Conical refraction of a high-M2 laser beam

Grigorii S. Sokolovskii, V.Yu Mylnikov, Sergey N. Losev, Ksenia A. Fedorova, Edik U. Rafailov

Research output: Chapter in Book/Published conference outputConference publication


We report on experiments with conical refraction of laser beams possessing a high beam propagation parameter M2. With beam propagation parameter values M2=3 and M2=5, unusual Lloyd's distributions with correspondingly three and five dark rings were observed. In order to explain this phenomenon, we extend the dual-cone model of the conical refraction that describes it as a product of interference of two cones that converge and diverge behind the exit facet of the crystal. In the extended model, these converging/diverging cones are represented as the cone-shaped quasi-Gaussian beams possessing the M2 parameter of an original beam. In this formalism, a beam-waist of these cone-shaped beams is proportional to the M2 value and defines the area of their interference which is a width of the Lloyd's ring. Therefore, the number of dark rings in the Lloyd distribution is defined by the M2 value and can be much greater than unity. The results of the numerical simulations within the extended dual-cone model are in excellent agreement with the experiment.

Original languageEnglish
Title of host publicationLaser Resonators, Microresonators, and Beam Control XIX 2017
EditorsAlexis V. Kudryashov, Alan H. Paxton, Vladimir S. Ilchenko
Place of PublicationBellingham, WA (US)
Number of pages6
ISBN (Electronic)978-1-5106-0621-0
Publication statusPublished - 20 Feb 2017
EventLaser Resonators, Microresonators, and Beam Control XIX 2017 - San Francisco, United States
Duration: 30 Jan 20172 Feb 2017

Publication series

NameSPIE Proceedings
ISSN (Print)0277-786X
ISSN (Electronic)2410-9045


ConferenceLaser Resonators, Microresonators, and Beam Control XIX 2017
Country/TerritoryUnited States
CitySan Francisco

Bibliographical note

G. S. Sokolovskii; V. Yu. Mylnikov; S. N. Losev; K. A. Fedorova and E. U. Rafailov "Conical refraction of a high-M2 laser beam", Proc. SPIE 10090, Laser Resonators, Microresonators, and Beam Control XIX, 100901R (February 20, 2017).

Copyright 2017. Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic electronic or print reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.



  • birefringence
  • conical refraction
  • crystal optics
  • Gaussian beams
  • geometric optics
  • laser diodes


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