Evolution of orbital angular momentum in a soft quasi-periodic structure with topological defects

A continuously deformative space possesses trivial or nontrivial topological characteristics depending on the associated homotopy groups associated with spaces describing the physical processes. Moreover, the interaction of spatial warping and structural symmetry always presents fantastic phenomena, especially in the systems with unique symmetrical properties such as quasicrystals. Here, we propose a quasi-periodic structure (QPS) with topological defects. The analytical expression of the corresponding Fourier spectrum is derived, which reflects the combined effects of topological structure and quasi-translational symmetry. Light-matter interaction therein brings unusual diffraction characteristics with exotic evolution of orbital angular momentum (OAM). Long-range correlation of QPS resulted in multi-fractal and pairwise distribution of optical singularities. A general conservation law of OAM is revealed. A liquid crystal photopatterned QPS is fabricated to demonstrate the above characteristics. Dynamic reconfigurable manipulation of optical singularities is achieved. Our approach offers the opportunity to manipulate OAM with multiple degrees of freedom, which has promising applications in multi-channel quantum information processing and high-dimensional quantum state generation.