Influence of the Radial Index on the Stability of Laguerre-Gaussian Vortex Beams in Turbulent Media

This paper explores the selective suppression of Laguerre-Gaussian modes that are most vulnerable to atmospheric turbulence. Decomposing these modes into an orthogonal Zernike polynomial basis reveals significant differences in stability depending on the radial and azimuthal indices. We demonstrate that modes with a higher radial index exhibit minimal distortion of the transverse beam profile, providing a clear criterion for filtering out less resilient modes in turbulent media. Furthermore, we derive an analytical expression relating the required receiver aperture to the radial and azimuthal indices.