Autocorrelation Function of the Principal State of Polarization Vector for Systems Having PMD

Abstract

Abstract-The autocorrelation function (ACF) for the principal state of polarization (PSP) vector is reported. It is shown that the PSP vector ACF and the magnitude of the polarization-mode dispersion vector, i.e., the differential group delay (DGD) ACF are not independent. The PSP vector correlation bandwidth is verified to be narrower than that of the DGD.Index Terms-Autocorrelation function (ACF), polarization-mode dispersion (PMD), principal state of polarization (PSP).single-mode fibers (SMFs) severely limits a communication system at speeds greater than 10 Gb/s. The PMD vector of an SMF can be described by its principal state of polarization (PSP) vector [1] in the Stokes space whose magnitude describes the differential group delay (DGD). The frequency dependence of the PSP vector can cause the reduction of the degree of polarization for an optical pulse and the distortion of its pulse shape ; for example, its magnitude (i.e., DGD) satisfies the Maxwellian probability density function for a highly mode-coupled SMF [4]. Its autocorrelation functions (ACFs) have also been studied [6]. In this letter, we present an analytical result confirming that the dealignment of the PSP vector is more significant than the mismatch of the PMD magnitude (i.e., DGD) between neighboring frequencies. We also show that the PSP vector ACF and DGD ACF are not independent. Furthermore, we will present the frequency correlation bandwidths for different ACFs which are needed to accurately measure the mean DGD.We follow the same mathematical procedure introduced by Karlsson and Brentel [6]. Here, we treat an SMF as having segments of polarization-maintaining fibers (PMFs), and each segment has a constant birefringence axis, described in Stokes space by unit vector , and a retardation . The Muller matrix of a single section can be written by the use of the matrix exponential:. The PMD vector of the first fiber segments can be obtained from the Gisin-Pellaux recursion relation where the average is done over . In the limit of highly modecoupled SMF, they obtained the following analytical result:where . This result cannot be trivially separated into the ACF of the PSP vector and the ACF of its corresponding magnitude ; instead, it can be treated as an approximation for the ACF of PSP vector within 15% [6], [7] when one divides (2) by . Our strategy to find the PSP vector ACF involves calculating two quantities: and . The second autocorrelation has been also reported [7], and it is (3)Following Karlsson and Brentel, we assume each fiber segment has the same DGD value except their direction can be pointing anywhere on the Poincaré sphere. The DGD value is related to the retardation by . Now we can have the following:Now averaging over the solid angle for the square of the last expression, we get the following expression: (5) where , , and . To proceed, we use the recursion relation derived by Karlsson and Brentel:

Simulating temporal evolution of PMD‐related variables in optical fibers and emulators

“…We also note that PSP uncorrelated faster than the DGD for neighboring channels, particularly for small PMD values, because PSP is a bi-dimensional variable, while DGD is a onedimensional variable. This result agrees with analytical calculations by Hadjifaradji et al [17].…”

Spectral correlations of pmd variables in optical fibers

“…This effect is explained because PSP is a bi-dimensional variable, while DGD is a one-dimensional variable. This result is in agreement with analytical calculations by Hadjifaradji et al [6]. …”

Time domain PMD simulations in optical fibers and emulators

“…This effect is explained because PSP is a bi-dimensional variable, while DGD is a one-dimensional variable. This result agrees with analytical calculations by Hadjifaradji et al [8]. We now compare simulated and experimental results for the SOP and detected RF signal statistics.…”