Characterising elegant and standard Hermite-Gaussian beam modes

S. Saghafi*, C. J R Sheppard, J. A. Piper

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)


Two tool parameters, the beam propagation factor M2 and kurtosis factor k, are used to analyse solutions of the paraxial scalar wave equation (for rectangular coordinates) i.e. the so-called the standard and elegant Hermite-Gaussian modes (SHG and EHG). Analytical expressions for M2 and k are derived and the correspondence between them for each form of solution is discussed in detail. These two parameters reveal information about the solutions, which leads us to derive the asymptotic representation of EHG modes (i.e. in the near-field, for a large number of modes).

Original languageEnglish
Pages (from-to)173-179
Number of pages7
JournalOptics Communications
Issue number3-6
Publication statusPublished - 8 May 2001


  • Beam propagation
  • Higher-order Gaussian
  • Kurtosis
  • M


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