Differential form representation of stochastic electromagnetic fields

Abstract. In this work, we revisit the theory of stochastic electromagnetic fields using exterior differential forms. We present a short overview as well as a brief introduction to the application of differential forms in electromagnetic theory. Within the framework of exterior calculus we derive equations for the second order moments, describing stochastic electromagnetic fields. Since the resulting objects are continuous quantities in space, a discretization scheme based on the Method of Moments (MoM) is introduced for numerical treatment. The MoM is applied in such a way, that the notation of exterior calculus is maintained while we still arrive at the same set of algebraic equations as obtained for the case of formulating the theory using the traditional notation of vector calculus. We conclude with an analytic calculation of the radiated electric field of two Hertzian dipole, excited by uncorrelated random currents.

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A primer on exterior differential calculus

Theoretical and Applied Mechanics ◽

10.2298/tam0302085b ◽

2003 ◽

pp. 85-162 ◽

Cited By ~ 9

Author(s):

D.A. Burton

Keyword(s):

Continuum Mechanics ◽

Differential Calculus ◽

Differential Forms ◽

Lie Derivative ◽

Exterior Differential ◽

Exterior Calculus ◽

Vector Calculus ◽

Exterior Forms ◽

Pedagogical Application

A pedagogical application-oriented introduction to the cal?culus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear con?nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi?tional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The numerous advantages of this calculus, over more traditional ma?chinery, are stressed throughout the article. .

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Discrete electromagnetic theory with exterior calculus

2016 Progress in Electromagnetic Research Symposium (PIERS) ◽

10.1109/piers.2016.7734512 ◽

2016 ◽

Cited By ~ 1

Author(s):

Shu Chen ◽

Weng Cho Chew

Keyword(s):

Electromagnetic Theory ◽

Exterior Calculus

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STRONG AND WEAK FORMS OF THE METHOD OF MOMENTS AND THE COUPLED DIPOLE METHOD FOR SCATTERING OF TIME-HARMONIC ELECTROMAGNETIC FIELDS

International Journal of Modern Physics C ◽

10.1142/s0129183192000385 ◽

1992 ◽

Vol 03 (03) ◽

pp. 583-603 ◽

Cited By ~ 93

Author(s):

AKHLESH LAKHTAKIA

Keyword(s):

Electromagnetic Fields ◽

Method Of Moments ◽

Electromagnetic Scattering ◽

Final Section ◽

The Other ◽

Numerical Techniques ◽

Scattering Problems ◽

Time Harmonic

Algorithms based on the method of moments (MOM) and the coupled dipole method (CDM) are commonly used to solve electromagnetic scattering problems. In this paper, the strong and the weak forms of both numerical techniques are derived for bianisotropic scatterers. The two techniques are shown to be fully equivalent to each other, thereby defusing claims of superiority often made for the charms of one technique over the other. In the final section, reductions of the algorithms for isotropic dielectric scatterers are explicitly given.

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