Momentum-Space Geometric Structure of Helical Evanescent Waves and Its Implications on Near-Field Directionality

Abstract

In this paper, a momentum-space geometrical structure in helical evanescent electromagnetic waves is revealed. It is shown that for every helical evanescent wave on a helicity-dependent half tangent line in momentum space, the orientation of each of its field, spin, and Poynting vectors is the same. This geometric structure is revealed in a remarkable relation between the far-field and near-field components of the angular spectrum. Any general evanescent wave vector is linked to two points on the ${k}_{\ensuremath{\rho}}={k}_{0}$ circle of propagating wave vectors via two helicity-dependent tangent lines. Knowing the field of a general dipolar source on the ${k}_{\ensuremath{\rho}}={k}_{0}$ circle is sufficient to determine its entire evanescent angular spectrum. By applying this concept, we gain insights into near-field directionality by showing that every zero in the angular spectrum is a helicity singularity where two half tangent lines of opposite helicity intersect. A powerful method for the synthetic design of near-field directional sources is also devised, using structured helical illumination to gain full control of the near-field directionality. The results provide fundamental insight into helical evanescent waves and have implications in areas where chiral light-matter interaction plays a central role.