METHOD OF SYNTHESIS OF MODELS OF DEPENDENT DISPERSION CHARACTERISTICS OF FREQUENCY AND COMPOSITION OF OPTICAL FIBER

Abstract

The article is devoted to the development of methods for the synthesis of models of the dependence of the refractive index on several parameters. The problem is solved with respect to the dependence of the refractive index on the frequency and concentration of alloying additives. As the initial dependence, the three-term Selmeyer formula is adopted. It is shown that the optimal model of the desired dependence is the representation in the form of a two-dimensional power polynomial. In this case, the dependence on the concentration of alloying additives is limited to the first degree. Frequency dependence is limited to the third degree. This view allows us to recommend the results obtained for engineering applications. Identification of models is carried out by the method of least squares with a balance of orders. Such a technique makes it possible to improve the conditionality of the corresponding information matrices. Also, a method for decomposing solutions to large-dimensional problems is proposed. This method allows us to reduce the solution of overdetermined systems of linear equations of order MxM to the solution of 2xM systems with M equations in each. The obtained numerical results have a high degree of interpolation accuracy and extrapolation stability. The offered methodology is approved for a next certain case. As alloying addition there is the chosen dioxide of germanium. As empiric data the values of the sought after parameters are got with the use of trinomial formula of Selmeyer. The values of coefficients of formula of Selmeyer are taken from well-known literary sources. Content of dioxide of germanium here changed from 0% to 13,5 %. As a trial selection the values of the interpolated and extrapolated parameters were used for maintenance of dioxide of germanium from 0% to 7,9%. Extrapolation was executed for the concentration of dioxide of germanium of 13,5%. The values of frequency for the construction of all models got out in a range from 175 ТГц to 375 ТГц. It approximately answers the working range of lengths of waves in the systems of transmission from 800 нм to 1700 нм. As dispersible descriptions considered: index of refraction, group index of refraction and group speed. The values of coefficients of two-dimensional models of dependences of these descriptions are got from frequency and concentration of alloying additions of dioxide of germanium.