Analysis of Anapole States in Dielectric Spheres and Application to Near-Field Enhancement

Anapole states in isolated, homogeneous, and isotropic dielectric spheres are studied theoretically in accordance with Mie theory, numerically by full-wave electromagnetic simulations and by measurements at microwave and millimeter-wave frequency. Depending on the size and material properties of the dielectric spheres, the practical limitations of detection and possible applications of nonradiating anapole states are investigated. The electromagnetic signature, generated by anapole states of a spherical dielectric scatterer, in terms of finite extinction cross section, is verified by measurements, for both its electric and magnetic versions, in silicon and alumina spheres, respectively. In addition, the existence and the detection of higher order and hybrid anapole states are demonstrated. Finally, an approach to engineer electric field hotspots in a subwavelength-sized gap between two magnetic anapole coupled alumina ceramic spheres is demonstrated.