Reactive helicity and reactive power in nanoscale optics: Evanescent waves. Kerker conditions. Optical theorems and reactive dichroism

Considering time-harmonic optical fields, we put forward the complex helicity and its alternating flow, together with their conservation equation: the complex helicity theorem. Its imaginary part constitutes a novel law that rules the build-up of what we establish as the reactive helicity through its zero time-average flow. Its associated reactive flow and the imaginary Poynting momentum that accounts for the accretion of reactive power are illustrated in two paradigmatic systems: evanescent waves and fields scattered from magnetodielectric dipolar nanoparticles. As for the former, we show that its reactive helicity may be experimentally observed as we introduce a reactive spin momentum and a reactive orbital momentum in terms of which we express the imaginary field momentum, whose transversal component produces an optical force on a magnetoelectric particle that, as we illustrate, may surpass and can be discriminated from the known force due to the so-called extraordinary momentum. We also uncover a nonconservative force on such a magnetoelectric particle, acting in the decay direction of the evanescent wave, and that may also be discriminated from the standard gradient force; thus making the reactive power of the wavefield also observable. Concerning the light scattered by magnetoelectric nanoparticles, we establish two optical theorems that govern the accretion of reactive helicity and reactive power on extinction of incident wave helicity and energy. Like a nule total, i.e., internal plus external, reactive power is at the root of a resonant scattered power, we show that a zero total reactive helicity underlies a resonant scattered helicity. These reactive quantities are shown to yield a novel interpretation of the two Kerker conditions, which we demonstrate to be linked to an absence, or minimum, of the overall scattered reactive energy. Further, we demonstrate that the first Kerker condition, under which the particle becomes dual on illumination with circularly polarized light, amounts to a nule overall scattered reactive helicity. Therefore these two reactive quantities are shown to underly the directivity of the particle scattering and emission. In addition, we discover a discriminatory property of the reactive helicity of chiral light incident on a chiral nanoparticle by excitation of the external reactive power. This should be useful for optical near field enantiomeric separation, an effect that we call reactive dichroism.

Automated summary

This paper introduces a new theorem in the study of time-harmonic optical fields, discussing complex helicity and its associated reactive quantities. The reactive properties are illustrated through experiments with evanescent waves and fields scattered from magnetodielectric dipolar nanoparticles. Additionally, two optical theorems are established to explain the accumulation of reactive helicity and power in scattered light. This study provides insights into the reactive behavior of light and nanoparticles, which can have applications in optical phenomena such as enantiomeric separation.