07. Gladkikh V.A., Vlasenko V.D. Investigation of Field and Energy in a Weakly-Conducting Optical Fiber with an Arbitrary Degree of Refractive Index Profile

DOI: 10.15507/2658-4123.032.202204.588-599

Investigation of Field and Energy in a Weakly-Conducting Optical Fiber with an Arbitrary Degree of Refractive Index Profile

Vyacheslav A. Gladkikh
Senior Researcher, Computer Center of the Far Eastern Branch of the Russian Academy of Sciences (65 Kim Yu Chen St., Khabarovsk 680000, Russian Federation), Cand. Sci. (Phys.-Math.), ORCID: https://orcid.org/0000-0002-3922-9609, Researcher ID: GLU-2712-2022, This email address is being protected from spambots. You need JavaScript enabled to view it.

Victor D. Vlasenko
Academic Secretary, Computer Center of the Far Eastern Branch of the Russian Academy of Sciences (65 Kim Yu Chen St., Khabarovsk 680000, Russian Federation), Cand.Sci. (Phys.- Math.), ORCID: https://orcid.org/0000-0001-7782-4532, Researcher ID: E-2432-2019, This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract
Introduction. We consider a weakly conductive gradient fiber in the single-mode regime and solve the equation for the electric field in the core of this fiber in a general form in the first approximation. The aim of this study is to study the field and energy in the core of a weakly conductive gradient fiber without taking into account the polarization in the single-mode regime in the case of a power-law (generally) refractive index profile.
Materials and Methods. From Maxwell’s equations for dielectric media, there was derived an equation for the field in a fiber with gradient refractive index profile. Making the appropriate substitutions, replacing the zero-order Bessel function with a Gaussian function, and making the necessary approximation of the resulting equation, we arrive at an equation that we solve by the Wentzel – Kramers – Brillouin method and obtain analytical expressions for the field and energy inside waveguide for an arbitrary degree of the refractive index.
Results. There was obtained a solution of the equation for the field in fiber with a powerlaw refractive index profile. Numerical calculations were carried out. A graph of the dependence of a dimensionless quantity – “normalized” energy – on the waveguide parameter for the first five powers of the profile (n = 1, 2, 3, 4, 5) was plotted.
Discussion and Conclusion. It is shown that the energy increases faster for the profile with n = 1, and after this value, the energy for the profile with n = 1 increases sharply, and for n > 1, the energy growth decreases with increasing n. The results obtained in this work can be used for creating an energy-efficient core, for carrying out a possible analysis of information transmission, and for designing waveguides taking into account specific applications.

Keywords: weakly conductive gradient fiber, single-mode regime, power-law refractive index profile, Maxwell equations, WKB method, normalized energy

Acknowledgements: The authors express their gratitude to the anonymous reviewers.

Conflict of interest: The authors declare no conflict of interest.

For citation: Gladkikh V.A., Vlasenko V.D. Investigation of Field and Energy in a Weakly-Conducting Optical Fiber with an Arbitrary Degree of Refractive Index Profile. Engineering Technologies and Systems. 2022;32(4):588‒599. doi: https://doi.org/10.15507/2658-4123.032.202204.588-599

Contribution of the authors:
V. A. Gladkikh – development of the concept and plan of the article, conducting theoretical research, review and analysis of the literature, formulation of conclusions.
V. D. Vlasenko – calculations, analysis of the results, preparation of the text with subsequent revision.

All authors have read and approved the final manuscript.

Submitted 27.06.2022; approved after reviewing 12.09.2022;
accepted for publication 19.10.2022

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