Talbot effect of skew-periodic structures under structured light beam illumination

In this study, we explore the near-field diffraction of Laguerre-Gaussian (LG) beams, including those with both zero and non-zero radial indices, through two-dimensional (2D) non-orthogonal periodic structures with a filling factor of approximately 0.1. The 2D periodic structure, characterized by rhombus-shaped unit cells, is fabricated by superimposing two one-dimensional (1D) binary gratings on glass substrates, enabling precise control of the angle between their lines. Our simulations and experiments reveal that specific angles between the grating lines induce the replication of the incident beam at designated Talbot distances. Furthermore, a minor adjustment in the angle, approximately 0.7 degrees, results in the formation of a 2D array of Hermite-Gaussian (HG) modes corresponding to the incident LG modes. We present findings on the replication of LG beams with various radial indices when diffracted by non-orthogonal 2D periodic structures, identifying specific angles where this phenomenon occurs relative to the Talbot planes. A general formulation is proposed to determine these angles, facilitating the multiplication of the incident beam or the creation of an HG mode array at specific Talbot distances. Experimental results confirm the accuracy of this formulation. This technique for generating HG/LG arrays in the near field at specific Talbot planes has potential applications in multi-particle trapping and manipulation within the micrometer to millimeter range, eliminating the need for microscopes or spatial light modulators.