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Updated: May 27, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Orbital angular momentum of Laguerre-Gaussian beams beyond the paraxial approximation
Alexander Cerjan1, Charles Cerjan
1Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA. alexander.cerjan@yale.edu
Abstract:
We derive a full field solution for Laguerre-Gaussian beams consistent with the Helmholtz equation using the angular spectrum method. Field components are presented as an order expansion in the ratio of the wavelength to the beam waist, f=λ/(2πw₀), which is typically small. The result is then generalized to a beam of arbitrary polarization. This result is then used to reproduce the signature angular momentum properties of Laguerre-Gaussian beams in the paraxial limit. The subsequent higher-order term is similarly obtained, which does not display a clear separation of orbital and spin angular momentum components.
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