Non-Diffracting Polarisation Features around Far-Field Zeros of Electromagnetic Radiation

Abstract: Light from any physical source diffracts over space, as spherical wavefronts grow and energy density is spread out. Diffractive effects pose fundamental limits to light-based technologies, including communications, spectroscopy, and metrology. Polarisation becomes paraxial in the far field limit and, by ignoring longitudinal field components, the rich physics of non-paraxial fields which exist in near-fields or a beam's tight focus are lost. The longitudinal field cannot, however, be ignored when transverse field components vanish (in a transverse field zero) and carry a small non-paraxial region to infinity. We show that a transverse field zero is always accompanied by non-diffracting polarisation structures, whose geometries are independent of the distance to the source, including an enclosing intensity ratio tube, and parallel, non-diverging polarisation singularities. We illustrate these features in multipole radiation and in double slit interference, two examples which have time-fixed transverse field zeros. Non-diffracting structures with changing position are coupled to time-varying zeros, which are present in all far field radiation.