Generalized angle-orbital-angular-momentum Talbot effect

\nLight containing twisted phase structures, i.e. light carrying orbital angular momenta (OAM), when propagating inside ring-core fibres leads to a complex interference dynamics resulting in the fundamental self-imaging phenomenon known as the Talbot effect in the angular domain. We study the effect in the classical and quantum optics domain and show that it can be used to implement higher-order beams splitters. Interestingly, such beam splitting operations become more compact the higher the splitting ratio. In addition, we show that a similar self-imaging effect appears for whispering gallery modes carrying OAM in step-index multi-mode fibres, which enables the application of the angular Talbot effect in off-the-shelf components. Finally, we extend the study of the angular Talbot effect through combing it with its Fourier-analogue, i.e. the Talbot effect in orbital angular momentum space. Thereby we implement the generalized angle-orbital-angular-momentum Talbot effect, which enables full control over the angular intensity distribution as well as the OAM spectrum of the light field. Moreover, the complex self-imaging dynamics can be used to sort OAM light fields, in principle, without any crosstalk and, thus, can be seen a promising method for OAM multiplexing schemes.\n