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.

Modern astronomers enjoy access to all-sky images across a wide range of the electromagnetic spectrum from long-wavelength radio to high-energy gamma rays. The most prominent feature in many of these images is our own Galaxy, with different features revealed in each wave band. Gravitational waves (GWs) have recently been added to the astronomers’ toolkit as a nonelectromagnetic messenger. To date, all identified GW sources have been extra-Galactic and transient. However, the Milky Way hosts a population of ultracompact binaries (UCBs), which radiate persistent GWs in the milliHertz band that is not observable with today’s terrestrial gravitational-wave detectors. Space-based detectors such as the Laser Interferometer Space Antenna will measure this population and provide a census of their location, masses, and orbital properties. In this work, we will show how this data can be used to form a false-color image of the Galaxy that represents the intensity and frequency of the gravitational waves produced by the UCB population. Such images can be used to study the morphology of the Galaxy, identify interesting multimessenger sources through cross-matching, and for educational and outreach purposes.