# Theory of Optical Nonlocality in Polar Dielectrics

## TL;DR

This paper develops a nonlocal theoretical framework for phonon polaritons in polar dielectrics, revealing unique phenomena in nanostructures that differ from plasmonic systems, with implications for mid-infrared nanophotonics.

## Contribution

It introduces a nonlocal theory for phonon polaritons in polar dielectrics, addressing limitations of local models and uncovering new nonlocal effects in nanostructures.

## Key findings

- Nonlocal effects significantly alter phonon polariton behavior in nanostructures.
- Polar dielectrics exhibit negative dispersion of phononic modes, unlike plasmonic systems.
- The theory explains phenomena in nanospheres and thin films that local models cannot capture.

## Abstract

Sub-wavelength confinement of mid-infrared light can be achieved exploiting the metal-like optical response of polar dielectric crystals in their Reststrahlen spectral region, where they support evanescent modes termed surface phonon polaritons. In the past few years the investigation of phonon polaritons localised in nanoresonators and layered heterostructures has enjoyed remarkable success, highlighting them as a promising platform for mid-infrared nanophotonic applications. Here we prove that the standard local dielectric description of phonon polaritons in nanometric objects fails due to the nonlocal nature of the phonon response and we develop the corresponding nonlocal theory. Application of our general theory to both dielectric nanospheres and thin films demonstrates that polar dielectrics exhibit a rich nonlocal phenomenology, qualitatively different from the one of plasmonic systems, due to the negative dispersion of phononic optical modes.