Efficient generation of coherently rotating galaxy-like beams via Gaussian diffraction from spiral-like structures

Recently, galaxy-like rotating beams have been introduced, generated by diffracting a plane wave (PW) from spiral-like structures (SLSs) possessing simultaneous radial and angular periodicities. Under PW illumination, the resulting diffraction field forms a beam-like pattern in which only the central region rotates during propagation, while the outer portions remain stationary. Here, we show that replacing the PW with a Gaussian beam (GB) fundamentally changes the propagation dynamics: the entire diffraction pattern undergoes coherent angular rotation, forming a fully rotating structured beam. This coherent rotation develops progressively as the beam propagates. The diffracted field does not emerge fully formed at the SLS plane; rather, a central region gradually develops into a fully rotating, non-diffracting galaxy-like beam. In this regime, the optical power transferred to the coherently rotating area becomes equal to the total transmitted power through the SLS-an efficiency not achievable under PW illumination. Over long-range propagation, despite retaining its non-diffracting nature, a central Gaussian-like peak gradually emerges and becomes increasingly dominant, while neighboring spots broaden and partially overlap, leading to a gradual degradation of spot visibility. We further analyze the impact of both the GB waist and the geometric curvature of the SLS spokes. Reducing the beam waist enhances power concentration in the central rotating spots, while increasing the spoke curvature by one order of magnitude induces a well-defined rotational shift that is two orders of magnitude smaller along the propagation distance. Most importantly, we establish a general design rule: under PW illumination, the radius of the circle on which the main intensity maxima are located stops growing beyond a certain propagation distance, defining the boundary radius of the rotating region. Coherent full-pattern rotation under GB illumination is then guaranteed whenever the beam waist does not exceed this boundary radius, with a smaller waist bringing the onset of full rotation to a shorter propagation distance. These results highlight effective routes for engineering high-efficiency rotating beams with arbitrary spot numbers, strong central-spot power, and stable propagation, offering promising applications in optical manipulation-such as simultaneous translation and rotation of microscopic objects-and providing a means for guiding microscopic particles across heterogeneous and structurally complex optical environments.