On the origin of the Kerker phenomena

TL;DR

This paper explains the Kerker phenomena by linking impedance and refractive index matching to space-time symmetries, using Poincaré group representations to identify invariants that govern electromagnetic wave behavior in materials.

Contribution

It introduces a group-theoretical framework based on Poincaré invariants to explain the origin of the Kerker phenomena, connecting electromagnetic symmetries with material properties.

Findings

Impedance and index matching relate to space-time symmetries.

Casimir invariants describe electromagnetic waves in matter.

Kerker phenomena linked to invariance conservation in media.

Abstract

We provide an insight into the origin of the phenomena reported 40 years ago by Kerker, Wang and Giles (Journal of the Optical Society of America, 73, 6, pp. 765-767, (1983)). We show that the impedance and refractive index matching conditions, discussed in Sections II and IV of the seminal paper, are intimately related with space-time symmetries. We derive our results starting from the theory of representations of the Poincar\'e group, as it is the theory on which one of the most elemental descriptions of electromagnetic waves is based. We show that fundamental features of electromagnetic waves in material environments can be derived from group theoretical arguments. In particular, we identify the Casimir invariants of $P_{\scriptscriptstyle{{3,1}}}$ subgroup as the magnitudes which describe the nature of monochromatic electromagnetic waves propagating in matter. Finally, we show that the emergence of the Kerker phenomena is associated with the conservation of such Casimir invariants in piecewise homogeneous media.