Dimensional properties of a diffracted vortex beam by triangular aperture

The vortex beam has become an indispensable tool in various fields such as particle physics, imaging, and optical communication systems. A key feature of the vortex beam is its topological charge (TC), which quantifies the amount of orbital angular momentum carried by the beam. Accurate determination of the TC is crucial for all vortex beam applications. A commonly used method for TC measurement involves diffraction through a triangular aperture. However, there remains a gap in the literature regarding the precise dimensional constraints between the vortex beam and the triangular aperture. In this study, we present a concise and rigorous mathematical model, supported by numerical simulations, to determine the dimensional limits of both vortex beams and triangular apertures, based on geometric considerations.