Observation of the spatially structured Montgomery effect in free space

Talbot effect is a lens-less self-imaging phenomenon with a wide range of applications in optics. A lesser-known yet potentially more versatile Montgomery effect generalizes self-imaging to aperiodic structures. We report the first, to our knowledge, direct observation of the spatially structured Montgomery effect in free space. Using a dynamic optical hologram to discretize radial spatial frequencies, we demonstrate self-imaging at distances ranging from 30 to 100 mm. Our method independently controls the focal spot size and self-imaging period, enabling dynamic three-dimensional light patterns. We also show the arbitrary tunability of the transverse profile by demonstrating revivals of Laguerre–Gaussian, Hermite–Gaussian, Ince–Gaussian modes, and Airy beams. These findings open opportunities for multi-plane microscopy, optical atom traps, and quantum atomic systems.