Cosine-multi-Gaussian correlated beam and its propagation properties in free space and oceanic turbulence

Abstract We introduce a cosine-multi-Gaussian correlated beam (cMGCB), and the intensity of cMGCB can evolve into four beamlets with flat-topped profiles under appropriate parameter settings. To describe its propagation in realistic underwater channels, we derive the corresponding propagation expressions of such cMGCB in anisotropic oceanic turbulence based on the Huygens–Fresnel integral. Using these expressions, we systematically investigate how the beam parameters, oceanic-turbulence strength, and propagation distance affect the evolution of the cMGCB during propagation. The results indicate that, in free space, increasing the multi-Gaussian order improves the preservation of beamlet flatness. In contrast, in oceanic turbulence the beamlet flatness degrades progressively and the beamlets tend to evolve toward a Gaussian-like profile. Furthermore, under stronger turbulence, the initially separated beamlets may merge into a single spot. These findings provide a useful model for generating four flat-topped beamlets and offer guidance for applying cMGCB in oceanic-turbulence environments.