Total angular momenta quantization of dielectric sphere modes

Abstract

Spherical particles both dielectric and metallic are essential building blocks in nanophotonics. During the recent rapid development of Mie-tronic — nanophotonics devices heavily using various features of the Mie-resonances — the deep fundamental investigation of the eigenmodes of such particles by using the novel tools is still relevant and currently important. Moreover, eigenmodes of a sphere are closely related to the Vector Spherical Harmonics (VSH) which are widely used in the multipolar decomposition to analyze less symmetric structures. In this work, we study in detail the canonical spin and angular momenta (AM), helicity, and other properties of the eigenmodes of dielectric (nondispersive) and metallic (dispersive) spheres. We show that the canonical momentum density of the AM is quantized and has a close relation to the quantum picture of a single photon. Our work provides a solid platform for future studies and applications of the AM transfer from near fields of spherical particles to the matter in its vicinity.