Space-time symmetries in classical and quantum electromagnetic scattering theory

Abstract

In this thesis we propose a novel approach to study electromagnetic wave dynamics based on thesystematic application of group theory. We show that this alternative approach leads to new insights onwell-studied topics such as linear electromagnetic scattering theory or the emergence of the Kerkerphenomena.First of all, we show that the monochromatic version of the Riemann-Silberstein (RS) vector is associatedwith the unitary irreducible representations of the P3,1 subgroup of the Poincaré group. Then, we showthat its application to scattering problems elucidates many fundamental properties of linearelectromagnetic samples. In this line, we show that losses preclude the existence of dielectric dualscatterers and that optical gain is a necessary condition to build antidual scatterers of any size and form.Also, we introduce the Single Characterization Angle (SCA) method that permits the opticalcharacterization of cylindrical samples in favourable experimental conditions.On the other hand, based on the monochromatic RS vector, we study the propagation of electromagneticwaves in inhomogeneous magnetic media. We show that systems made from different materials with thesame refractive index are optimal for flipping the helicity of light. Moreover, we also identify aconserved quantity associated with this kind of environments, i.e. the square of linear momentum, whoseemergence can be well-understood in terms of the P3,1 subgroup of the Poincaré group. Finally, weprovide an alternative interpretation of the Kerker phenomena based on group theoretical arguments.Our last contribution focuses on the quantum scattering of multiphoton states of light with cylindricalsamples. We show that there are multiphoton states of light, i.e. the so-called symmetry-protected states,which are left invariant in the interaction with this kind of scatterers. We propose their use in theconstruction of decoherence-free subspaces.