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ACCURATE FINITE ELEMENT ANALYSIS OF POLARIZATION-MAINTAINING OPTICAL FIBERS

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Abstract

Single-mode polarization-maintaining optical fibers that can maintain a state of polarization over a long length play an important role in coherent optical communications [1] and optical fiber sensing systems [2]. These fibers are realized by using axially nonsymmetrical refractive-index distribution [3] or by a nonsymmetrical stress distribution [4] to reduce mode coupling between two orthogonally polarized modes. Eigenmodes of these special fibers cannot be found analytically, they must be determined by approximate methods. So far some numerical techniques have been tried to analyze such fibers among them point-matching method [5], mode-matching method [6] and finite element method [7] can be mentioned. In this paper some polarization-preserving optical fibers are investigated rigorously using an accurate vector H-field finite element method. The finite element method is particularly suitable for the analysis of arbitrarily shaped waveguides hence it is a very flexible analysis tool for fibers with axially nonsymmetrical cross-section or refractive-index distribution. The present finite element formulation is made via a full H-vector field [8], which is particularly suitable for optical waveguides as field continuity is automatically satisfied at dielectric interfaces. By contrast, in the previous Ez/Hz formulation [7] continuity conditions needed to be specifically imposed. The present H formulation is also valid for general anisotropic refractive indices (lossless) without destroying the canonical form of the eigenvalue matrix and this formulation is accurate for the analysis of high-birefringence fibers. A divergence free constraint is imposed by using a penalty technique to eliminate spurious modes. A highly efficient sparse matrix solver has been developed using subspace iteration along with adaptive remeshing techniques to optimize the computer resources. An user-friendly pre- and post-processing package is also used to define a specific waveguide cross-section, and to interpret the results [9].

© 1992 Optical Society of America

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