Optical lattices and optical vortex arrays in clustered speckles

Clustered speckle, optical lattices, and their optical vortex array are subjects of interest in optical wave manipulation. In this study, disordered optical lattices and vortex arrays with different unit structures were found in the clustered speckles generated by a circularly-distributed multi-pinhole scattering screen when it was illuminated by coherent light. These structures included hexagonal lattices, kagome lattices, and honeycomb lattices. Moreover, optical lattices with asymmetric units generated by modulation of phases with non-integer multiples of 2π were discussed. Theoretical analysis and numerical calculations demonstrated that optical lattices in clustered speckles in the observation plane were generated by the phase modulations of the random scattering screen. The lattice type depended on the number of 2π multiples of the summed phase difference between the pinholes. Additionally, the conditions for the formation of periodical optical lattices and their vortex arrays were given. Different optical lattices and their vortex arrays appearing simultaneously in the clustered speckle were difficult to generate using the common multi-beam interference system. This phenomenon is of great significance in the study of the orbital angular momentum of photons and other fields.