Physics of Wave Processes and Radio SystemsPhysics of Wave Processes and Radio Systems1810-31892782-294XPovolzhskiy State University of Telecommunications and Informatics1065610.18469/1810-3189.2022.25.3.73-81Research ArticleThe calculation of a two-cascade long-period fiber grating of the refractive indexBudaraginRoman V.<p>Doctor of Technical Sciences, Head of the Department of General and Nuclear Physics</p>rbudaragin@mail.ruKurzenkovMikhail I.<p>Postgraduate of the Department of General and Nuclear Physics</p>cheetah10@mail.ruRadionovAleksandr A.<p>Doctor of Technical Sciences, Professor of the Department of General and Nuclear Physics</p>radionow.aleck@yandex.ruSalasenkoZinaida Yu.<p>Undergraduate of the Department of Physics and Technology of Optical Communication</p>zina.salasenko@mail.ruhttps://orcid.org/0000-0003-3609-2632Nizhny Novgorod State Technical University named after R.E. Alekseev29092022253738129092022Copyright © 2022, Budaragin R.V., Kurzenkov M.I., Radionov A.A., Salasenko Z.Y.2022<p>A method is proposed for calculating the spectral characteristics of cascade long-period fiber gratings of the refractive index of the core based on the method of partial regions and decomposition. According to the method, the structure is represented as a cascade connection of basic inhomogeneities, each of which is a junction of several optical fibers with different dielectric and geometric parameters. Approbation of the method was carried out by reducing the structure to a single long-period fiber grating and comparing the results with the results obtained using other calculation methods. The results matched graphical accuracy. The advantage of the method is the possibility to theoretically study the effect of dielectric and geometric parameters on the spectral properties of the structure, as well as significantly save time resources. The transmission spectra of gratings with different parameters of period <em>T</em>, grating length <em>L</em>, and distance between gratings <em>L<sub>f</sub></em> are presented.</p>метод частичных областейметод декомпозициидлиннопериодные волоконные решеткиволоконный световодcross-section methoddecomposition methodlong-period gratingsfiber light guide[Vasil'ev S.A. et al. Refractive index fiber gratings and their applications. Kvantovaya elektronika, 2005, vol. 35, no. 12, pp. 1085–1103. URL: http://mi.mathnet.ru/qe13041 (In Russ.)][Berintsev A.V. et al. Investigation of the transmission spectra of long-period fiber gratings under the influence of high temperatures. Izvestiya Samarskogo nauchnogo tsentra Rossiyskoy akademii nauk. Fizika i elektronika, 2012, vol. 14, no. 4, pp. 1081–1085. (In Russ.)][Butov O.V. et al. All-fiber high-sensitivity bend sensor for the nuclear industry. Foton-ekspress, 2019, no. 6, pp. 26–27. (In Russ.)][Vengsarkar A.M. et al. Long-period fiber gratings as band rejection filters. Journal of Lightwave Technology, 1996, vol. 14, no. 1, pp. 58–65. DOI: https://doi.org/10.1109/50.476137][Budaragin R.V., Raevskiy A.S. Electrodynamic calculation of long-period fiber gratings. Physics of Wave Processes and Radio Systems, 2012, vol. 15, no. 2, pp. 42–48. (In Russ.)][Ibragimov D.N., Turchak E.E. On one decomposition method in the time-optimal problem for a linear discrete system with bounded control. Modelirovanie i analiz dannykh, 2019, vol. 9, no. 4, pp. 157–161. DOI: https://doi.org/10.17759/mda.2019090413 (In Russ.)][Nikol'skiy V.V., Nikol'skaya T.I. Decomposition Approach to Problems of Electrodynamics. Moscow: Nauka, 1983, 304 p. (In Russ.)][Budaragin R.V., Salasenko Z.Yu., Kurzenkov M.I. Electrodynamic calculation of basic inhomogeneities based on optical fibers in the design of sensors for the nuclear industry. Vysokie tekhnologii atomnoy otrasli. Molodezh' v innovatsionnom protsesse: sb. materialov XV nauchno-tekhnicheskoy konferentsii molodykh spetsialistov Rosatoma. Sarov: FGUP «RFYaTs-VNIIEF», 2021, pp. 178–182. (In Russ.)][Budaragin R.V. On the method for calculating the problem of diffraction by a dielectric inhomogeneity in a shielded waveguide by the method of partial regions. Antenny, 2016, no. 2 (227), pp. 83–90. (In Russ.)][Chen S. et al. Tunable multiband optical filter based on series-connected long-period fiber gratings. Pis'ma v ZhTF, 2005, vol. 31, no. 5, pp. 76–83. URL: http://journals.ioffe.ru/articles/viewPDF/11510 (In Russ.)]