Talbot-effect-based multiplication of Laguerre–Gaussian beams with non-zero radial indices: From theory to experimental realization

We present a Talbot self-imaging inspired method for multiplying Laguerre–Gaussian (LG) beams of non-zero radial indices. We explore theoretically and experimentally the LG beam diffraction from two-dimensional (2D) periodic structures. In particular, we determine near-field LG beam diffraction patterns from a 2D binary grating of a small opening ratio (OR). We demonstrate that incident LG beam intensity patterns are reproduced as images of individual square apertures of the grating in certain Talbot planes. We also investigate the impact of the number of fractional-Talbot and Talbot planes on the quality of the generated 2D array of multiplexed LG modes. Our theoretical predictions are in good agreement with our experiments. Our method can find applications in optical communication, optical tweezing, multi-particle trapping, screening, and micro-manipulation.