Strong coupling of IR photons and optical phonons — Reststrahlen band and hyperbolic dispersion
Phonon polaritons arise from strong coupling between IR photons and optical phonons near the TO frequency. The dielectric function ε(ω) = ε∞(ω²_LO−ω²)/(ω²_TO−ω²) goes negative in the Reststrahlen band [ω_TO, ω_LO], creating a photonic bandgap. In 2D materials like hBN, the anisotropy enables hyperbolic dispersion (ε_x·ε_z < 0) with ray-like propagation and deeply sub-wavelength confinement.