Non-orthogonal domain parabolic equation and its tilted gaussian beam solutions

Yakir Hadad*, Timor Melamed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A non-orthogonal coordinate system which is a priori matched to localized initial field distributions for time-harmonic wave propagation is presented. Applying, in addition, a rigorous paraxial-asymptotic approximation, results in a novel parabolic wave equation for beam-type field propagation in 3D homogeneous media. Localized solutions to this equation that exactly match linearly-phased Gaussian aperture distributions are termed tilted Gaussian beams. These beams serve as the building blocks for various beam-type expansion schemes. Application of the scalar waveobjects to electromagnetic field beam-type expansion, as well as reflection and transmission of these waveobjects by planar velocity (dielectric) discontinuity are presented. A numerical example which demonstrates the enhanced accuracy of the tilted Gaussian beams over the conventional ones concludes the paper.

Original languageEnglish
Article number5398869
Pages (from-to)1164-1172
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Issue number4
StatePublished - Apr 2010
Externally publishedYes


  • Electromagnetic propagation
  • Electromagnetic theory
  • Gaussian beams
  • Propagation


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