Electromagnetic Vortex Topologies from Sparse Circular Phased Arrays

Structured vortex waves have numerous applications in optics, plasmonics, radio-wave technologies and acoustics. We present a theoretical study of a method for generating vortex states based on coherent superposition of waves from discrete elements of planar phased arrays, given limitations on an element number. Using Jacobi-Anger expansion, we analyze emerging vortex topologies and derive a constraint for the least number of elements needed to generate a vortex with a given leading-order topological charge.