Scattering of tunable Laguerre–Gaussian modes: controlled functional engineering of speckle size

Abstract Optical random patterns, commonly known as speckles, have gained significant interest due to their wide range of applications in imaging, metrology, and cryptography. In this work, we utilise controlled spatial modes of light to generate speckle patterns whose size can be precisely tuned to obtain the desired functional variations. Unlike conventional approaches, where the speckle size varies inversely with the topological charge, we demonstrate that speckle patterns exhibit inverse, constant, or modulated (sinusoidal and Gaussian) functional dependencies on TC. To realize this control, we scatter four tunable Laguerre–Gaussian beams through a rough surface and show that the resulting speckle sizes can be tailored and even rendered invariant through an appropriate scaling factor. These speckle size invariant characteristics open new avenues for robust orbital angular momentum encoding, with potential benefits for free-space optical communications, imaging through scattering media, and speckle-based information processing.