Fine structure has been observed in the low-temperature Raman spectrum of the 128-${\mathrm{cm}}^{-1\mathrm{}}$ $E$ mode in $\alpha$-quartz. This structure is a manifestation of an allowed linear dependence of the optical-phonon frequency on wave vector. Since Raman scattering probes a small but finite wave vector, it is possible to observe these frequency shifts using high-resolution thermal or simulated Raman spectroscopy. The linear splitting of the 128-${\mathrm{cm}}^{-1\mathrm{}}$ $E$-mode doublet is 0.86±0.05×${10}^5$ cm/sec as determined by backscattering with several laser wavelengths. Such linear wave-vector shifts lead to optical activity in the far infrared (IR). The theory of the strength and dispersion of infrared rotary power is developed in order to establish the connection between the two phenomena. The rotary power for the 128-${\mathrm{cm}}^{-1\mathrm{}}$ resonance can be estimated from the measured linear shift, lifetime, and IR oscillator strength. However, a direct IR rotation measurement would be hindered by the associated absorption.

• Received 7 July 1969

DOI:https://doi.org/10.1103/PhysRev.188.1489