= Lyddane-Sachs-Teller relation
{c}
{title2=$\epsilon_r(0)/\epsilon_\infty=\omega_{\rm LO}^2/\omega_{\rm TO}^2$}
For a single lossless polar optical oscillator with frequency-independent electronic background, $\epsilon_r(\omega)=\epsilon_\infty(\omega_{\rm LO}^2-\omega^2)/(\omega_{\rm TO}^2-\omega^2)$. Setting frequency to zero yields the displayed static-to-background ratio. Multiple infrared-active branches require the corresponding product relation, rather than selecting an arbitrary pair of modes.
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