Telegraphist's Equations for Rectangular Waveguides and Analysis in Nonorthogonal Coordinates

Dusséaux, Richard; Faure, Claire

doi:10.2528/pier08101707

Cited by 8 publications

(5 citation statements)

References 18 publications

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“…In order to keep the presentation as simple as possible without essential loss of generality, we shall proceed by considering the Sturm-Liouville problem (2.3) with Q = 0. 6 On physical grounds, this problem will be referred to as the water-wave reference waveguide. For any x, the eigenvalues k n = k n (η, h) = k n (H), n ≥ 0 (also called local wave numbers) are given as the roots of the transcendental equations…”

Section: The X-derivatives Of the Vertical Eigensystemmentioning

confidence: 99%

“…The origin of the CMT goes back to early 1950 s, first appearing in connection with electromagnetic [2] and acoustic [3] waveguides of varying cross sections (horns). Since then, the CMT has been applied to the study of almost all types of elongated waveguides 2 : microwave and optical waveguides (sometimes under the name generalized telegraphist's equations) [4][5][6]; duct acoustics (horns) [7][8][9]; duct acoustics with mean flow [10]; elastic waveguides [11][12][13]; hydroacoustics [1,Sec. 7.1], [14][15][16][17]; seismology and geophysics [18,19]; water waves [20][21][22][23][24][25][26][27][28][29][30][31]; hydroelasticity [26].…”

Section: Introductionmentioning

confidence: 99%

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Exact semi-separation of variables in waveguides with non-planar boundaries

Athanassoulis

Papoutsellis

2017

Proc. R. Soc. A.

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Series expansions of unknown fields n n Z ϕ Φ = å in elongated waveguides are commonly used in acoustics, optics, geophysics, water waves and other applications, in the context of coupled-mode theories (CMTs). The transverse functions n Z are determined by solving localSturm-Liouville problems (reference waveguides). In most cases, the boundary conditions assigned to n Z cannot be compatible with the physical boundary conditions of Φ , leading to slowly convergent series, and rendering CMTs mild-slope approximations. In the present paper, the heuristic approach introduced in (Athanassoulis & Belibassakis 1999 J. Fluid Mech. 389, 275-301) is generalized and justified. It is proved that an appropriately enhanced series expansion becomes an exact, rapidly-convergent representation of the field Φ , valid for any smooth, nonplanar boundaries and any smooth enough Φ . This series expansion can be differentiated termwise everywhere in the domain, including the boundaries, implementing an exact semi-separation of variables for non-separable domains. The efficiency of the method is illustrated by solving a boundary value problem for the Laplace equation, and computing the corresponding Dirichlet-to-Neumann operator, involved in Hamiltonian equations for nonlinear water waves. The present method provides accurate results with only a few modes for quite general domains. Extensions to general waveguides are also discussed.

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Section: The X-derivatives Of the Vertical Eigensystemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact semi-separation of variables in waveguides with non-planar boundaries

Athanassoulis

Papoutsellis

2017

Proc. R. Soc. A.

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“…A number of papers consider the propagation of electromagnetic waves in an inhomogeneous coaxial waveguide [1][2][3][4][5][6]. In [1], the analysis of inhomogeneities in a coaxial waveguide was carried out on the basis of telegraph equations.…”

Section: Introductionmentioning

confidence: 99%

Application of the method of integral equation for calculating a step-transition in a coaxial waveguide

Mоrоzоv

Magro

2020

JPhysElectron

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The stepwise transition in the coaxial waveguide is calculated by the integral equation method. To solve the problem, the entire region of field definition is conditionally divided into three partial areas for which the field components are recorded. A system of equations is obtained that allows one to calculate the reflection coefficient of a T-wave from this homogeneity. The geometric dimensions of the waveguide, which provide the minimum value of the reflection coefficient, are given.

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“…A reader can find additional information on this topic in other publications, e.g., [11][12][13][14][15][16][17].…”

Section: H(rt) = I(z T)h(r) and E(rt) = V (Z T)e(r) + E(z T)z(r)mentioning

confidence: 99%

Time-Domain Real-Valued Tm-Modal Waves in Lossy Waveguides

Tretyakov¹,

Kaya²

2013

PIER

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Abstract-The waveguide has a perfectly conducting surface. Its cross section domain is bounded by a singly-connected contour of a rather arbitrary but enough smooth form. Possible waveguide losses are modeled by a homogeneous conductive medium in the waveguide. The boundary-value problem for the system of Maxwell's equations with time derivative is solved in the time domain. The real-valued solutions are obtained in Hilbert space L 2 in a form of transverselongitudinal decompositions. Every field component is a product of the vector element of the modal basis dependent on transverse coordinates, and the modal amplitudes dependent on time and axial coordinate. Three examples are included. The dynamic properties of the modal waves and concomitant energetic waves are studied and their dependence on time illustrated graphically.

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Telegraphist's Equations for Rectangular Waveguides and Analysis in Nonorthogonal Coordinates

Cited by 8 publications

References 18 publications

Exact semi-separation of variables in waveguides with non-planar boundaries

Exact semi-separation of variables in waveguides with non-planar boundaries

Application of the method of integral equation for calculating a step-transition in a coaxial waveguide

Time-Domain Real-Valued Tm-Modal Waves in Lossy Waveguides

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