Evolution Equations for Analytical Study of Digital Signals in Waveguides

Aksoy, Serkan; Tretyakov, Oleg A.

doi:10.1163/156939303322760209

Cited by 27 publications

(27 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This coincides with our previous result obtained by a more general method requiring a deep mathematical background, see in [6]. The infinite set (20) of T E-modes is generated by the eigensolutions to the problem (17) , corresponding to all the eigenvalues ν 2 n = 0 only.…”

Section: Complete Set Of the Te Time-domain Modessupporting

confidence: 90%

“…To this purpose, he amended Maxwell's equations by introducing magnetic current density as a real physical quantity and also adding magnetic equivalent of Ohm's law to the set of constitutive relations. It is possible, however, to study propagation of digital signals in waveguides and oscillations in cavities excited by Walsh signals still remaining within the scope of generally accepted theory [6,7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Tretyakov¹,

Akgun²

2010

PIER

View full text Add to dashboard Cite

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.

show abstract

Section: Complete Set Of the Te Time-domain Modessupporting

confidence: 90%

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

View full text Add to dashboard Cite

show abstract

“…The mode amplitudes e H m (r, t) are calculated numerically using the finite-difference scheme (22). This problem also has the analytical solution:…”

Section: Numerical Resultsmentioning

confidence: 99%

“…It can be applied to solve problems with arbitrary geometry. METD is more special method, which is appropriate to solve problems of electromagnetic waves excitation and propagation in waveguides [17][18][19][20][21][22][23][24][25][26][27][28], cavities [29][30][31][32][33], free space, some other media and structures [34][35][36][37][38][39]. Also METD is developed for studying the transient electromagnetic processes in conical transmission lines [40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Axially Symmetric Transient Electromagnetic Fields in a Radially Inhomogeneous Biconical Transmission Line

Kochetov¹,

Butrym²

2013

PIER B

View full text Add to dashboard Cite

Abstract-In the present paper a novel mathematical model of physical processes of transient electromagnetic waves excitation and propagation in a biconical transmission line with radially inhomogeneous magneto-dielectric filling is proposed. The model is based on time domain mode expansions over spherical waves. The basis functions of the mode expansions are calculated analytically. The mode expansion coefficients are governed by Klein-Gordon-Fock equation with coefficients depending on a radial spatial coordinate. The explicit finite difference time domain computational scheme is derived to calculate the mode expansion coefficients. Dependences of cutoff frequencies of higher modes of TE and TM waves on the line geometry and dielectric filling are studied. In order to calculate electromagnetic field in the line with higher accuracy, just finite number of terms in the mode expansions is required. Electromagnetic field excited by the transient electric ring current is calculated in both homogeneous and radially inhomogeneous biconical transmission line. It is shown that there is a possibility to increase the bandwidth of the line via introduction of partial dielectric filling without changing the line geometrical size.

show abstract

“…Herein, we considered the solutions that correspond to Miller's orbit 1 and orbit 2. One can find: (i) the derivation of the modal basis for a waveguide in [11] and [12], (ii) the presentation of the solutions to the KGE corresponding to Miller's orbit 3 in [13] and orbit 7 in [14].…”

Section: Energetic Functions Of the Waveguide Modesmentioning

confidence: 99%

Study of the energetic field characteristics of the TE-modalwaves in waveguides

Erden¹

2017

Turk J Phys

View full text Add to dashboard Cite

Abstract:The energetic characteristics of cylindrical medium-free time-domain waveguide fields are solved within the framework of the evolutionary approach to electromagnetics. Solving the boundary-eigenvalue problem for transverse Laplacian yields a configurational basis in the waveguide cross section. Elements of the basis depend on transverse coordinates, whereas the modal amplitudes depend on the longitudinal coordinate, z, and time, t . Solving the resulted Klein-Gordon equation yields a basis for analysis of the modal amplitudes. Exact solutions for the amplitudes of TE-modes are obtained, and the energetic field characteristics are derived in accordance with the causality principle.

show abstract

Evolution Equations for Analytical Study of Digital Signals in Waveguides

Cited by 27 publications

References 4 publications

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

Axially Symmetric Transient Electromagnetic Fields in a Radially Inhomogeneous Biconical Transmission Line

Study of the energetic field characteristics of the TE-modalwaves in waveguides

Contact Info

Product

Resources

About