Photon Echoes in Gases

The behavior of the photon echo produced by an inhomogeneously broadened spectral line is analyzed, with particular emphasis on the effect of spatial degeneracy of the molecular energy levels. The theoretical results are used to aid in the identification of the states involved in the echoes produced from gaseous S${\mathrm{F}}_6$ excited by pulses of C${\mathrm{O}}_2$ laser radiation near 10.6 μ. The analysis demonstrates that for the $\left|{\Delta }_j\right|=1\mathrm{}$ transitions ($P$ and $R$ branches) the echo induced by two linearly polarized pulses propagating along the same direction, with an angle $\psi$ between their electric vectors, is polarized at an angle greater than $\psi$ with respect to the first pulse, and the echo intensity decreases to a minimum, but not zero, as $\psi$ approaches $\frac{\pi }{2}$. An exception is the $j=1\mathrm{}\leftrightarrow j=0\mathrm{}$ transition, for which the echo is always polarized along the second pulse and the intensity varies as ${cos}^2\psi$. For ${\Delta }_j=0\mathrm{}$ transitions ($Q$ branch) the echo polarization generally lies at an angle smaller than $\psi$, i.e., between the first two pulses, and its intensity also decreases as $\left|\psi \right|$ approaches $\frac{\pi }{2}$. The exceptions for the ${\Delta }_j=0\mathrm{}$ transitions are the cases $j=\frac{1}{2}\leftrightarrow j=\frac{1}{2}$ and $j=1\mathrm{}\leftrightarrow j=1\mathrm{}$. In the former case, the echo is polarized at an angle $2\psi$ with respect to the electric field vector of the first pulse, and the echo intensity is independent of $\psi$; whereas in the latter case, the echo behaves like that for $j=1\mathrm{}\leftrightarrow j=0\mathrm{}$. The dependence of the echo behavior on the angular momentum of states involved in the transition can serve to identify the transitions when measurements of the echo polarization and intensity are possible.