= Phonon polariton
A phonon polariton is a normal mode mixing an electromagnetic field with a polar optical lattice vibration. In a lossless isotropic oscillator model, $c^2k^2=\omega^2\epsilon_\infty(\omega_{\rm LO}^2-\omega^2)/(\omega_{\rm TO}^2-\omega^2)$. With $u=c^2k^2/\epsilon_\infty$, its two transverse branches obey $\omega_\pm^2=[\omega_{\rm LO}^2+u\pm\sqrt{(\omega_{\rm LO}^2+u)^2-4u\omega_{\rm TO}^2}]/2$. The nearly flat longitudinal optical mode is distinct from the upper transverse branch.
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