Optical Response of Solid CO$_2$ as a Tool for the Determination of the High Pressure Phase

We report first-principles calculations of the frequency dependent linear and second-order optical properties of the two probable extended-solid phases of CO$_2$--V, i.e. $I\bar42d$ and $P2_12_12_1$. Compared to the parent $Cmca$ phase the linear optical susceptibility of both phases is much smaller. We find that $I\bar42d$ and $P2_12_12_1$ differ substantially in their linear optical response in the higher energy regime. The nonlinear optical responses of the two possible crystal structures differ by roughly a factor of five. Since the differences in the nonlinear optical spectra are pronounced in the low energy regime, i.e. below the band gap of diamond, measurements with the sample inside the diamond anvil cell are feasible. We therefore suggest optical experiments in comparison with our calculated data as a tool for the unambiguous identification of the high pressure phase of CO$_2$.