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The Talbot self-imaging phenomenon is a fundamental interference effect that is natural to all waves with a periodic structure. We theoretically and experimentally study the Talbot effect for optical waves in the transverse angular domain using whispering-gallery modes of step-index multimode fibers, which carry a high orbital angular momentum and fulfill the required quadratic dispersion relation. By using the complex interference along the core-cladding interface of these fibers, we experimentally demonstrate that the high-order fractional Talbot effect can be used to implement 9- and 30-port beamsplitters using only off-the-shelf components in a compact arrangement. In addition, we show that the beamsplitters can be efficiently interfaced with single-mode fibers, such that our work not only extends the recent developments on the angular Talbot effect to widely available step-index multimode fibers, but also demonstrates a powerful application as a signal multiplexer, which becomes more compact as the number of channels is increased., Comment: 10 pages, 8 figures

The Talbot effect describes periodic revivals of field patterns and is ubiquitous across wave systems. In optics, it is mostly known for its manifestations in space and time, but is also observed in the wavevector and frequency spectra owing to the Fourier duality. Recently, the Talbot self-imaging has been shown separately in the azimuthal angle and orbital angular momentum (OAM) domains. Here, we unveil the missing link between them and demonstrate the generalized angle-OAM Talbot effect. Versatile transformations of petal fields and OAM spectra are experimentally showcased, based on the synergy of angular Talbot phase modulation and light propagation in a ring-core fiber. Moreover, the generalized self-imaging concept leads to new realizations in mode sorting, which separate OAM modes in a modulo manner, theoretically free from any crosstalk within the congruence classes of OAM modes. We design and experimentally construct various mode sorters with excellent performance, and show the unconventional behavior of Talbot-based sorters where neighboring OAM modes can be mapped to positions far apart. Besides its fundamental interest, our work finds applications in OAM-based information processing, and implies that the physical phenomena in time-frequency and angle-OAM domains are broadly connected as well as their processing techniques may be borrowed interchangeably.

Wave propagation on the surface of cylinders exhibits interferometric self imaging, much like the Talbot effect in the near-field diffraction at periodic gratings. We report the experimental observation of the cylindrical Talbot carpet in weakly-guiding ring-core fibers for classical light fields. We further show that the ring-core fiber acts as a high-order optical beamsplitter for single photons, whose output can be controlled by the relative phase between the input light fields. By also demonstrating high-quality two-photon interference between indistinguishable photons sent into the ring-core fiber, our findings open the door to applications in optical telecommunications as a compact beam multiplexer as well as in quantum information processing tasks as a scalable realization of a linear optical network., Comment: 9 pages, 8 figures