Laser transverse modes with SU(2) representation

Yung Fu Chen*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The direct generation of a structured beam from a laser resonator is closely related to the formation of transverse modes. For a long time, the representation of the transverse mode of the spherical cavity is usually divided into Hermite-Gaussian (HG) and Lager-Gaussian (LG) modes. A large number of experimental results show that the generalized representation of the transverse mode is the Hermite-Laguerre-Gaussian (HLG) mode. We give a detailed overview of the theoretical description of the HLG mode from the representation of SU(2) in the Jordan-Schwinger diagram. We further show that the HLG modes can be exactly derived as the superposition of the elliptical modes without involving Hermite and Laguerre polynomials.

Original languageEnglish
Title of host publicationOptical Manipulation and Structured Materials Conference 2021
EditorsTakashige Omatsu, Kishan Dholakia, Hajime Ishihara, Keiji Sasaki
ISBN (Electronic)9781510647206
StatePublished - 2021
EventOptical Manipulation and Structured Materials Conference 2021 - Virtual, Online, Japan
Duration: 20 Apr 202122 Apr 2021

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferenceOptical Manipulation and Structured Materials Conference 2021
CityVirtual, Online


  • Hermite-Laguerre-Gaussian mode
  • Spherical cavity
  • SU(2)
  • Transverse mode


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