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Optics Letters

Optics Letters


  • Editor: Alan E. Willner
  • Vol. 38, Iss. 17 — Sep. 1, 2013
  • pp: 3325–3328

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

Mark R. Dennis and James D. Ring  »View Author Affiliations

Optics Letters, Vol. 38, Issue 17, pp. 3325-3328 (2013)

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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.

© 2013 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.3185) Fourier optics and signal processing : Invariant optical fields
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: July 5, 2013
Manuscript Accepted: July 23, 2013
Published: August 23, 2013

Mark R. Dennis and James D. Ring, "Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams," Opt. Lett. 38, 3325-3328 (2013)

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Fig. 1. Fig. 2. Fig. 3.

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