Linear transformation of polarization modes in coiled optical spun fibers. III. Approximate analytic presentation

We have obtained approximate analytical dependences of the integrated values of effective elliptic birefringence of eigenpolarization modes on the length of coiled spun optical fibers by using approximations of numerical simulation. The dependence of the integrated elliptic birefringence of the polarization eigenmodes on the length of these optical fibers very quickly reaches its limiting value. This dependence also has a complex periodic structure including two substantially different spatial periods. The shape of the considered dependences is determined by the lengths of the polarization beats of the initial linear birefringence of the spun fiber, unperturbed by coiling, and circular birefringence due to torsion of the spun fiber.