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Updated: Jun 2, 2026
12:14
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Diffraction of a Gaussian beam by a logarithmic axicon.
Victor V Kotlyar1, Alexey A Kovalev, Sergey S Stafeev
1Laser Measurements Laboratory, Image Processing Systems Institute of the Russian Academy of Sciences, 151 Molodogvardejskaya Street, Samara 443001, Russia.
Summary
Researchers derived an analytical relationship for Gaussian beam diffraction by a logarithmic axicon (LA). This optical element allows for sub-wavelength focusing, potentially breaking the diffraction limit for enhanced light intensity control.
Area of Science:
- Optics and Photonics
- Diffraction Theory
- Beam Shaping
Background:
- Gaussian beams are fundamental in laser optics.
- Axicons are optical elements that transform a Gaussian beam into a non-diffracting Bessel beam.
- The diffraction limit restricts the minimum focused spot size.
Purpose of the Study:
- To derive an analytical relationship for axial light intensity of a Gaussian beam diffracted by a logarithmic axicon (LA).
- To investigate the relationship between the effective radius of the diffraction pattern and the LA parameter.
- To explore the potential of LA for sub-wavelength focusing beyond the conventional diffraction limit.
Main Methods:
- Analytical derivation of light intensity distribution.
- Development of an evaluation formula for the effective radius of the diffraction pattern.
- Finite-difference time-domain (FDTD) based simulation for validating the findings.
Main Results:
- An explicit analytical relationship for axial light intensity was derived.
- The effective radius of the diffraction pattern is inversely proportional to the LA 'force' parameter.
- FDTD simulations demonstrated that LA can achieve a Full Width at Half Maximum (FWHM) as small as one-fifth of the illumination wavelength, surpassing the diffraction limit.
Conclusions:
- Logarithmic axicons offer a novel approach to control and focus light.
- LA enables overcoming the diffraction limit, leading to highly confined light spots.
- This research has implications for applications requiring ultra-fine light manipulation.
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