  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 quasitranslational
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 conversation law of OAM was
revealed. A liquid crystal photopatterning QPS is fabricated to demonstrate the
above characteristics. Dynamic reconfigurable manipulation of optical
singularities was 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 highdimensional quantum state
generation.
