SIMULATION OF THE REFLECTION SPECTRUM OF A COMBINED FIBER-OPTICAL SENSOR

Abstract

The paper investigates and compares methods for forming the spectral response of a fiber Bragg grating (FBG), based on determining the reflection and transmission coefficients of plane waves through layered structures, followed by solving a system of linear equations for the transmission and reflection coefficients in each layer by the sweep method. Methods based on the construction of transfer matrices for the FBG as a whole, the output of the recording form of which differs or is not complete in a variety of sources, are studied. For a comparative analysis, two dependencies of the reflection coefficient on the wavelength for a homogeneous FBG, as often cited in various publications, are chosen. The dependencies of the FBG reflection coefficients, which are formed on the basis of the transmission matrix, which has Chebyshev polynomials of the second kind in its structure, are excluded from consideration. Modeling options based on recurrence relations, including the need to calculate Chebyshev polynomials, were deliberately excluded from consideration, since they do not benefit in performance compared to the method of transmission and reflection coefficients. A modification of the method of reflection and transmission coefficients has been proposed and studied, which involves modeling FBGs by a layered structure, representing FBGs as a set of "light" and "dark" layers, allows reducing the number of layers of the simulated layered structure to the number of FBG half-periods, and is reduced to successive multiplication of two-dimensional matrices.