Multiple oil drops bouncing on the surface of a vertically vibrating bath of the same oil exhibit self-organization behavior in two dimensions [S. Protière, Y. Couder, E. Fort, and A. Boudaoud, J. Phys.: Condens. Matter 17, S3529 (2005)]. We describe further the morphology and dynamic behavior of stable assemblies of large bouncing oil drops, for which we find that both the spacing and the lattice structure itself change with frequency, with variants of both square and hexagonal structures being observed. Large "rafts" of drops form soft triangular lattices with faceted boundaries. Small clusters of drops are unstable to coherent, collective spinning under certain driving conditions, manifesting spontaneous rotational symmetry breaking.

The optical Talbot effect has been used to explore the topological charges of optical vortices. We recorded the self-imaging of a diffraction grating in the near-field regime with the optical vortex of several topological charges. Our twisted light was generated by a spatial light modulator (SLM). Previous studies showed that interferometric methods can determine the particular orbital angular momentum (OAM) states, but a large number of OAM eigenvalues are difficult to distinguish from the interference patterns. Here, we show that the Talbot patterns can distinguish the charges as well as the OAM of the vortices with high orders. Owing to the high sensitivity and self-imaging of the Talbot effect, several OAM eigenvalues can be distinguished by direct measurement. We check the experimental results with our theory. The present results are useful for classical and quantum metrology as well as future implementations of quantum communications.

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