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A study and modeling of non-cumulative attenuation in coiled optical fiber with small radii of curvature
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Recently, the usage of optical fiber coils has increased significantly, especially in the design of physics and chemical sensors. Therefore, it is important to test the theoretical current models developed to predict the power loss throughout an optical fiber coiled bent. In this paper, a pioneer and popular model, the Marcuse model of power loss and a model derived from this, the Schermer and Cole model, were studied and evaluated for optical fiber coils of small radii. Power attenuation in a bent fiber data was collected using an optical time domain reflectometer (OTDR), and they were compared to the theoretical predictions of the Marcuse model and Schermer and Cole model. It was observed that the models predicted correctly the attenuation behavior for usual curvature radii, however, these failed to predict accurately the attenuation behavior for small curvature radii, underestimating considerably the actual power loss. The main factor that Marcuse’s model (coefficient of power loss 2α) fails to predict the behavior of the attenuation when the fiber is bent at small radii of curvature is because we consider the parameter β (mode propagation of the wave guide) as a constant. Schermer and Cole [16] made clarifying remarks about the propagation constant β, but even so its model does not predict correctly the behavior of the attenuation when the fiber is bent in small radii of curvature. When the fiber is bent at small radii of curvature, it is possible that new mechanisms of light leaking are present, due to the extreme distortion of the mode configuration. In this paper, we propose a new model function of the optical path, where the parameter β is not constant, but it depends on the number of loops and the radii of curvature. Theoretical behavior of this model correctly predicts the behavior of the experimental data of attenuation. The terms of this model are based in the form (a b), thus correspond exponential behavior of basis (a b), that have the modes LP.
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