Birefringence is a term used to describe a phenomenon that occurs in certain types of materials. This phenomenon occurs because these materials have difference indices of refraction, depending on the direction of polarization.
On a circular weakly guiding single mode fiber, the fields of the fundamental mode are rationally invariant about the fiber axis, so that any pair of orthogonal directions can be chosen for its two polarization states that have identical propagation constants.
In this situation, the fundamental mode is said to be degenerate. But this case only occurs in theory. In practical applications the circularity of the fiber is disturbed for example by temperature differences in the fiber or bending etc… In general, the stress-induced birefringence dominates the geometry-induced one.
In the case of a non-circular fiber, such as the elliptical core fiber shown in Figur 4.2, the fundamental mode is no longer degenerate.
Working within the weak guidance approximation, the two polarization directions of the planar transverse electric field are parallel to one of the optical axes of the fiber. This approximation means that the guiding material is homogeneous, isotropic, and the fundamental mode is split into two orthogonally polarized stated aligned in directions determined by the fiber´s symmetry conditions.