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Cylindrically symmetric transverse magnetic full Gaussian wave

Cylindrically symmetric transverse magnetic full Gaussian wave

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The fundamental Gaussian beam and wave are generated by the magnetic/electric vector potential, oriented perpendicular to the direction of propagation. If the vector potential is oriented parallel to the propagation direction and is cylindrically symmetrical, transverse magnetic (TM) and transverse electric (TE) beams and waves are excited [1-5]. The lowest order solution is used for the vector potential and is the same as for the fundamental Gaussian beam and wave. The resulting electromagnetic fields are one order higher, which is one order of magnitude in kw0 smaller, than those for the fundamental Gaussian beam. For the TM paraxial beam, the electric field component Er(r, z) is discontinuous across the secondary source plane z = 0, resulting in an azimuthally directed magnetic current sheet on the secondary source plane. Therefore, the problem of the cylindrically symmetric TM Gaussian paraxial beam and full wave is formulated directly in terms of the electromagnetic fields and the source current density. The solution is first obtained in the paraxial approximation. The electromagnetic fields are determined and the characteristics of the real power, the radiation intensity distribution, and the reactive power are obtained. The reactive power of the TM Gaussian beam vanishes.The full-wave generalization of the cylindrically symmetric TM paraxial beam is carried out. The procedure involves the analytic continuation of the asymptotic (IzI → ∞) field from IzI to IzI - ibt, where the length parameter bt is in the range 0 ≤ bt ≤ b and b is the Rayleigh distance. The limiting case of bt=b = 1 is identical to the full-wave treatment introduced by Deschamps [6] and Felsen [7] for the fundamental Gaussian beam [4]. For the cylindrically symmetric TM full Gaussian wave, the required magnetic current density is deduced and the relevant components of the generated electromagnetic fields are determined. The characteristics of the real power, the reactive power, and the radiation intensity distribution are analyzed. The reactive power of the cylindrically symmetric TM full Gaussian wave does not vanish. The dependence of the characteristics of the various physical quantities on bt/b and kw0 is examined.

Chapter Contents:

  • 1 Cylindrically symmetric transverse magnetic beam
  • 2 Current source in complex space
  • 3 Cylindrically symmetric TM full wave
  • 4 Real power
  • 5 Reactive power
  • 6 Radiation intensity distribution
  • References

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

Other keywords: paraxial approximation; TE wave; full Gaussian wave; transverse magnetic beams; TE beam; transverse magnetic wave; cylindrically symmetric wave; electromagnetic field; transverse electric beam; propagation direction; magnetic vector potential; TM wave; azimuthally directed magnetic current sheet; electric field component; TM Gaussian paraxial beam; radiation intensity distribution; fundamental Gaussian beam; electric vector potential; source current density; transverse electric wave; reactive power

Subjects: Electromagnetic waves: theory; Electromagnetic wave propagation; Probability theory, stochastic processes, and statistics; Interpolation and function approximation (numerical analysis); Other topics in statistics; Numerical approximation and analysis

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