Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complex coordinate transforms and ray transfer matrices

T. Graf, D. N. Christodoulides, M. S. Mills, Jerome V Moloney, Shankar C Venkataramani, Ewan M Wright

Research output: Contribution to journalArticle

4 Scopus citations


We investigate the linear propagation of Gaussian-apodized solutions to the paraxial wave equation in free-space and first-order optical systems. In particular, we present complex coordinate transformations that yield a very general and efficient method to apply a Gaussian apodization (possibly with initial phase curvature) to a solution of the paraxial wave equation. Moreover, we show how this method can be extended from free space to describe propagation behavior through nonimaging first-order optical systems by combining our coordinate transform approach with ray transfer matrix methods. Our framework includes several classes of interesting beams that are important in applications as special cases. Among these are, for example, the Bessel-Gauss and the Airy-Gauss beams, which are of strong interest to researchers and practitioners in various fields.

Original languageEnglish (US)
Pages (from-to)1860-1869
Number of pages10
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number9
Publication statusPublished - Sep 1 2012


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Electronic, Optical and Magnetic Materials
  • Computer Vision and Pattern Recognition

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