Ideal Kerker scattering by homogeneous spheres: the role of gain or loss

TL;DR

This paper revisits the conditions for ideal Kerker scattering in homogeneous spheres, revealing that gain or loss can sometimes aid in achieving zero backward scattering when multiple multipoles are considered.

Contribution

It clarifies the role of gain and loss in multipole matching for Kerker scattering, extending previous results by considering multiple multipole orders simultaneously.

Findings

Perfect multipole matching of a fixed order cannot produce ideal Kerker scattering when two multipoles are involved.

Loss or gain can help eliminate backward scattering when multiple multipoles of different orders are considered.

Ideal Kerker scattering is hindered by gain or loss when only a single multipole order is involved.

Abstract

We reexamine a recent work [Phys. Rev. Lett. \textbf{125}, 073205 (2020)] that investigates how the optical gain or loss (characterized by isotropic complex refractive indexes) influences the ideal Kerker scattering of exactly zero backward scattering. There it has been rigourously proved that, for non-magnetic homogeneous spheres with incident plane waves, either gain or loss prohibits such ideal Kerker scattering, provided that only electric and magnetic multipoles of a specific order are present and contributions from other multipoles can all be made precisely zero. Here we reveal that, when two multipoles of a fixed order are perfectly matched in terms of both phase and magnitude, multipoles of at least the next two orders cannot possibly be tuned to be all precisely zero or even perfectly matched, and consequently cannot directly produce ideal Kerker scattering. Moreover, we further demonstrate that, when multipoles of different orders are simultaneously taken into consideration, the loss or gain can serve as a helpful rather than harmful contributing factor, for the eliminations of backward scattering.