A note on the general solution of the paraxial wave equation: A Lie algebra view

A. Torre

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The paraxial wave equation in one space dimension is reconsidered from the viewpoint of the Lie algebra formalism, according to a method which is well documented in the literature (Kalnins and Miller Jr 1974 J. Math. Phys. 15 1728). As a result, we obtain the expression of the general solution of the wave equation in Cartesian coordinates. Although such a solution is not new, being recently reported (Bandres and Gutiérrez-Vega 2007 Opt. Lett. 32 3459), the formalism applied here may give a deeper insight into the nature of such a solution, also revealing interesting relationships between apparently unrelated formulations. © IOP Publishing Ltd.
Original languageEnglish
Article number055006
Pages (from-to)-
JournalJournal of Optics A: Pure and Applied Optics
Issue number5
Publication statusPublished - 1 May 2008
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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