We have investigated the symmetry properties and the associated conserved quantities of the electromagnetic field in search for an optimum set of tools allowing us to extract as much information as possible from electromagnetic radiation in Nature, notably radio and radar signals from space. Whereas the well-known EM linear momentum, associated with translational dynamics and force action, and the spin part of the angular momentum (SAM, wave polarisation), have been used in everyday physics and technology for nearly a century, the related but distinctively different orbital part of the EM angular momentum (OAM, “twisted photons”), associated with rotational dynamics and torque action, has only recently been recognised and utilised. Our work includes, but is not limited to, the electromagnetic orbital angular momentum (OAM) and other, related topological degrees of freedom, but aims at investigating all 23 continuous symmetries of the EM field and suggesting optimised sensor technologies.

Examples of applications of OAM such as spiral imaging of turbulent space plasma, possible tests of GR by observing Kerr metric-induced OAM in radiation from nearby rotating black holes, high-contrast coronagraphy (ten orders of magnitude), and super-resolution that exceeds the Rayleigh limit by an order of magnitude will be presented. Outlooks on and applications in wireless communications with high spectral efficiency will be made. Finally, recent experimental results on the generation and spiral spectrum analysis of radio beam vorticity will be presented.