Phonon Polariton — Hyperbolic Dispersion
Light-phonon coupling in anisotropic polar crystals (hBN, α-MoO₃)
In hyperbolic phonon polaritons (Type I or II), the dielectric function ε(ω) becomes negative in a Reststrahlen band between ω_TO and ω_LO. Lorentz oscillator model: ε(ω) = ε_∞(1 + (ω_LO²−ω_TO²)/(ω_TO²−ω²−iγω)). When Re(ε) < 0, propagating modes have hyperbolic isofrequency contours, enabling ray-like sub-diffractional canalization seen in crystals like hBN and α-MoO₃.