Hello Vincent. Thank you for this reply. Indeed I agree that index does follow a Kramers-Kronig relationship, and I would say that the strong IR absorption that serves as the pole is the single-phonon energy of the lattice. Based on fitting of the Sellmeier curves of IR-transparent materials, we typically put that pole somewhere between several hundred and several thousand microns, so the onset of transmission loss is clearly an overtone of that fundamental absorption.

I didn't phrase it well initially, but what I am curious about is the "photon's-eye-view" of the situation. I cannot seem to picture a way in which the photon exciting an overtone phonon could actually *increase* the group velocity of the photon.

Hi David! There is no single phonon energy - from dispersion analysis of reflectance spectra in the infrared spectral region we know that there are most probably 8 different phonon modes and we also know there locations. In terms of wavelength they are much closer (between about 8 - 24 microns) than you assume from the fitting of the Sellmeier curves - they are definitely no overtones, but all are fundamentals. Please have a look at the attachment.

Okay, this is great Thomas Mayerhöfer , thank you for sharing this image. Lets stick with the SiO2 system and use these phonon modes as the resonant states that the system is approaching to continue the discussion.

To expand or clarify my question: what does this look like from the "photon's-eye-view"?

For example if I take my spectrometer and sweep the wavelength from 350 to 10,000 nm what do photons of those different energies "see" when they interact with the lattice? At 350 nm the photon phase velocity is low due to a process of absorption and re-emission from virtual electronic states in the lattice. As I increase the wavelength, the photons no longer have sufficient energy to interact electronically, so the phase velocity increases (due to lack of lattice interaction) and the Refractive Index decreases. Now I continue to increase my wavelength (lower my photon energy) until I approach the phonon resonance on the IR side of the spectrum. Again, the photon begins to interact with the lattice via the creation of phonons. Yet in this case, the phase velocity continues to *increase* as I approach the resonance. As the photon energy approaches the phonon energies and the systems become coupled again, I would expect the phase velocity to decrease as energy is transferred from the photon to the lattice, but the continued decrease of the refractive index as we approach the pole from this side indicates that the phase velocity increases. How is the phase velocity increased through increasing lattice interaction?

J. David Musgraves I would suggest that you begin your sweep at lower wavelengths, even lower than the first absorptions in the UV. Because then you would see that the absorptions in the UV are in principle not different from those in the IR spectral region, at least for a glass or for molecular substances. In both cases you can expand the empiric Sellmeier equations by assuming both for the transitions of the electrons in the UV as well as for phonon modes in the IR a damped harmonic oscillator model. The result is classical dispersion theory (corresponding names are e.g. Helmholtz, Lorentz and Drude), which becomes equivalent with the Sellmeier Formula in non-absorbing regions. To explain what happens it is better to start at wavelengths above the oscillator eigenfrequency. At these low frequencies, electromagnetic field change and dipole moment change are in phase. If the frequency of the electromagnetive wave approaches the eigenfrequency of the oscillator there is a phase lag of about 90°. For frequencies higher than the eigenfrequency, the oscillator is too slow to follow, accordingly the amplitude is small and the phase lag becomes 180°. Correspondingly, the index of refraction increases until close to the eigenfrequency where the increasing phase lag leads to a decrease of the index of refraction and a low value at higher frequencies before it starts to increase again towards the next oscillator.