Electromagnetic Helicity in Complex Media

Optical helicity density is usually discussed for monochromatic electromagnetic fields in free space. It plays an important role in the interaction with chiral molecules or nanoparticles. Here we introduce the optical helicity density in a dispersive isotropic medium. Our definition is consistent with biorthogonal Maxwell electromagnetism in optical media and the Brillouin energy density as well as with the recently introduced canonical momentum and spin of light in dispersive media. We consider a number of examples, including electromagnetic waves in dielectrics, negative-index materials, and metals, as well as interactions of light in a medium with chiral and magnetoelectric molecules.

Figure 1

Schematic picture of the helicity ($\overline{\mathfrak{S}}=\omega \mathfrak{S}/W$), canonical momentum, and spin, when a circularly polarized plane wave (a) propagates through an interface between positive-index ($ϵ>0$, $\mu >0$) and negative-index ($ϵ<0$, $\mu <0$) media, (b) is reflected from a metallic semispace ($ϵ<0$, $\mu >0$), and (c) is partially transmitted through a metal film. The red curves and magenta arrows indicate the spatial distribution of the instantaneous electric field $\mathrm{Re}(\mathbf{E}{e}^{-i\omega t})$, whereas the gray circles show the time evolution of the field at fixed positions.