Quantum Theory of Longitudinal-Transverse Polaritons in Nonlocal Thin Films

Abstract

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.

Polaritonic quantisation in nonlocal polar material

“…4. These components relate to the longitudinal and transverse phonon velocities in the quadratic dispersion limit β L , β T introduced phenomenologically in other works [17,30] through…”

“…by expanding the hyperbolic functions into Mittag-Leffler series and exploiting the analytic dispersion of the SPhP ω T k in the local limit. As has previously been noted this is the dispersion relation arising from a Hamiltonian where a single photonic mode is coupled to a bath of LO phonons with coupling frequency [30]…”

“…1 for a 10nm 3C-SiC film embedded between two high-index cladding regions. The epsilon-near- zero SPhP dispersion red-shifts with increasing wavevector [34] undergoing avoided crossings [40] with each coupled LO phonon branch [30]. As each polariton branch heads toward it's asymptotic frequency its group velocity tends to zero.…”

“…These modes are especially interesting in nanophotonics as they allow for strong enhancement of the out-of-plane field in the nanolayer with applications in sensing and mid-infrared nano-waveguiding [33,34]. These systems are especially interesting in optical nonlocality, where classical studies ahve demonstrated hybridisation between them and localised longitudinal phonons in the nanolayer [17,30].…”

“…Polariton systems are typically described in secondquantisation formalisms [22][23][24][25] which are attractive because they allow for a transparent understanding of energy distribution between the different light and matter excitations from which the polariton is composed, and for calculation of nonlinear polariton-polariton [26][27][28] or electron-polariton scattering [29]. Although recently a second-quantisation theory of LTPs was presented, this was based on a demonstration of equivalence between Maxwell's equations and a model Hamiltonian in a planar waveguide [30] and is not suitable for extension to describe the complex modal geometries typically utilised in SPhP optics. In this work we develop a full quantum theory of LTPs.…”