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Author Dmitriy, Divakov ♦ Anastasiia, Tiutiunnik ♦ Anton, Sevastianov
Source Directory of Open Access Journals (DOAJ)
Content type Text
Publisher EDP Sciences
File Format PDF
Date Created 2018-08-13
Copyright Year ©2018
Language English ♦ French
Subject Domain (in LCC) TA1-2040
Subject Keyword Engineering (General) ♦ Technology ♦ Civil engineering (General)
Abstract In this paper the algorithm of finding eigenvalues and eigenfunctions for the leaky modes in a three-layer planar dielectric waveguide is considered. The problem on the eigenmodes of open three-layer waveguides is formulated as the Sturm-Liouville problem with the corresponding boundary and asymptotic conditions. In the case of guided and radiation modes of open waveguides, the Sturm-Liouville problem is formulated for self-adjoint second-order operators on the axis and the corresponding eigenvalues are real quantities for dielectric media. The search for eigenvalues and eigenfunctions corresponding to the leaky modes involves a number of difficulties: the boundary conditions for the leaky modes are not self-adjoint, so that the eigenvalues can turn out to be complex quantities. The problem of finding eigenvalues and eigenfunctions will be associated with finding the complex roots of the nonlinear dispersion equation. In the present paper, an original scheme based on the method of finding the minimum of a function of several variables is used to find the eigenvalues. The paper describes the algorithm for searching for eigenvalues, the algorithm uses both symbolic transformations and numerical calculations. On the basis of the developed algorithm, the dispersion relation for the weakly flowing mode of a three-layer open waveguide was calculated in the Maple computer algebra system.
ISSN 2261236X
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 2018-01-01
e-ISSN 2261236X
Journal MATEC Web of Conferences
Volume Number 186
Starting Page 01009


Source: Directory of Open Access Journals (DOAJ)