Science and Education Publishing American Journal of Modeling and Optimization 1 1 2013 05 15 Theoretical Analysis of the Complex Polarization Mode Dispersion Vector in Single Mode Fibers 19 24 EN Hassan Abid Yasser Physics Dept, Science College, Thi-Qar Univ, Iraq Nizar Salim Shnan AJMO2013123 10.12691/ajmo-1-2-3 2013 04 21 2013 05 14 2013 05 15 The presence of polarization mode dispersion (PMD) vector leads to differential group delay (DGD) between the polarization components, while the presence of polarization dependent loss (PDL) vector leads to attenuating one of the components and increases the other by a magnitude determined by PDL value. The study of each phenomenon individually does not give a proper description of the physical nature of the optical fiber system, because these two phenomena arise together at the same time. In this paper, we examine the combined effects of PMD and PDL to generate the random vectors at each section. We are derived a novel relations to explain the complex PMD vector through single section and concatenation sections, which lead to study the DGD and orthogonality of principal states of polarization (PSPs). However, the proposed recursive formulas proved that the PMD vector is complex. The results proved that the real/imaginary part of DGD has a Maxwellian (or Gaussian-Maxwellian)/ distribution and the PSPs vectors may be not orthogonal in presence of PDL.