Introduction to Helicity and Electromagnetic Duality Transformations in Optics

This chapter presents a detailed introduction to a fundamental non-geometrical symmetry of electromagnetic fields: electromagnetic duality. This symmetry appears in free-space Maxwell equations which remain invariant under the exchange of electric and magnetic fields E → H and H → - E. More generally, they also remain invariant under certain parametric combinations of the electric and magnetic vector fields of which the exchange referred to before is a particular case. This continuous symmetry is called electromagnetic duality. The conserved quantity related to electromagnetic duality is the optical helicity. The chapter also presents a detailed account of the fundamental properties of both electromagnetic duality and optical helicity and how to use and measure them in photonics experiments.