On the representation of electromagnetic fields in closed waveguides using four scalar potentials

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.

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“…Applying the separation of variables method, we obtain the equation for the transverse and longitudinal parts [4][5][6][7][8][9]   2 2 2 2 0 0…”

Section: Introductionmentioning

confidence: 99%

Symbolic-Numeric Computation of the Eigenvalues and Eigenfunctions of the Leaky Modes in a Regular Homogeneous Open Waveguide

2018

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“…As the 2nd step, the standard approach suggests using the Krylov Subspace Methods [11], but in modern computer algebra system Sage [12] we may work over the field of algebraic numbers without any numerical errors. This approach to computing eigenmodes was tested on several waveguides [13]. Our computing experiments have shown that in such a way we can calculate all the running modes (that is, modes with real eigenvalues β) and the small locked modes with correct multiplicities.…”

Section: Normal Modes Of a Waveguidementioning

confidence: 99%

Diffraction of Electromagnetic Waves on a Waveguide Joint

et al. 2018

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Abstract. In general, the investigation of the electromagnetic field in an inhomogeneous waveguide doesn't reduce to the study of two independent boundary value problems for the Helmholtz equation. We show how to rewrite the Helmholtz equations in the "Hamiltonian form" to express the connection between these two problems explicitly. The problem of finding monochromatic waves in an arbitrary waveguide is reduced to an infinite system of ordinary differential equations in a properly constructed Hilbert space. The calculations are performed in the computer algebra system Sage.

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“…In our works [30], [31], a previously unknown representation of electromagnetic fields in a waveguide using four potentials was proposed.…”

Section: Introductionmentioning

confidence: 99%

“…But even in the case when the permittivity and permeability are described by discontinuous functions, they turn out to be quite smooth functions. The Maple system has developed a symbolic-numerical method for finding normal modes based on a combination of this representation of the field and the incomplete Galerkin method [30], [32], [33]. Comparison of the calculation results with the results obtained using the mixed finite element method was significantly complicated by the lack of a public version of the finite element implementation.…”

Section: Introductionmentioning

confidence: 99%

Calculation of the normal modes of closed waveguides

Malykh

Divakov

Egorov

et al. 2020

Discrete and Continuous Models

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The aim of the work is the development of numerical methods for solving waveguiding problems of the theory of waveguides, as well as their implementation in the form of software packages focused on a wide range of practical problems from the classical issues of microwave transmission to the design of optical waveguides and sensors. At the same time, we strive for ease of implementation of the developed methods in computer algebra systems (Maple, Sage) or in software oriented to the finite element method (FreeFem++). The work uses the representation of electromagnetic fields in a waveguide using four potentials. These potentials do not reduce the number of sought functions, but even in the case when the dielectric permittivity and magnetic permeability are described by discontinuous functions, they turn out to be quite smooth functions. A simple check of the operability of programs by calculating the normal modes of a hollow waveguide is made. It is shown that the relative error in the calculation of the first 10 normal modes does not exceed 4%. These results indicate the efficiency of the method proposed in this article.

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On the representation of electromagnetic fields in closed waveguides using four scalar potentials

Cited by 15 publications

References 34 publications

Symbolic-Numeric Computation of the Eigenvalues and Eigenfunctions of the Leaky Modes in a Regular Homogeneous Open Waveguide

Symbolic-Numeric Computation of the Eigenvalues and Eigenfunctions of the Leaky Modes in a Regular Homogeneous Open Waveguide

Diffraction of Electromagnetic Waves on a Waveguide Joint

Calculation of the normal modes of closed waveguides

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