Phonon-polaritons arise when infrared light couples to the transverse optical (TO) phonon in a polar crystal (like GaAs, LiNbO₃). Near the phonon resonance, photons and phonons hybridize into mixed quasiparticles.
The dielectric function is ε(ω) = ε∞ · (ωLO² − ω²)/(ωTO² − ω²). Light propagates only where ε(ω) > 0. The Reststrahlen band (ωTO to ωLO) has ε < 0 — total reflection. The avoided crossing gap is the hallmark of strong coupling. Used in nanophotonics for extreme light concentration below the diffraction limit.