Electromagnetic vortex topologies from sparse circular phased arrays

Abstract

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 leading-order vortex with a given topological charge.

Topology and Polarization of Optical Vortex Fields from Atomic Phased Arrays

“…For the scalar fields, this transition was previously demonstrated in Ref. [16]. The present paper fully considers a vector nature of the electromagnetic fields.…”

“…Summation over j selects certain orders of Bessel vortices n, while other order terms are canceled, as was demonstrated for scalar fields in [16]. After the summation of radiation from individual atoms, the final result for the field is:…”

“…If it is satisfied, then all three components of the field have vortex structures (i.e., show a phase singularity). When m z = −1, the condition becomes N ≥ 2l + 1, which is the condition for a scalar vortex field [16]. However, for m z = +1, the conditions are different.…”

“…[15]). In the previous theoretical study [16], we considered scalar fields from 2D arrays of point-like emitters. In the present paper, we extend our formalism to 3D vector fields of a phased atomic antenna array and analyze the topological and polarization properties of the emitted radiation.…”