Generation of coaxial arrays of petal-like beams and ring lattice structures with controllable rotation using composite spiral multi-value zone plates

We present an approach for generation of axial arrays of petal-like beams and optical ring lattices. Petal-like modes are remarkably structured optical vortices generated by superposition of two Laguerre-Gauss beams with opposite signs, which are capable of applying torques to micro-particles. However, interferometric approaches are complex and sensitive to experimental errors. The approach is based on the concept of multi-value phase Fresnel zone plates (MVZPs) to generate a required number of coaxial foci with uniform intensity, and the combinatory methods of zone plates. Here, we make a phase structure using a composite spiral multi-value phase zone plate (CSMVZP) which combines two spiral MVZPs (SMVZP) with two different embedded topological charges (TCs). For a CSMVZP which is generated by two SMVZPs with two different and oppositely signed TCs, a petal-like mode will be generated at the mth diffraction order in each focal plane along the optical axis. In addition, we can achieve a constant rotation rate, regardless of the diffraction order in the generated structured modes by introducing a transverse phase shift between the two composited SMVZPs.