Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams

Mark R. Dennis*, James D. Ring

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

15 Citations (Scopus)

Abstract

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wave packets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator that interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation. (C) 2013 Optical Society of America

Original languageEnglish
Pages (from-to)3325-3328
Number of pages4
JournalOptics Letters
Volume38
Issue number17
DOIs
Publication statusPublished - 1 Sep 2013

Keywords

  • ORBITAL ANGULAR-MOMENTUM
  • MATHIEU BEAMS
  • OSCILLATOR
  • FIELDS

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