Longitudinal polaritons in crystals

The collective excitations of solids are classified as longitudinal and transverse depending on their relative polarization and propagation direction. This seemingly formal classification results in surprisingly distinct types of excitations if calculated within the Coulomb gauge. Transverse modes couple to free-space photons and hybridize into polaritons for strong light-matter coupling. Longitudinal modes, in contrast, are seen as pure matter excitations that produce a dynamic polarization inside the material without photon coupling. Here we show that both longitudinal and transverse modes manifest as polaritons in the explicitly covariant Lorenz gauge. Longitudinal excitations couple to longitudinal and scalar photons, which have been considered elusive so far. We show that the dipolar excitations become systematically threefold degenerate in the long-wavelength limit when including all photonic degrees of freedom, as expected from symmetry. Our findings demonstrate how choosing a gauge determines our thinking about materials excitations and how gauge fixing reveals new pathways for tailoring polaritons in crystals, metamaterials, and surfaces. Longitudinal polaritons will interact with longitudinal near fields located at surfaces, which provides additional excitation channels to engineer scanning near-field microscopy and surface-enhanced spectroscopy.