KEYWORDS: 3D modeling, Fiber Bragg gratings, Finite element methods, Birefringence, Manufacturing, Optical fibers, Refractive index, 3D metrology, Temperature metrology, Cladding
A 3D-FEM model has been developed to improve the understanding of multi-parameter sensing with Bragg gratings in attached or embedded polarization maintaining fibers. The material properties of the fiber, especially Young's modulus and Poisson's ratio of the fiber's stress applying parts, are crucial for accurate simulations, but are usually not provided by the manufacturers. A methodology is presented to determine the unknown parameters by using experimental characterizations of the fiber and iterative FEM simulations. The resulting 3D-Model is capable of describing the change in birefringence of the free fiber when exposed to longitudinal strain. In future studies the 3D-FEM model will be employed to study the interaction of PANDA fibers with the surrounding materials in which they are embedded.
A 3D FEM model of an FBG in a PANDA fiber with an extended fiber length of 25.4 mm is presented. Simulating long fiber lengths with limited computer power is achieved by using an iterative solver and by optimizing the FEM mesh. For verification purposes, the model is adapted to a configuration with transversal loads on the fiber. The 3D FEM model results correspond with experimental data and with the results of an additional 2D FEM plain strain model. In further studies, this 3D model shall be applied to more sophisticated situations, for example to study the temperature dependence of surface-glued or embedded FBGs in PANDA fibers that are used for strain-temperature decoupling.
The linear matrix approach is the common method for multi-parameter FBG-based strain and temperature sensing. As it
does not include non-linear temperature responses and hence lacks accuracy, the application of an iterative matrix
inversion technique can be used to remedy this deficiency. Employing this method in a set-up using a multi-parameter
sensor system that consists of two FBGs in fibers, which differ in cladding diameters, significantly reduced temperature
uncertainties of ± 1°C could be achieved within a temperature range between -20°C and 150°C.
Glue-induced stresses decrease the accuracy of surface-mounted fiber Bragg gratings (FBG). Significant temperature dependent glue-induced birefringence was verified when a thermally cured epoxy-based bonding technique had been used. Determining the peak separation of two azimuthally aligned FBGs in PM fibers combined with a polarization resolved measurement set-up in a temperature range between -30°C and 150°C revealed high glue-induced stresses at low temperatures. Peak separations of about 60 pm and a nonlinear temperature dependence of the glue-induced birefringence due to stress relaxation processes and a visco-elastic behavior of the used adhesive have been shown.
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