Selection of numerical differentiation method for calculation of group refractive index of air over all calculable wavelengths

The paper considers a group of polynomial models of various characteristics of an optical fiber (OF) depending on the wavelength and chemical composition of the fiber. A method for structural identification of such models is proposed. The following characteristics are considered: the refractive index of the fiber core and cladding, group refractive index, group velocity, dispersion coefficients, numerical aperture, cutoff wavelength of the fundamental mode, etc. An analysis of the well-known Cauchy, Lorentz-Lorenz equations, Sellmeier’s formulas, etc. is given in relation to the problem being solved. The applied method of structural identification provides for the decomposition of a complex computational problem into simpler ones. This technique involves the identification of polynomial models for different samples of a substance. After that, structural identification is performed by the parameter of the additives to quartz glass. The proposed method and models are tested on the example of parameter values: the wavelength range is from 0.8 to 1.8 μm, the type of optical fiber is single-mode, and the refractive index is stepped. For calculations, the tabular values of the coefficients of the Sellmeier formula for SiO2 with GeO2 additions from 0% to 13.5% were used. It is shown that the dependence of the main characteristics of OF on wavelength and chemical composition is modeled with sufficient accuracy by a polynomial model. Indicators of the highest degree on two arguments can be limited to the third degree. The synthesized models have an interpolation and extrapolation error in the considered ranges of the order of 0.001%. This makes it possible to recommend them for scientific and engineering applications, as well as for solving problems of the production of organic matter with predictable characteristics.

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Section: метод структурної ідентифікації моделейunclassified