Quantum theory of longitudinal-transverse polaritons in nonlocal thin films

When mid-infrared light interacts with nanoscale polar dielectric structures optical phonon propagation cannot be ignored, leading to a rich nonlocal phenomenology which we have only recently started to uncover. In properly crafted nanodevices this includes the creation of polaritonic excitations with hybrid longitudinal-transverse nature, which are predicted to allow energy funnelling from longitudinal electrical currents to far-field transverse radiation. In this work we study the physics of these longitudinal-transverse polaritons in a dielectric nanolayer in which the nonlocality strongly couples epsilon-near-zero modes to longitudinal phonons. After having calculated the system's spectrum solving Maxwell's equations, we develop an analytical polaritonic theory able to transparently quantify the nonlocality-mediated coupling as a function of the system parameters. Such a theory provides a powerful tool for the study of longitudinal-transverse polariton interactions and we use it to determine the conditions required for the hybrid modes to appear.