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

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.