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We study the generalized fractional Hermite-Gaussian (GFHG) beams, a type of structured light based on the fractionalization of Hermite functions. By using a fractional derivative based on Fourier transform, we find that these beams act as a bridge between integer-order Hermite-Gaussian beams, yet they display an asymmetric light field distribution in their transverse profile. Notably, unlike traditional integer-order Hermite-Gaussian beams, we find that to ensure light localization, there is a critical threshold value between the fractional Hermite functions and the corresponding Gaussian apodization.

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Fractionalization of Hermite-Gaussian Optical Beams by a Fourier Approach

  • 章节

  • 发表日期：

    2025年

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  • Ruben Aguilar-Marquez,
  • Javier Alejandro Pérez-Garza,
  • Arath Maldonado-Traconis,
  • Pedro Oliva-Sanchez,
  • Servando Lopez-Aguayo

摘要

We study the generalized fractional Hermite-Gaussian (GFHG) beams, a type of structured light based on the fractionalization of Hermite functions. By using a fractional derivative based on Fourier transform, we find that these beams act as a bridge between integer-order Hermite-Gaussian beams, yet they display an asymmetric light field distribution in their transverse profile. Notably, unlike traditional integer-order Hermite-Gaussian beams, we find that to ensure light localization, there is a critical threshold value between the fractional Hermite functions and the corresponding Gaussian apodization.