Direct generation of helical Mathieu-Gauss beams using phase-only profile

Zheng Xu; Yubo Shi; Xuemei Ren; Jianrong Shi; Boyuan Tang; Xiaojun Liu

doi:10.1121/10.0037091

Direct generation of helical Mathieu-Gauss beams using phase-only profile

J Acoust Soc Am. 2025 Jul 1;158(1):99-107. doi: 10.1121/10.0037091.

Authors

Zheng Xu¹, Yubo Shi¹, Xuemei Ren¹, Jianrong Shi¹, Boyuan Tang¹, Xiaojun Liu²

Affiliations

¹ Institute of Acoustics, Tongji University, Shanghai 200092, China.
² Key Laboratory of Modern Acoustics, School of Physics, Nanjing University, Nanjing 210093, China.

PMID: 40607779
DOI: 10.1121/10.0037091

Abstract

Diffraction-free beams, which maintain invariant transverse amplitude profiles during free-space propagation and are self-reconstructing after interactions with obstacles, provide important advantages for applications, including particle manipulation, imaging, and communication systems. This work demonstrates a simplified phase-only method to generate helical Mathieu-Gauss (HMG) beams using a single-step phase modulation process during diffraction. Numerical simulations confirm that the beams generated using this method exhibit propagation invariance and spatial characteristics that match theoretical HMG beam properties closely. An approximate analytical expression for the required phase distribution that eliminates the conventional computationally intensive Mathieu function calculations is proposed. When compared with existing techniques, this approach achieves mathematical simplification without compromising the beam quality and, thus, offers a practical alternative for acoustic applications that require structured beam fields.