Mathematical model of optical information channels

DOI: 10.31673/2412-4338.2020.019999

Abstract

An analysis is made of the functioning of the telecommunications network of the forensic information system. It is determined that the use of fully optical technologies will allow fulfilling the requirements for the quality of service of the telecommunication network of the system. As a result of the analysis, it was found that during the propagation of an optical signal in communication channels, the main problems arise due to the nonlinear nature of this propagation and the heterogeneity of the propagation medium. Therefore, the problem arises of providing control over the state of information transfer at the physical level in optical communication channels. To solve this complex and multifaceted problem, the article carried out mathematical modeling of the process of transmitting optical signals based on the study of spatio-temporal and spatio-frequency correlations of the electromagnetic field of an optical wave. To describe the process of information transfer in an inhomogeneous nonlinear medium, it was proposed to use the formalism of Feyman path integrals (PI). The article formulates the distribution problem and defines the main restrictions for the parameters used. All analytical relations will be obtained under conditions of small perturbations of the field and propagation medium, as well as in conditions of approximation of the Markov process. Based on the described limitations, a solution to the parabolic wave equation using the Feyman PI was presented. In the process of solving, relations were obtained for the statistical moments of the complex amplitude through the moments of the Green's function. Further studies were devoted to obtaining analytical expressions for the mean field of a point source. To do this, the operation of averaging the Green's function of the field of a point source was carried out. As a result, for the case of homogeneous fluctuations of the magnetic field, an expression was obtained that describes the exponential decay of the coherent component of the wave field in a randomly inhomogeneous medium, including the optical channel for transmitting information. Thus, a theoretical possibility arose of creating a mathematical model of optical information transmission channels based on the use of the PI formalism.

Keywords: telecommunication network, forensic information system, optical communication channel, mathematical model, path integral, parabolic wave equation.

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