Raman optical activity and stimulated Raman scattering along the $c$ axis in $\alpha$-quartz

Stimulated Raman scattering of the 132- and 468-${\mathrm{cm}}^{-1\mathrm{}}$ optical lattice vibrations was investigated along the $c$ axis ($z$ direction) of $\alpha$-quartz. We measured the dependence of the Raman threshold intensity on the polarization of the neodymium-doped yttrium aluminum garnet (Nd: YAG) laser pump light and on temperature from 10 to 70 K. The polarization of the stimulated Raman Stokes light was determined for different pump light polarizations. Raman optical activity was observed for the 132-${\mathrm{cm}}^{-1\mathrm{}}$ mode of $\alpha$-quartz. In a right-handed, optically active quartz crystal the Raman threshold intensity for left-handed, circularly polarized pump light was lower by a factor of about 1.5 than for right-handed circularly polarized light. Raman optical activity was not observed for the 468-${\mathrm{cm}}^{-1\mathrm{}}$ mode within our experimental accuracy. A theory of stimulated Raman scattering including the effects of Raman optical activity is applied to quartz. Relations between the Raman circular intensity difference and the magnetic dipole and electric quadrupole polarizabilities are derived. The experimental results for both Raman modes are compared with a traveling wave and an oscillator theory of stimulated Raman scattering.