Polaritonic quantisation in nonlocal polar material

TL;DR

This paper develops a comprehensive quantum theory of longitudinal-transverse polaritons in nonlocal polar materials, revealing their potential to enhance and tune near-field emission for mid-infrared sensing applications.

Contribution

It introduces a full second-quantised theoretical framework for longitudinal-transverse polaritons, extending previous macroscopic models to include nonlocal effects and lattice elasticity.

Findings

Demonstrates the equivalence of polariton equations of motion to macroscopic electromagnetism.

Shows how to reconstruct electromagnetic fields from polariton states.

Reveals nonlocality can narrow, enhance, and spectrally tune near-field emission.

Abstract

In the Reststrahlen region, between the transverse and longitudinal phonon frequencies, polar dielectric materials respond metallically to light and the resulting strong light-matter interactions can lead to the formation of hybrid quasiparticles termed surface phonon polaritons. Recent works have demonstrated that when an optical system contains nanoscale polar elements these excitations can acquire a longitudinal field component as a result of the material dispersion of the lattice, leading to the formation of secondary quasiparticles termed longitudinal-transverse polaritons. In this work we build on previous macroscopic electromagnetic theories developing a full second-quantised theory of longitudinal-transverse polaritons. Beginning from the Hamiltonian of the light-matter system we treat distortion to the lattice introducing an elastic free energy. We then diagonalise the Hamiltonian, demonstrating the equations of motion for the polariton are equivalent to the those of macroscopic electromagnetism and quantise the nonlocal operators. Finally we demonstrate how to reconstruct the electromagnetic fields in terms of the polariton states and explore polariton induced enhancements of the Purcell factor. These results demonstrate how nonlocality can narrow, enhance and spectrally tune near field emission with applications in mid-infrared sensing.