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Two higher-order full Gaussian waves

Two higher-order full Gaussian waves

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A treatment of the higher-order hollow Gaussian beam is presented. The required higher-order point source in the complex space is introduced. The higher-order hollow full Gaussian wave generated by the complex space source is derived. The basic full Gaussian wave is obtained as a special case of the higher-order hollow full Gaussian wave. The cosh-Gauss paraxial beam is deduced by the two-dimensional Fourier transform technique. The required array of point sources situated on the corners of a square in the complex space is introduced. The full-wave generalization of the cosh-Gauss beam is determined. The basic full Gaussian wave is obtained as a special case of the full cosh-Gauss wave as the side of the square reduces to zero.

Chapter Contents:

  • 1 Higher-order hollow Gaussian wave
  • 1.1 Paraxial beam
  • 1.2 Complex space source
  • 1.3 Hollow Gaussian wave
  • 2 cosh-Gauss wave
  • 2.1 cosh-Gauss beam
  • 2.2 Complex space source
  • 2.3 cosh-Gauss wave
  • References

Inspec keywords: Fourier transforms; electromagnetic waves; Gaussian distribution

Other keywords: higher-order full Gaussian waves; two-dimensional Fourier transform; higher-order point source; higher-order hollow Gaussian beam; complex space source; cosh-Gauss paraxial beam

Subjects: Integral transforms; Other topics in statistics; Electromagnetic waves: theory; Function theory, analysis; Electromagnetic wave propagation; Probability theory, stochastic processes, and statistics

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