abstract
- 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. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.