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Updated: May 22, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Hankel-Bessel laser beams.

Victor V Kotlyar¹, Alexey A Kovalev, Victor A Soifer

¹Laser Measurements Laboratory, Image Processing Systems Institute of the Russian Academy of Sciences, 151 Molodogvardejskaya Street, Samara 443001, Russia.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|May 8, 2012

Summary

This study derives an analytical solution for laser light beam propagation using the scalar Helmholtz equation. It reveals beam amplitude is proportional to solutions of Kummer

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Area of Science:

Optics and Photonics
Mathematical Physics

Background:

Laser beam propagation is fundamental to optics.
The scalar Helmholtz equation models wave phenomena, including light.
Kummer's differential equation arises in various physics problems.

Purpose of the Study:

To derive an analytical solution for laser beam propagation along the optical axis.
To investigate the mathematical relationship governing beam complex amplitude.
To analyze a specific class of beams: Hankel-Bessel (HB) beams.

Main Methods:

Solving the scalar Helmholtz equation analytically.
Utilizing solutions of Kummer's differential equation.
Deducing relationships for Hankel-Bessel (HB) beams.

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Main Results:

An analytical solution for laser beam propagation was derived.
Beam complex amplitude is directly proportional to a product of two solutions to Kummer's equation.
Specific relationships for Hankel-Bessel (HB) beams were deduced.

Conclusions:

The derived analytical solution provides a new framework for understanding laser beam propagation.
Hankel-Bessel (HB) beams exhibit unique properties related to Kummer's equation solutions.
Further study on the focusing characteristics of HB beams is warranted.