Ultra-Wideband, Short-Pulse Electromagnetics 3 pp 165-176 | Cite as

# Theorems on Time-Domain Far Fields

## Abstract

The far-field characteristics of classical electromagnetic fields satisfying Maxwell’s equations have been investigated quite thoroughly for sources radiating at a single frequency, that is, for frequency-domain or time-harmonic fields [1]. For example, frequency-domain far fields radiated by integrable sources in a volume of finite extent decay as 1/*r* or faster as the distance *r* to the far field approaches infinity. In addition, these far fields are entire analytic functions of their angular variables *θ* and *ø*. Using a plane-wave decomposition, frequency-domain near fields can be expressed as an integral of the far-field pattern and its analytic continuation to complex angles of observation [2],[3].

## Keywords

Point Charge Finite Time Interval Finite Region Finite Extent Entire Analytic Function## Preview

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## References

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*r*unless the secant slope, [**J**(**r**,t + Δt) −**J**(**r**,*t*)]Δ*/t*,becomes infinite for some*t*and Δ*t*[17],[7, sec.246, p.355]. Of course, if the limit of the secant slope exists as Δt → 0, the limit equals the time derivative. These concepts are illustrated in Blejer*et al*. [17] for the specific case of the fields radiated by the current on a disk.Google Scholar - [17]D.J. Blejer, R.C. Wittmann and A.D. Yaghjian, in
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