Numerical Analysis of Asymmetrical-Core Two-Mode Fiber Interferometers Subjected to Bending

Abstract

A finite element formulation for solving the scalar wave equation is described. The proposed formulation leads to an eigenvalue problem defined in terms of positive definite matrices. Therefore, convergence of the two first eigenvectors/eigenvalues to modes LP₀₁ and LP₁, and their correspondent propagation constants is guaranteed. A computer code was written to implement the finite element formulation. The software assembles the matrix eigenvalue problem and solves it either with the sub-space iteration method or the power iteration method. The software also computes the coordinates of the centroid of the modal field distribution of each mode. The finite element model can be used to assess the effects of bending the optical fiber about an arbitrary axis on the guided light. The numerical analysis accounts for the mechanical deformation of the fiber cross section and the variation of the refractive index profile due to all strain components present in pure bending.

A comparison of the analyses of light propagation in the fiber under unstrained and strained conditions enables one to estimate the bend sensitivity of a two-mode fiber interferometer. Numerical results confirm experimental observations that a small asymmetry of the core index profile may lead to a significant bend sensitivity of a two-mode fiber interferometer. The present model was used to assess the influence of several parameters on the bend sensitivity of an asymmetrical core two-mode fiber interferometer. The excellent agreement between the numerical and experimental results indicates that this numerical model is a reliable tool to analyze the effect of bending strains in twomode fiber interferometers.