical and physical parameters on the performance of the Bragg gratings has been established. A clear explanation of the physical phenomena related to the index modulation amplitude changes is presented, including the photonic bandgap effect, which is not easily described by the finite-difference time-domain method and cannot be described by the widely used coupled-mode theory.