Perturbation Model for Computing Optical-Fiber Birefringence from a 2-D Refractive Index Profile

In a cylindrically symmetric optical fiber the vector modes are twofold degenerate. Two orthogonally polarized modes have the same propagation constant. Any deviation from perfect azimuthal symmetry would remove the polarization degeneracy, introducing birefringence. For a weakly- guiding fiber scalar perturbation theory have been used successfully to investigate birefringence caused by an elliptic deformation [1-4]. A vector correction to the scalar modes, i.e., a second order perturbation theory, is necessary to compute the birefringence. For an arbitrary 2-D profile these computations are complicated. However, if we start with the vector modes of a radially varying but azimuthally symmetric fiber and then treat the azimuthal variation as a perturbation to the vector modes, only first order perturbation suffice. Here we present a perturbation model based on the above idea. We closely follow the derivation of Ref. [4]. The formulation is applicable to planar waveguides once the vector modes are known.