Evolutionary equations for the theory of waveguides

Tretyakov, Oleg A.

doi:10.1109/aps.1994.408101

Cited by 25 publications

(25 citation statements)

References 1 publication

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“…It is pertinent to note that there are other interesting publications listed chronologically [8][9][10][11][12][13][14][15][16][17][18]. It is possible to find herein useful mathematical details on the analytical methods and description of various physical phenomena extracted from the analytical solutions.…”

Section: Introductionmentioning

confidence: 99%

Derivation of Klein-Gordon Equation From Maxwell's Equations and Study of Relativistic Time-Domain Waveguide Modes

Tretyakov¹,

Akgun²

2010

PIER

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Abstract-An initial-boundary value problem for the system of Maxwell's equations with time derivative is formulated and solved rigorously for transient modes in a hollow waveguide. It is supposed that the latter has perfectly conducting surface. Cross section, S, is bounded by a closed singly-connected contour of arbitrary but smooth enough shape. Hence, the T E and T M modes are under study. Every modal field is a product of a vector function of transverse coordinates and a scalar amplitude dependent on time, t, and axial coordinate, z. It has been established that the study comes down to, eventually, solving two autonomous problems: i) A modal basis problem. Final result of this step is definition of complete (in Hilbert space, L 2 (S)) set of functions dependent on transverse coordinates which originates a basis. ii) A modal amplitude problem. The amplitudes are generated by the solutions to Klein-Gordon equation (KGE), derived from Maxwell's equations directly, with t and z as independent variables. The solutions to KGE are invariant under relativistic Lorentz transforms and subjected to the causality principle. Special attention is paid to various ways that lead to analytical solutions to KGE. As an example, one case (among eleven others) is considered in detail. The modal amplitudes are found out explicitly and expressed via products of Airy functions with arguments dependent on t and z.

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Section: Introductionmentioning

confidence: 99%

Derivation of Klein-Gordon Equation From Maxwell's Equations and Study of Relativistic Time-Domain Waveguide Modes

Tretyakov¹,

Akgun²

2010

PIER

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“…The solution to the evolutionary equation can be presented in the form of convolution of initial-boundary conditions with some transport operator. Such method has been used under different names by many other researches, see for example papers by Geyi [8,9], Kurokawa [10], Kristensson [11], and a series of papers by Tretyakov and his followers [3,4,12,[13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Charge Transport by a Pulse E-Wave in a Waveguide With Conductive Medium

Legenkiy¹

2009

PIER B

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Abstract-An E-wave excites longitudinal conductivity currents in a waveguide filled with lossy medium. Total flow of this current through a cross-section is nonzero for odd E-modes; it means that some charge is transported by the pulse along the waveguide. This phenomenon is considered in the paper using analytical approach based on mode expansion of the fields in Time Domain (known as Mode Basis Method) and using Finite Difference in Time Domain method (FDTD). Volume conductivity charges being moved by the pulse wave are determined. In order to set the problem as much physically as possible we consider diffraction of a pulse E-wave on the boundary between a hollow waveguide and a waveguide with conductive medium. Behavior of the transient fields and surface charges at the interface are also examined. It is shown that an incident pulse wave excites a surface wave at the interface that results in transversal resonance with relaxation time much greater than that of the conductive medium. Characteristics of the travelling charge pulse wave are studied based on the obtained closed-form solution.

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“…We find the solutions to this problem within the framework of a waveguide version of the evolutionary approach to electromagnetics ‡ , see [2][3][4][5]. The TM -wave solutions are obtained directly in the Hilbert space, L 2 , of the real-valued functions in a form, which can be exhibited symbolically as follows: (2) where H(r) and E(r) are the two-component basis vectors in the waveguide cross section; Z(r) is a one-component basis vector with the unit vector z, z the axial variable, and r a projection of R onto the waveguide cross section.…”

Section: Introductionmentioning

confidence: 99%

“…The TM -wave solutions are obtained directly in the Hilbert space, L 2 , of the real-valued functions in a form, which can be exhibited symbolically as follows: (2) where H(r) and E(r) are the two-component basis vectors in the waveguide cross section; Z(r) is a one-component basis vector with the unit vector z, z the axial variable, and r a projection of R onto the waveguide cross section. The scalar factors, I(z, t), V (z, t) and e(z, t), are the amplitudes, physically.…”

Section: Introductionmentioning

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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Evolutionary equations for the theory of waveguides

Cited by 25 publications

References 1 publication

Derivation of Klein-Gordon Equation From Maxwell's Equations and Study of Relativistic Time-Domain Waveguide Modes

Derivation of Klein-Gordon Equation From Maxwell's Equations and Study of Relativistic Time-Domain Waveguide Modes

Charge Transport by a Pulse E-Wave in a Waveguide With Conductive Medium

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

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