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Shaping Gaussian modes through truncation and apodization: theory and interpretation.

Abdelhalim Bencheikh, Sofiane Haddadi

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

|December 18, 2025

Summary

This study introduces a low-cost method for beam shaping by truncating Gaussian beams. This technique efficiently creates structured light patterns like flat-top and ring shapes for compact optical systems.

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Area of Science:

Optics and Photonics
Laser Physics
Optical Engineering

Background:

Transforming Gaussian beams into desired intensity profiles (e.g., flat-top, ring-shaped) is crucial for various applications.
Traditional beam-shaping methods (spatial light modulators, digital micromirror devices, interferometry) are often complex, bulky, and costly.

Purpose of the Study:

To investigate a simpler, cost-effective approach for generating structured light beams.
To theoretically analyze the beam-shaping capabilities of soft and hard truncation methods.
To explore the formation of various beam profiles in both Cartesian and cylindrical coordinates.

Main Methods:

Mathematical asymptotics and Fourier optics were employed for theoretical analysis.
The study examined beam shaping in Cartesian and cylindrical coordinate systems.
Various beam types, including Hermite-Gaussian, Laguerre-Gaussian, and Bessel beams, were analyzed under truncation.

Main Results:

Truncation of Gaussian beams effectively generates structured intensity profiles like flat-top and ring shapes.
The theoretical framework explains the far-field beam profile formation based on truncation and spatial modulation.
Both soft and hard truncation methods were analyzed for their effectiveness in beam shaping.

Conclusions:

Soft and hard truncation offer a simple, low-cost alternative for Gaussian beam shaping.
The developed framework aids in understanding and designing compact, passive beam-shaping systems.
This approach facilitates the creation of structured light for diverse optical applications.