A note on scalar Hertz potentials for gyrotropic media

Przeźiecki, S.; Hurd, R. A.

doi:10.1007/bf00895002

Cited by 31 publications

(6 citation statements)

References 3 publications

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“…Hertz potentials known from the start of electromagnetic theory [36] do not seem to have been extensively used in spite of noticeable exception [3,37] They are a useful tool to analyze electric and magnetic multipole radiation in wave guides [38][39][40][41][42] as well as to cope with anisotropy, bi-anisotropy and chiral isotropy [43][44][45][46]. Finally Hertz and Debye potentials intervene to tackle electromagnetism in General Relativity [23,40].…”

Section: Resultsmentioning

confidence: 99%

Spinor and Hertzian Differential Forms in Electromagnetism

Hillion¹

2011

PIER M

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Abstract-The purpose of this paper is to extend to spinor electromagnetism the differential forms, based on the Cartan exterior derivative and originally developed for tensor fields, in a very compact way. To this end, differential electromagnetic forms are first compared to conventional tensors. Then, using the local isomorphism between the O(3,C) and SL(2,C) groups supplying the well known connection between complex vectors and traceless second rank spinors, they are generalized to spinor electromagnetism and to Proca fields. These differential forms are finally expressed in terms of Hertz potentials.

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Section: Resultsmentioning

confidence: 99%

Spinor and Hertzian Differential Forms in Electromagnetism

Hillion¹

2011

PIER M

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“…The opportunity to express all vector-field components through two scalar functions was noted back in a long time publication by Whittaker [14] (more detailed reference list can be found in paper by Nisbet [15]). The approach has proven to be quite productive, and not for uniform systems only but also for some systems with gyrotropic properties [16][17][18]. Yet, for a long time it was not possible to extend the approach to arbitrary nonhomogeneous systems, which has substantially reduced the capability of the method.…”

Section: Introductionmentioning

confidence: 99%

A method of effective potentials for calculating the frequency spectrum of eccentrically layered spherical cavity resonators

Eremenko,

Tarasov,

Volovichev

2020

Preprint

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A novel method for the calculation of eigenfrequencies of non-uniformly filled spherical cavity resonators is developed. The impact of the system symmetry on the electromagnetic field distribution as well as on its degrees of freedom (the set of resonant modes) is examined. It is shown that in the case of angularly symmetric cavity, regardless of its radial non-uniformity, the set of resonator modes is, as anticipated, a superposition of TE and TM oscillations which can be described in terms of a single scalar function independently of each other. The spectrum is basically determined through the introduction of effective "dynamic" potentials which encode the infill inhomogeneity. The violation of polar symmetry in the infill dielectric properties, the azimuthal symmetry being simultaneously preserved, suppresses all azimuthally non-uniform modes of electric-type (TM) oscillations. In the absence of angular symmetry of both electric and magnetic properties of the resonator infill, only azimuthally uniform distribution of both TM and TE fields is expected to occur in the resonator. The comparison is made of the results obtained through the proposed method and of the test problem solution obtained with use of commercial solvers. The method appears to be efficient for computational complex algorithms for solving spectral problems, including those for studying the chaotic properties of electrodynamic systems' spectra.

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“…Nisbet generalized this approach by showing that the constant vectors need not be the same for both Hertz potentials, and also that the fields can be described by a single Hertz vector potential with two components. 8,9 Przeździecki and Hurd, 10 Przeździecki and Laprus, 11 and Weiglhofer and Papousek 12 extended the use of scalar potentials to gyrotropic media.…”

Section: Introductionmentioning

confidence: 99%

Use of electromagnetic scalar potentials in boundary value problems

Lahart

2003

American Journal of Physics

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Expressions for the electric and magnetic fields in terms of scalar potentials are derived, and boundary conditions that the scalar potentials obey at dielectric interfaces and at conducting surfaces are discussed. The relationship of the scalar potentials to source charges and currents is described. It is shown that scalar potentials can be defined that do not obey the wave equation, but the source charge and current configurations that can be associated with such potentials are more limited than those that do obey the wave equation. Examples are given of the use of electromagnetic scalar potentials in boundary value problems.

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A note on scalar Hertz potentials for gyrotropic media

Cited by 31 publications

References 3 publications

Spinor and Hertzian Differential Forms in Electromagnetism

Spinor and Hertzian Differential Forms in Electromagnetism

A method of effective potentials for calculating the frequency spectrum of eccentrically layered spherical cavity resonators

Use of electromagnetic scalar potentials in boundary value problems

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