An approach to the completeness of normal waves in a waveguide with magnetodielectric filling

Delitsyn, A. L.

doi:10.1007/bf02754228

Cited by 29 publications

(8 citation statements)

References 1 publication

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“…Introduce the following Definition 1.1: If there exist nontrivial functions u e and u m corresponding to some γ ∈ C such that these functions are the solutions (12) for ρ > r, solve system (14) for r 0 ≤ ρ ≤ r, and satisfy conditions (11), then γ is called a characteristic number of the problem.…”

Section: Statement Of the Problemmentioning

confidence: 99%

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Surface waves in an open circular waveguide filled with inhomogeneous chiral media

Smolkin

Smirnov

Shestopalov

2021

Journal of Electromagnetic Waves and Applications

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Propagation of surface waves in a radially inhomogeneous chiral waveguide is considered. The setting is reduced to a boundary eigenvalue problem for the longitudinal components of the electromagnetic field in Sobolev spaces. To find the solution, variational formulation is used. The variational problem is reduced to the analysis of an operator-valued function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operator-valued function on the complex plane is determined. The results of numerical modeling of the spectrum of propagating surface waves in an open chiral waveguide are presented.

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Section: Statement Of the Problemmentioning

confidence: 99%

“…The method of operator pencils has proved to be an efficient technique for the analysis of the wave propagation in open and shielded waveguides. Operator pencils were applied to the analysis of electromagnetic problems in [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Surface waves in an open circular waveguide filled with inhomogeneous chiral media

Smolkin

Smirnov

Shestopalov

2021

Journal of Electromagnetic Waves and Applications

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“…The inverse assertion is true. Choosing u and v with a support in Ω j we have that equations (6) are fulfilled in terms of distributions. The first condition in (7), the first condition in (8), and ( 9) are fulfilled by the definition of spaces H 1 0 (Ω) and ⌢ H 1 (Ω).…”

Section: Statement Of the Problem On Normal Waves In A Waveguidementioning

confidence: 99%

“…Note that the theory of operator pencils is very close to the theory of nonselfadjoint operators [2,9] and allows one to apply powerful methods of the latter. Operator pencils were applied to the analysis of electromagnetic problems in [6,55,27].…”

Section: Introductionmentioning

confidence: 99%

Eigenwaves in Waveguides with Dielectric Inclusions: Spectrum

Smirnov¹,

Shestopalov²

2012

Preprint

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We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue problem for an operator pencil. We formulate the definition of eigenwaves and associated waves using the system of eigenvectors and associated vectors of the pencil and prove that the spectrum of normal waves forms a nonempty set of isolated points localized in a strip with at most finitely many real points.

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“…For a hollow waveguide, this theorem was proved by A. N. Tikhonov and A. A. Samarsky as a consequence of Steklov's theorem, while in the case of a waveguide filled with inhomogeneous medium, one has to use the general Keldysh theorem on the completeness of the system of eigenvectors and adjoined vectors [16], [17], [21]- [23]. At present, the completeness of the system of principal vectors of a waveguide has been proved, however, the question about the possibility to use this system as a basis has already been answered in the affirmative sense only for the case of a circular waveguide, the filling of which depends only on the radius [24], [25].…”

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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An approach to the completeness of normal waves in a waveguide with magnetodielectric filling

Cited by 29 publications

References 1 publication

Surface waves in an open circular waveguide filled with inhomogeneous chiral media

Surface waves in an open circular waveguide filled with inhomogeneous chiral media

Eigenwaves in Waveguides with Dielectric Inclusions: Spectrum

Calculation of the normal modes of closed waveguides

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