On the helicity conservation for Mie optical cavities

TL;DR

This paper investigates the behavior of light helicity inside spherical cavities, showing that in lossless spheres helicity cannot be conserved or flipped, while in lossy or gain materials the helicity behavior differs significantly.

Contribution

It provides a comprehensive analytical analysis of helicity conservation inside Mie spheres, revealing conditions under which helicity is conserved, flipped, or not conserved.

Findings

Helicity inside lossless spheres cannot be conserved or sign-flipped.

Helicity can be conserved inside lossy spheres.

Helicity can be flipped in spheres with gain.

Abstract

The study of helicity in the context of light-matter interactions is an increasing area of research. However, some fundamental aspects of the helicity content of light fields inside scatterers have been overlooked. In this work, we demonstrate that the helicity of light fields inside lossless spherical cavities cannot be either conserved or sign-flipped as a result of a scattering event. The underlying reason is that the internal electric and magnetic Mie coefficients cannot simultaneously oscillate with equal amplitude and equal/opposite phase. Our analytical demonstration is fulfilled regardless of the refractive index, sphere size, and multipolar order. In addition, we show that the helicity of light fields inside lossy spheres can be conserved. This fact is in striking contrast to the behavior of the scattered field, whose helicity content cannot be conserved precisely when the sphere has losses. Finally, we show that the helicity content of internal fields can be flipped for materials with gain.