We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.
The Talbot effect has been extensively investigated in one-dimensional and orthogonal two-dimensional periodic structures; however, its manifestation in skew-periodic lattices remains unexplored. Here, we investigate the Talbot effect in skew-periodic structures using Laguerre-Gaussian beams with both zero and non-zero radial indices. The skew-periodic structures are fabricated by superimposing two one-dimensional binary gratings with small filling factors, forming rhombus-shaped unit cells with tunable vertex angles. We show that the vertex angle serves as a control parameter for modulating near-field diffraction. At specific angles, self-replication of the incident beam occurs at certain Talbot distances, while slight deviations lead to the Hermite-Gaussian mode arrays. A theoretical model predicts the critical vertex angles for self-imaging and mode transformation, supported by experimental results. We also introduce the vertex-angle Talbot carpet, a tool for identifying true self-imaging planes in skewed lattices by mapping diffraction intensity versus vertex-angle, rather than propagation distance. This approach opens a regime in Talbot physics and enables the generation of structured light fields with adjustable geometries, offering potential applications in optical trapping, lattice-based systems, and multi-atom interactions-providing a low-cost alternative to spatial light modulators.