Probability density functions of the differential group delay in optical fiber communication systems

Fiber communication systems limited by polarization-mode dispersion (PMD) are usually analyzed using statistics. The probability density function (pdf) of the differential group delay (DGD) is then crucial to know. There are cases for which the commonly used Maxwellian pdf is only approximate, e.g., PMD emulators, or systems with components having single components with large deterministic PMD. Those cases are discussed in this paper, and their pdfs are derived. To do this, we present a very general theory that allows for the derivation of the pdf for almost any birefringent transmission line. As a side result, we are able to prove that the square-sum concatenation formula is valid in almost every case of interest, even if the pdf is far from Maxwellian