Airy polynomials, three-variable Hermite polynomials and the paraxial wave equation

A. Torre

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2 Citations (Scopus)


Within the context of an investigation of the potential of functions, which directly or indirectly relate to the Airy functions, to yield solutions of the 2D paraxial wave equation, we consider here the Airy polynomials. We see that appropriate Gaussian-modulated versions of such polynomials, which could in a sense parallel the HermiteGaussian wavefunctions of both elegant and standard type, yield, when assumed as initial functions, solutions of the 2DPWE shaping in the form of a complex Gaussian modulation of three-variable Hermite polynomials. A basic characterization of these wavefunctions is provided, having as a touchstone the HermiteGaussian wavefunctions. © 2012 IOP Publishing Ltd.
Original languageEnglish
Article number045704
Pages (from-to)-
JournalJournal of Optics
Issue number4
Publication statusPublished - Apr 2012
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics

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