Calculation of the mean differential group delay of periodically spun, randomly birefringent fibers

Abstract

Spinning is one of the most effective and well-known ways to reduce polarization mode dispersion of optical fibers. In spite of the popularity of spinning, a detailed theory of spin effects is still lacking. We report an analytical expression for the mean differential group delay of a randomly birefringent spun fiber. The result holds for any periodic spin function with a period shorter than the fiber's beat length.

An analytical formula for the mean differential group delay of randomly birefringent spun fibers

“…If the spin function belongs to one of these two classes, then, exploiting the symmetry properties of , we show in Appendix C that . So that , notwithstanding that, in this case, is still given by (10).…”

“…In a recent paper [10], we provided, without proof, a formula [(9) in this paper] for the calculation of the mean differential group delay (DGD) of a periodically spun fiber. In this paper, we report the complete demonstration of this formula, which is obtained assuming that the spin period is short compared with the fiber beat length and also that the strength of the birefringence is constant, while its orientation is random and the fiber correlation length for the random orientations can have any value.…”

“…From (18), it follows that we must determine the average over a period of , which can be calculated from (23) and (24), to yield with and being defined as in (10). By means of some algebra that we defer to Appendix B, we find that (25) so that the average over a period of is Then, owing to (18), we obtain…”

“…APPENDIX C SIMPLIFICATION OF (10) In some cases, the integrals (10) can be simplified. The first case that we consider is when so that for all , and ; this case was considered also by Chen et al [17] using secular perturbation theory.…”

Analytical treatment of randomly birefringent periodically spun fibers

“…In recent papers, spun fibers have been studied in special limits, where the analysis can be simplified. In [7] and [8], the case of a short spin period compared with the beat length was considered ( ). In [7], [9], and [10], the fiber birefringence was assumed to be deterministic, corresponding to .…”