The Research On Statistical Characteristics Of Polarization Mode Dispersion Based On Jones Transfer Matrix

High-rate fiber communication has become the popular research topic, and fiber optic cables, as well as optical network devices, have been developing fast. With the development of long-haul high bit rate communication system, PMD problem neglected in the past becomes more and more important, which is an important factor limiting transmission distance and capacity. PMD would cause pulse broadened, like other kinds of dispersion. One-order PMD induces differential group delay (DGD) between two principle state of polarization (PSP), which cause the pulse broadened, and even splinted. Second-order PMD seems as six replication pulse, which make the pulse overshoot and side lobe. So as mentioned above, PMD increases the bit error rate, limits the bandwidth of the communication system, and it comes to be one of the main factors to cause system worse. Moreover, PMD is random varying, and easily affected by circumstance, which is hardly compensated.This paper described the transmission matrix, and deduced Jones matrix and its equation. Then established model, and demonstrated the statistical characteristics of polarization mode dispersion (PMD) investigated by Jones transfer matrix method. Simulations are performed in different frequency. It is shown numerically that the results are consistent with the theory when the value of PMD is 25ps. And the values are varying with the frequency, especially the difference up to 2ps in rang of 125GHz. Given the frequency statistics, it is necessary to high-order compensation. In addition, the real fiber parameters are used in numerical simulation, which is more practical and provide the basis for evaluating the system and PMD compensation.And a hybrid method which employs layer-peeling algorithm (LP) and genetic algorithm (GA) is demonstrated to be efficient for the design of multi-channel fiber Bragg gratings. Optimized by genetic algorithm, a set of optimal constant phases are introduced to the phase responses of the multiple channels, which leads to a modified complex reflection spectrum of the multi-channel fiber Bragg grating. Then, the layer-peeling algorithm is applied to extract the grating index profile from the modified spectral response. The simulation results show that this hybrid method reduces the maximum refractive index modulation required for 8 channels to approximate 8 times that for the single channel.