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The distortions of pulse signal, arising under action of linear and nonlinear birefringence in fiber-optical lines


A.H. Sultanov, I.L. Vinogradova, Sh.B. Yanyshev

Is shown, that the increasing of networks throughput is impossible without application high-speed TDM with speeds more than 10 GB/sec. But on such speeds already essentially begin to have an effect such factors, as chromatic and polarizing mode dispersion (CD and PMD). And if up to the specified speed CD and PMD brought in distortions, but could not result to stop in work of networks, for high-speed perspective networks the specified effects owe it necessary be taken into account with designing, and also the development of measures under their control and indemnification is necessary. If CD is the quite determined size and nowadays can be rather successfully compensate, PMD displays rather complex influence on a signal and much more difficult gives in of indemnification. The existing PMD model is based on representation of the following factors: PDL, dPMD and dPMD2, with which application is possible to calculate an additional losses level and increase of a pulse duration. Last, in particular, is measured by the majority of the network analyzers, submitted in sale. But the practice of operation shows, that the PMD action on a pulse signal is displayed more difficultly, than is submitted as such «technical» model. In particular, these factors should be spectra depended, and, besides there is an additional distortion, caused on a pulse duration, and, apparently, on its form. However within the framework of existing model quantitatively to estimate the specified distortion, which in a number of cases can appear rather significant, it is not obviously possible. In this connection the mathematical model of the form pulse change dynamics extending in fiber, under action of birefringence effect is developed. The model is under construction on the basis of simplification of the equations of electrodynamics (with reception of the unique equation of a rather peak component of a field) and further - splitting of the specified equation into orthogonal polarizing components. Is shown, that in a linear case without attenuation the system of the equations has the analytical decision, with which use (form,) bending around to optical capacity, of a pulse on an output a fiber line is received. The graphic dependences for specified bending around in absence are received and with presence of an entrance pulse chirp. Is established, that the pulse really is exposed to expansion in temporary area, but besides there is its displacement. The numerical decision of the received equations for two cases is executed: presence selective to a condition of polarization of attenuation, and for a case of nonlinear interaction of an orthogonal peak component. Is established, that the selective attenuation results in essential change of the form of a pulse, in particular, to occurrence of its multipeak structure. In a nonlinear case the distortion of the form amplifies, but a little displacement of a pulse decreases. Thus the general character of its form comes nearer to triangular and there is some asymmetry of fronts. Last in a greater degree has an effect for amplitude of peaks, than on duration of fronts. The considered nonlinear effect has some similarity to effect of phase cross-modulation (CM) two in passing of extending waves. But as against CM, the behavior of one (unique) mode with factor, inherent in it, of distribution is investigated, which division on a part and the interaction of these parts is connected to selectivity of properties of a material to condition of polarization of radiation. In a number of the known references the given effect is treated as nonlinear двулучепреломление. It is necessary to notice, that the used today PMD model does not take into account display of the specified effect, though, according to specify of modern networks, do not influence of nonlinear effects (for example, of four wave mixing) is practically obligatory condition of a substantiation of their serviceability. Certainly, the fiber birefringence, used in telecommunications, and its PMD, has stochastic character, that results in «mixing» factors, participating in model. Therefore, accordingly, decreasing also weaken distortions, about which there was a speech above. But the submitted model allows even in general to investigate process of change of the form of a pulse in a considered task and to offer a set of «technical» factors more full describing kinds of its distortions. So for a quantitative estimation of distortions connected to polarizing effects, it is offered to enter the following factors (except dPMD and PDL): a displacement factor, describing a deviation in time of a pulse centre; a harmonics factor describing the relation of total harmonics intensity to entrance peak intensity of a pulse; and factor of fronts asymmetry describing a degree of difference of their duration. All these factors, obviously, are spectra depended and depended from an entrance pulse parameters

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