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Updated: Jul 20, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Generalized Helmholtz-Gauss beam and its transformation by paraxial optical systems
Manuel Guizar-Sicairos1, Julio C Gutiérrez-Vega
1The Institute of Optics, University of Rochester, Rochester, New York 14627, USA.
Abstract:
We introduce the generalized Helmholtz-Gauss (gHzG) beam and analyze its propagation through optical systems described by ABCD matrices with real and complex elements. The transverse mathematical structure of the gHzG beam is form invariant under paraxial transformations and reduces to those of ordinary HzG and modified HzG beams as special cases. We derive a closed-form expression for the fractional Fourier transform of gHzG beams.
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