Electromagnetic vortex topologies from sparse circular phased arrays

H Wang,K Szekerczes,A Afanasev

doi:10.1088/2399-6528/ac5089

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 vortex with a given leading-order topological charge.

Highlights

Introduction and MotivationExcitation of topological states from a discrete number of wave sources was considered for quantum optics with atomic phase arrays [1], plasmonic nano-antenna arrays [2, 3], acoustic actuators [4], and RF vortices for quantum networking [5]
We address a question of what vortex topologies are possible given a limited number of elements
We provide a mathematical formalism for vortex formation with arbitrary element numbers that may be used as a guidance for generation of topological states with sparse phased arrays or a superposition of laser beams

Summary

Introduction and Motivation

Excitation of topological states from a discrete number of wave sources was considered for quantum optics with atomic phase arrays [1], plasmonic nano-antenna arrays [2, 3], acoustic actuators [4], and RF vortices for quantum networking [5]. We provide a mathematical formalism for vortex formation with arbitrary element numbers that may be used as a guidance for generation of topological states with sparse phased arrays or a superposition of laser beams. Vortex waves may be generated by a smaller number of elements - the term sparse arrays - with an input phase parameter l not necessarily matching a topological charge of the generated vortex. Higher-order topological charges are involved, but choosing a smaller area around the origin where kr < 1 would lead to power suppression of higher-order states It follows from Bessel function’s behavior at small arguments, Jn(kr) ∝ (kr)n, that is in agreement with leading terms of Taylor expansion from Table 1

Extension to 3D Case

Numerical Examples and Discussion

Summary