Differential form representation of stochastic electromagnetic fields

Abstract

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.

Stochastic electromagnetic field propagation— measurement and modelling

“…Heaviside's vector notation for Maxwell's equations has become standard, providing a balance in complexity and intuitiveness which makes it appealing for engineering. Further frameworks have been developed and applied to EM theory in the meantime which, unlike Maxwell's original formulation, provide a more intuitive insight such as the framework based on exterior differential forms [ 9 , 10 ]. Besides Heaviside's work on the generation and motion of wavefronts in open media and telegraphic lines, he soon focused on the definition of energy flux in electromagnetism.…”

Principal component analysis for efficient characterization of stochastic electromagnetic fields

“…However, one can characterize noisy EM fields originating from spatially distributed random sources with Gaussian probability distribution and with arbitrary degree of correlation by auto-and cross-correlation spectra. Such a method is discussed in previous studies [3][4][5][6] and can be applied to compute the propagation of the spectral energy density after transforming the field problem into a frequency domain network problem by applying a boundary element method. The approach of characterizing noisy EM fields by correlation information has been also extended to the transmission line matrix method in the time domain 7,8 and to the transverse wave formulation.…”