How does zero forward-scattering in magnetodielectric nanoparticles comply with the optical theorem?

Abstract

A few decades ago, Kerker et al. [J. Opt. Soc. Am. 73, 765-767 (1983)] theoretically pointed out the interesting possibility of conceiving small magnetodielectric spheres that may provide zero scattering in the forward direction, despite significantly larger scattering in any other direction. Recent experimental and theoretical papers on the topic have further discussed this possibility in more realistic scenarios. Inspecting some of their analyses, it seems indeed possible to conceive nanoparticles characterized by a scattering pattern with a sharp minimum, although not zero, in the forward direction. From a theoretical standpoint, however, it is well known that the total scattered power from any object has to be proportional to a portion of the scattered field in the forward direction, implying that very small or zero forward scattering should be synonymous to even smaller or zero total scattering, regardless of the nature of the object and of its design. Using analytical theory and an accurate scattering formulation, we clarify the nature of this apparent paradox and the limitations of this anomalous phenomenon in terms of particle size. In this way, we shed some new light on theoretical and experimental papers on the topic, identifying relevant missteps in some of their physical interpretation, and considering the general possibility of verifying these effects. This discussion may also be relevant to some cloaking applications using exotic artificial materials. 765-767 (1983)] theoretically pointed out the interesting possibility of conceiving small magnetodielectric spheres that may provide zero scattering in the forward direction, despite significantly larger scattering in any other direction. Recent experimental and theoretical papers on the topic have further discussed this possibility in more realistic scenarios. Inspecting some of their analyses, it seems indeed possible to conceive nanoparticles characterized by a scattering pattern with a sharp minimum, although not zero, in the forward direction. From a theoretical standpoint, however, it is well known that the total scattered power from any object has to be proportional to a portion of the scattered field in the forward direction, implying that very small or zero forward scattering should be synonymous to even smaller or zero total scattering, regardless of the nature of the object and of its design. Using analytical theory and an accurate scattering formulation, we clarify the nature of this apparent paradox and the limitations of this anomalous phenomenon in terms of particle size. In this way, we shed some new light on theoretical and experimental papers on the topic, identifying relevant missteps in some of their physical interpretation, and considering the general possibility of verifying these effects. This discussion may also be relevant to some cloaking applications using exotic artificial materials.

Magnetoelectric point scattering theory for metamaterial scatterers

“…(18), the optical theorem is indeed satisfied, and forward scattering is low but not zero, in accordance with Ref. 65. First, this simple example shows that magnetoelectric point dipoles can have counterintuitive properties, such as highly anisotropic radiation patterns, very much unlike simple electric dipoles.…”

“…For instance, Alù and Engheta have recently resolved an interesting paradox first introduced by Kerker et al concerning the possibility of realizing zero-forward-scattering magnetodielectric nanoparticles that appear to violate the optical theorem. 65,66 Alú and Engheta used a size parameter expansion of the Mie coefficients of small magnetodielectric spheres to show that magnetodielectric spheres with electric and magnetic polarizabilities that are almost equal in magnitude but opposite in sign have a highly anisotropic scattering pattern, and violate the optical theorem unless one includes size expansion terms beyond the quasistatic limit. We note that all the essential physics of this problem can also be studied with ease using our formalism.…”

Optically resonant dielectric nanostructures

“…This is conceptually similar to the condition for the zerobackward scattering derived by Kerker et al in 1983 (32) for a particle having similar electric and magnetic properties, e = m, often called the first Kerker condition. Although the total suppression of the forward scattering is forbidden by the optical theorem (33), it is also possible to find the other condition for a minimal ratio of the forward and backward scattering, often called the second Kerker condition (34).…”

Comparison of frequency responses of cloaking devices under nonmonochromatic illumination

“…In addition, it is noticed that, according to the optical theorem, 39 the forward scattering amplitude is proportional to the total scattering cross section of an object. 40,41 It is therefore qualitatively expected that a larger scattered field at a point in the forward direction corresponds to a larger total scattering cross section of the object. The Fourier-transformed scattered electric field then, normalized to the amplitude of the total field in free space, is plotted in Fig.…”