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Basic full Gaussian wave

Basic full Gaussian wave

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Complex Space Source Theory of Spatially Localized Electromagnetic Waves — Recommend this title to your library

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The field of a point source of suitable strength with the location coordinates in the complex space reproduces the fundamental Gaussian beam in the paraxial approximation. The resulting full wave is designated the basic full Gaussian wave. The vector potential that generates the basic full Gaussian wave is obtained. The resulting electromagnetic fields are found, the radiation intensity distribution is determined, and its characteristics are described. The time-averaged power transported by the basic full Gaussian wave in the +z and the -z directions is obtained. This power increases monotonically and approaches the limiting value of the fundamental Gaussian beam as kw0 is increased. The surface electric current density on the secondary source plane z = 0 is deduced. In the paraxial approximation, this electric current density reduces to the source electric current density that generates the fundamental Gaussian beam. In the paraxial approximation, both the fundamental Gaussian wave and the basic full Gaussian wave reduce to the same fundamental Gaussian beam. The complex power is evaluated and the reactive power is determined. For the basic full Gaussian wave, the reactive power is infinite. In contrast, for the corresponding paraxial beam, namely the fundamental Gaussian beam, the reactive power vanishes.

Chapter Contents:

  • 1 Point source in complex space
  • 2 Electromagnetic fields
  • 3 Radiation intensity
  • 4 Radiative and reactive powers
  • 5 General remarks
  • References

Inspec keywords: reactive power; Gaussian processes; electromagnetic fields; electromagnetic wave propagation; current density; approximation theory

Other keywords: secondary source plane; limiting value; point source; source electric current density; full Gaussian wave; radiation intensity distribution; vector potential; paraxial approximation; surface electric current density; location coordinates; fundamental Gaussian beam; reactive power; time-averaged power; electromagnetic fields

Subjects: Steady-state electromagnetic fields; electromagnetic induction; Interpolation and function approximation (numerical analysis); Fluctuation phenomena, random processes, and Brownian motion; Electromagnetic wave propagation; Electromagnetic waves: theory; Other topics in statistics; Numerical approximation and analysis

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