Single-mode birefringent fibers: An analytical theory

We investigate whether, in a linearly birefringent step-index single-mode fiber, Maxwell\´s equations can be solved rigorously by separation of variables. If the initial assumptions are the same as in an isotropic fiber, then, although many more steps are needed, the final equations are simple and easy to compare with the isotropic case. It is shown that their solutions are never exactly self-consistent. Consequently, the states of polarization of the transverse fields are sensitive to anisotropy, as it had already been proved experimentally. Furthermore, an isotropic fiber "equivalent" to the anisotropic one for what concerns one individual polarization state can be defined only within an uncertainty range comparable to the birefringence.