The presence of (first and second orders) polarization mode dispersion (PMD), chromatic dispersion, and initial chirp makes effects on the propagated pulses in single mode fiber. Nowadays, there is not an accurate mathematical formula that describes the pulse shape in the presence of these effects. In this work, a theoretical study is introduced to derive a generalized formula. This formula is exactly approached to mathematical relations used in their special cases. The presence of second-order PMD (SOPMD) will not affect the orthogonality property between the principal states of polarization. The simulation results explain that the interaction of the SOPMD components with the conventional effects (chromatic dispersion and chirp) will cause a broadening/narrowing and shape distortion. This changes depend on the specified values of SOPMD components as well as the present conventional parameters. 1. Introduction As a pulse propagates through a light-wave transmission system with a polarization mode dispersion (PMD), the pulse is spilt into a fast and slow one and therefore becomes broadened. This kind of PMD is commonly known as first-order PMD (FOPMD). Under FOPMD, a pulse at the input of a fiber can be decomposed into two pulses with orthogonal states of polarization (SOP). Both pulses will arrive at the output of the fiber undistorted and polarized along different SOPs, the output SOPs being orthogonal [1]. Both the PSPs and the differential group delay (DGD) are assumed to be frequency independent when only first-order PMD is being considered [2]. PMD also has higher-order components. Second-order PMD (SOPMD) is formed due to dependence of DGD on wavelength, because of that PMD is random variable. Statistical nature of PMD makes compensation very difficult [3]. Statistical properties of first- and second-order PMD have been reported in [4–6]. In these approaches, mean DGD plays a central role. Further, analytical calculations of pulse broadening and PMD compensation have also been reported [7, 8]. However, these analytical results make use of autocorrelation of the PMD vector [4]. Also, it is shown that FOPMD and SOPMD vectors are statistically dependent and tend to be mutually perpendicular. It is important to calculate the probability that a certain value of SOPMD happens, when the value of DGD is known in a transmission line [8, 9]. The frequency dependence of the DGD causes polarization-dependent chromatic dispersion (PCD), resulting in polarization-dependent pulse compression and broadening. While PCD is a simple mechanism, it is a relatively
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