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Analytical Approach to Polarization Mode Dispersion in Linearly Spun Fiber with Birefringence 时间:2017-09-05 23:49 来源:未知作者:admin 点击: 次 Abstract:The behavior of Polarization Mode Dispersion (PMD) in spun optical fiber is a topic of great interest in optical networking. Earlier work in this area has focused more on approximate or numerical solutions. In this paper we present analytical results for PMD in spun fibers with triangular spin profile function. It is found that in some parameter ranges the analytical results differ from the approximations.
1. Introduction
The Polarization Mode Dispersion (PMD) is a well-known phenomenon in optical fibers and its role in the propagation of light pulse in various kinds of optical fibers has been a subject of intensive investigation [1–6] in the past. Its physical origin lies in the birefringence property of an optical fiber so that the orthogonal modes of the light electromagnetic wave acquire different propagation speeds resulting in a phase difference between them. The optical fiber at granular level is nonhomogeneous and also has other defects accumulated during the manufacturing process. Due to these issues, the birefringence in a physical fiber becomes random as pointed out by Foschini and Poole in [7]. In addition, Menyuk and Wai [8] have also considered the nonlinear effects arising from higher order susceptibility that also becomes important under certain physical conditions.
Sometime ago, Wang et al. [1] derived expressions for the Differential Group Delay (DGD) of a randomly birefringent fiber in the Fixed Modulus Model (FMM) in which the DGD has both modulus and the phase. The FMM assumes that the modulus of the birefringence vector is a random variable. They presented analytical results with the following assumptions: (i) the spin function is periodic (a sine function) and (ii) the periodicity length () of the fiber is much smaller than the fiber correlation length () or . Later they also generalized the FMM and presented the Random Modulus Model (RMM), which includes the randomness in the direction of the birefringence vector. But then the RMM equations could only be solved numerically.

The present work is a contribution to the analytical calculations within FMM and so is only valid for a short fiber distance. This limitation arises because beyond that distance the birefringence randomness [7] becomes dominant. In the present work the full implications of the FMM have been explored under the following conditions: (i) The approximation has been relaxed, (ii) a nonzero twist has been included, and (iii) the periodic spin rate has been replaced with a constant spin rate. We give the analytical solutions of the exact FMM equations under these conditions and also present some numerical results based on them showing the effect of different physical conditions. The analytical methods are those applicable to the coupled mode theory calculations adapted to the optical fibers [9].

2. Theoretical Analysis
2.1. The Model with Periodic Spin Function
The starting point is the well-known vector equation describing the change in the Jones local electric field vector with the angular frequency and distance along a twisted fiber.