Origin of the Kerker phenomena

We provide an insight into the origin of the phenomena reported 40 years ago by Kerker et al. [J. Opt. Soc. Am. 73, 765 (1983)]. We show that the impedance and refractive index matching conditions, discussed in Secs. II and IV of the seminal paper, are intertwined and both lead to the conservation of a Casimir invariant. We derive our results starting from the theory of representations of the Poincaré group, as it is a theory on which one of the most elemental descriptions of electromagnetic waves is based. We show that fundamental features of electromagnetic waves in continuous material environments can be derived by applying the symmetry-breaking principle. In particular, we identify the Casimir invariants of the 𝑃�3,1 subgroup as the magnitudes that 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.