Generation of the compound optical vortex array wave field

We give out an universal function of the compound vortex lattice fields through Fourier transform of several δ functions with different phases. Based on this method, we study different classes of vortex lattice and conclude a series of interesting laws. As special cases, we introduce the classes of fivefold and eightfold lattice fields from the intensity modulation to phase modulation in detail, in which the lattice pattern for varying phase difference of adjacent δ functions may be nearly similar. The experimental realization of this compound vortex lattices is by using the numerically calculated phase mask and a spatial light modulator(SLM).