On the Representation of Electromagnetic Fields in Discontinuously Filled Closed Waveguides by Means of Continuous Potentials

Malykh, M. D.; Sevastyanov, L. A.

doi:10.1134/s0965542519020118

Cited by 4 publications

(8 citation statements)

References 7 publications

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“…Assume for brevity that According to theorem 2 in [31], the transverse components of such field can be always presented in terms of four scalar potentials in the following form…”

Section: Methods Of Four Potentialsmentioning

confidence: 99%

“…Here and below for the Laplace operator div( ∇ ) we use the notation Δ . The existence of at least generalised solutions of the Dirichlet problems is apparent, for the Neumann problems we have checked the fulfilment of the conditions for the existence of a solution [31]. For simplicity, let us assume that these solutions are classical, which can be proved under certain additional assumptions of the smoothness of boundary and the considered fields based on the Weyl lemma [34].…”

Section: Methods Of Four Potentialsmentioning

confidence: 99%

“…It should be emphasized that, due to condition 2, the components of electromagnetic fields suffer discontinuities at the interfaces, and the factors in the formulas (6) are specially selected in [31] so that the potentials are smooth functions. In fact, Eq.…”

Section: Remarkmentioning

confidence: 99%

“…Note that any field of the form (6) satisfies theorem 1 of [31] at the interface between media, therefore, the appropriate conditions are automatically fulfilled below.…”

Section: Remarkmentioning

confidence: 99%

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

Section: Introductionmentioning

confidence: 99%

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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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“…Assume for brevity that According to theorem 2 in [31], the transverse components of such field can be always presented in terms of four scalar potentials in the following form…”

Section: Methods Of Four Potentialsmentioning

confidence: 99%

Section: Methods Of Four Potentialsmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

“…Note that any field of the form (6) satisfies theorem 1 of [31] at the interface between media, therefore, the appropriate conditions are automatically fulfilled below.…”

Section: Remarkmentioning

confidence: 99%

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

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Calculation of the normal modes of closed waveguides

Malykh

Divakov

Egorov

et al. 2020

Discrete and Continuous Models

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On Normal Modes of a Waveguide

Kroytor

Malykh

Sevastyanov

2022

Comput. Math. and Math. Phys.

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Normal modes of a waveguide as eigenvectors of a self-adjoint operator pencil

Malykh

2021

Discrete and Continuous Models

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A waveguide with a constant, simply connected section S is considered under the condition that the substance filling the waveguide is characterized by permittivity and permeability that vary smoothly over the section S, but are constant along the waveguide axis. Ideal conductivity conditions are assumed on the walls of the waveguide. On the basis of the previously found representation of the electromagnetic field in such a waveguide using 4 scalar functions, namely, two electric and two magnetic potentials, Maxwells equations are rewritten with respect to the potentials and longitudinal components of the field. It appears possible to exclude potentials from this system and arrive at a pair of integro-differential equations for longitudinal components alone that split into two uncoupled wave equations in the optically homogeneous case. In an optically inhomogeneous case, this approach reduces the problem of finding the normal modes of a waveguide to studying the spectrum of a quadratic self-adjoint operator pencil.

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On the Representation of Electromagnetic Fields in Discontinuously Filled Closed Waveguides by Means of Continuous Potentials

Cited by 4 publications

References 7 publications

Calculation of the normal modes of closed waveguides

Calculation of the normal modes of closed waveguides

On Normal Modes of a Waveguide

Normal modes of a waveguide as eigenvectors of a self-adjoint operator pencil

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