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Updated: Jul 18, 2026
12:14
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Normalization of the Mathieu-Gauss optical beams.
Julio C Gutiérrez-Vega1, Miguel A Bandres
1Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey, México. juliocesar@itesm.mx
Summary
A new series scheme determines normalization constants for Mathieu-Gauss (MG) optical beams. This method uses Bessel-Gauss (BG) beams for synthesis, ensuring accurate normalization for advanced optical beam applications.
Area of Science:
- Optics and Photonics
- Mathematical Physics
Background:
- Mathieu-Gauss (MG) beams are complex optical beam solutions with unique propagation properties.
- Accurate normalization of these beams is crucial for theoretical and experimental studies.
Purpose of the Study:
- To develop a robust series scheme for calculating normalization constants of MG beams.
- To determine the optimal number of Bessel-Gauss (BG) beams required for synthesizing MG beams within a specified tolerance.
Main Methods:
- Expansion of MG beams using a series of Bessel-Gauss (BG) beams.
- Analysis of the structure of normalization factors for MG beams.
- Development of rapidly convergent series for calculating normalization constants.
Main Results:
- A systematic scheme for determining normalization constants of even and odd MG beams is presented.
- The study quantifies the number of BG beams needed for accurate MG beam synthesis.
- The proposed normalization factors are independent of the Mathieu function normalization choice.
Conclusions:
- The developed series scheme provides a precise and efficient method for normalizing MG beams.
- This approach facilitates the practical application and further research of MG optical beams.
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