Can a nonradiating mode be externally excited? Nonscattering states vs. embedded eigenstates

TL;DR

This paper clarifies the conditions under which nonradiating modes, such as embedded eigenstates and anapoles, can be externally excited in open cavities, emphasizing the role of Lorentz reciprocity and external fields.

Contribution

It demonstrates that Lorentz reciprocity prevents external excitation of radiationless eigenmodes, clarifying misconceptions about exciting nonradiating states in open cavities.

Findings

Radiationless scattering states are not true eigenmodes and can be externally excited.

Lorentz reciprocity theorem forbids external excitation of embedded eigenstates.

External fields are necessary to sustain radiationless anapole distributions.

Abstract

In this Letter, we discuss the general problem of exciting radiationless field distributions in open cavities, with the goal of clarifying recent findings on this topic. We point out that the radiationless scattering states, like anapoles, considered in several recent studies, are not eigenmodes of an open cavity; therefore, their external excitation is neither surprising nor challenging (similar to the excitation of nonzero internal fields in a transparent, or cloaked, object). Even more, the radiationless anapole field distribution cannot be sustained without the actual presence of external incident fields. Conversely, we prove that the Lorentz reciprocity theorem prevents the external excitation of radiationless optical eigenmodes, as in the case of embedded eigenstates and bound states in the continuum in open cavities. Our discussion clarifies the analogies and differences between invisible bodies, nonradiating sources, anapole scatterers and emitters, and embedded eigenstates, especially in relation to their external excitation.