Elliptic Laguerre-Gaussian beams
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Updated: Aug 11, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Victor V Kotlyar1, Svetlana N Khonina, Anton A Almazov
1Image Processing Systems Institute, Russian Academy of Sciences, Samara State Aerospace University, 151 Molodogvardejskaya, Samara 443001, Russia.
Abstract:
An analytical expression for the diffraction of an elliptic Laguerre-Gaussian (LG) beam is derived and analyzed. We show that a beam with even singularity order has nonzero axial intensity for any degree of ellipticity and at any finite distance z from the initial plane, whereas at z = 0 and z = infinity the axial intensity is zero. We show that for a beam with a small degree of ellipticity and even order of singularity, two isolated intensity zeroes appear in the Fresnel zone on a straight line at an angle of 45 deg or -45 deg, depending whether the beam's spin is right or left. The theoretical conclusions are confirmed by numerical simulation and physical experiments.
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